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Science News Explores

Explainer: all about orbits.

An orbit is the route that one space object repeatedly takes around another

A photo of the sky at dusk with a comet streaking down across the middle of the image

Comets — such as Neowise C/2020 F3, seen here — travel around the sun in very elliptical orbits.

Anton Petrus/Moment/Getty Images Plus

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By Trisha Muro

May 3, 2022 at 6:30 am

Even in ancient times, stargazers knew that planets differed from stars. While stars always appeared in the same general place in the night sky, planets shifted their positions from night to night. They appeared to move across the backdrop of stars. Sometimes, planets even appeared to move backward. (This behavior is known as retrograde motion.) Such strange movements across the sky were hard to explain.

Then, in the 1600s, Johannes Kepler identified mathematical patterns in the planets’ movements. Astronomers before him had known that the planets orbited , or moved around the sun. But Kepler was the first to describe those orbits — correctly — with math. As if putting together a jigsaw puzzle, Kepler saw how the pieces of data fit together. He summed up the math of orbital motion with three laws:

  • The path a planet takes around the sun is an ellipse, not a circle. An ellipse is an oval shape. This means that sometimes a planet is closer to the sun than at other times.
  • A planet’s speed changes as it moves along this path. The planet speeds up when passing closest to the sun and slows as it gets farther away from the sun.
  • Each planet orbits the sun at a different speed. The more distant ones move more slowly than those closer to the star.

Kepler still couldn’t explain why planets follow elliptical paths and not circular ones. But his laws could predict planets’ positions with incredible accuracy. Then, about 50 years later, physicist Isaac Newton explained the mechanism for why Kepler’s laws worked: gravity . The force of gravity attracts objects in space to each other — causing the motion of one object to continually bend toward another.

Throughout the cosmos, all sorts of celestial objects orbit each other. Moons and spacecraft orbit planets. Comets and asteroids orbit the sun — even other planets. Our sun orbits the center of our galaxy , the Milky Way. Galaxies orbit each other, too. Kepler’s laws describing orbits hold true for all these objects across the universe.

Let’s have a look at each of Kepler’s laws in more detail.

an image showing more than 2000 orbits of asteroids, Earth, Mercury, Venus and Mars around the sun

Kepler’s First Law: Ellipses

To describe how oval-like an ellipse is, scientists use the word eccentricity (Ek-sen-TRIS-sih-tee). That eccentricity is a number between 0 and 1. A perfect circle has an eccentricity of 0. Orbits with eccentricities closer to 1 are really stretched-out ovals.

The moon’s orbit around Earth has an eccentricity of 0.055. That’s almost a perfect circle. Comets have very eccentric orbits. Halley’s Comet, which whizzes by Earth every 75 years, has an orbital eccentricity of 0.967.

(It is possible for an object’s motion to have an eccentricity greater than 1. But such a high eccentricity describes an object whipping around another in a wide U-shape — never to return. So, strictly speaking, it would not be orbiting the object its path was bent around.)

Ellipses are very important for planning a spacecraft’s orbit. If you want to send a spacecraft to Mars, you have to remember that the spacecraft starts from Earth. That might sound silly at first. But when you launch a rocket, it will naturally follow the ellipse of Earth’s orbit around the sun. To reach Mars, the spacecraft’s elliptical path around the sun will have to change to match Mars’ orbit.

With some very complex math — that famous “rocket science” — scientists can plan how fast and how high a rocket needs to launch a spacecraft. Once the spacecraft is in orbit around Earth, a separate set of smaller engines slowly widens the craft’s orbit around the sun. With careful planning, the spacecraft’s new orbital ellipse will exactly match Mars’ at just the right time. That allows the spacecraft to arrive at the Red Planet.

Kepler’s Second Law: Changing speeds

The point where a planet’s orbit comes closest to the sun is its perihelion . The term comes from the Greek peri , or near, and helios , or sun.

Earth reaches its perihelion in early January. (This may seem strange to people in the Northern Hemisphere, who experience winter in January. But Earth’s distance from the sun is not the cause of our seasons. That’s due to the tilt of Earth’s axis of rotation .) At perihelion, Earth is moving fastest in its orbit, about 30 kilometers (19 miles) per second. By early July, Earth’s orbit is at its farthest point from the sun. Then, Earth is traveling most slowly along its orbital path — about 29 kilometers (18 miles) per second.

Planets are not the only orbiting objects that speed up and slow down like this. Whenever something in orbit gets closer to the object it’s orbiting, it feels a stronger gravitational pull. As a result, it speeds up.

Scientists try to use this extra boost when launching spacecraft to other planets. For instance, a probe sent to Jupiter might fly past Mars on the way. As the spacecraft gets closer to Mars, the planet’s gravity causes the probe to speed up. That gravitational boost flings the spacecraft toward Jupiter much faster than it would travel on its own. This is called the slingshot effect. Using it can save a lot of fuel. Gravity does some of the work, so the engines need to do less.

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Kepler’s Third Law: Distance and Speed

At an average distance of 4.5 billion kilometers (2.8 billion miles), the sun’s gravitational pull on Neptune is strong enough to hold the planet in orbit. But it’s much weaker than the sun’s tug on Earth, which is a mere 150 million kilometers (93 million miles) from the sun. So, Neptune travels along its orbit more slowly than Earth does. It cruises around the sun at about 5 kilometers (3 miles) per second. Earth zooms around the sun at about 30 kilometers (19 miles) per second.   

Since more distant planets travel more slowly around wider orbits, they take much longer to complete one orbit. This time span is known as a year. On Neptune, it lasts about 60,000 Earth days. On Earth, far closer to the sun, a year is just a bit more than 365 days long. And Mercury, the planet closest to the sun, wraps up its own year every 88 Earth days.

This relationship between an orbiting object’s distance and its speed affects how fast satellites zoom around Earth. Most satellites — including the International Space Station — orbit about 300 to 800 kilometers (200 to 500 miles) above Earth’s surface. Those low-flying satellites complete one orbit every 90 minutes or so.

Some very high orbits — around 35,000 kilometers (20,000 miles) off the ground — cause satellites to move more slowly. In fact, those satellites move slowly enough to match the speed of Earth’s rotation. These craft are in geosynchronous (Gee-oh-SIN-kron-ous) orbit. Since they seem to stand still above a single country or region, these satellites are often used to track weather or relay communications.

On collisions and ‘parking’ spots

Space may be huge, but everything in it is always in motion. Occasionally, two orbits cross one another. And that can lead to collisions.

Some places are packed with objects on crisscrossing orbits. Consider all of the space junk orbiting Earth . These bits of debris are constantly colliding with each other — and occasionally with important spacecraft. Predicting where potentially hazardous pieces of debris are headed in this swarm can be quite complex. But it’s worth it, if scientists can foresee a collision and move a spacecraft out of the way.

a diagram showing where Lagrange points are located

Sometimes, the target of a potential collision may not be able to divert its path. Consider a meteor or other space rock whose orbit may put it on a collision course with Earth. If we’re lucky, that incoming rock will burn up in Earth’s atmosphere . But if the boulder is too big to fully disintegrate on its way through the air, it could smash into Earth . And that could prove disastrous — just as it was for the dinosaurs 66 million years ago . To head off these problems, scientists are investigating how to divert the orbit of the incoming space rocks . That takes an especially challenging number of orbital calculations.

Saving satellites — and potentially warding off the apocalypse — are not the only reasons to understand orbits.

In the 1700s, mathematician Joseph-Louis Lagrange identified a special set of points in space around the sun and any given planet. At these points, the gravitational pull of the sun and the planet strike a balance. As a result, a spacecraft parked in that spot can stay there without burning much fuel. Today, these are known as Lagrange points.

One of those points, known as L2, is especially useful for space telescopes that need to stay very cold. The new James Webb Space Telescope , or JWST, takes advantage of that.

Orbiting at L2, JWST can point away from both the Earth and sun. This allows the telescope to make observations anywhere in space. And since L2 is about 1.5 million kilometers (1 million miles) away from Earth, it is far enough from both the Earth and the sun to keep JWST’s instruments extremely cool. But L2 also allows JWST to stay in constant communication with the ground. As JWST orbits the sun at L2 , it will always be the same distance from Earth — so the telescope can send its stunning views home while facing out into the universe.

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What Is an Orbit?

Watch this quick video to see how the Moon orbits Earth! Credit: NASA's Scientific Visualization Studio. Click here to download this video (28 MB, video/mp4).

What shape is an orbit?

Orbits come in different shapes. All orbits are elliptical, which means they are an ellipse, similar to an oval. For the planets, the orbits are almost circular. The orbits of comets have a different shape. They look like a "squashed" circle. They look more like thin ellipses than circles.

Satellites that orbit Earth, including the Moon, do not always stay the same distance from Earth. Sometimes they are closer, and at other times they are farther away. The closest point a satellite comes to Earth is called its perigee . The farthest point is the apogee . For planets, the point in their orbit closest to the Sun is perihelion . The farthest point is called aphelion . Earth reaches its aphelion during summer in the Northern Hemisphere. The time it takes a satellite to make one full orbit is called its orbital period . For example, Earth has an orbital period of one year.

An illustration of Earth’s orbit around the Sun, and the Moon’s orbit around Earth. The aphelion, perihelion, perigee, and apogee points are labeled.

The point at which a planet is closest to the Sun is called perihelion. The farthest point is called aphelion. Credit: NOAA

How Do Objects Stay in Orbit?

An object in motion will stay in motion unless something pushes or pulls on it. This statement is called Newton's first law of motion . Without gravity , an Earth-orbiting satellite would go off into space along a straight line. With gravity, it is pulled back toward Earth. A constant tug-of-war takes place between the satellite's tendency to move in a straight line, or momentum, and the tug of gravity pulling the satellite back.

Credit: NASA/JPL-Caltech

An object's momentum and the force of gravity have to be balanced for an orbit to happen. If the forward momentum of one object is too great, it will speed past and not enter into orbit. If momentum is too small, the object will be pulled down and crash. When these forces are balanced, the object is always falling toward the planet, but because it's moving sideways fast enough, it never hits the planet.

Where Do Satellites Orbit Earth?

The International Space Station is in low Earth orbit , or LEO . LEO is the first 100 to 200 miles of space. LEO is the easiest orbit to get to and stay in. One complete orbit in LEO takes about 90 minutes.

Astronaut James H. Newman waves during a spacewalk preparing for release of the first combined elements of the International Space Station. The astronaut wears a big white space suit and reflective helmet and waves at the camera in the foreground. The ISS’ solar panels and metallic body are behind him. Earth’s horizon is in the distance, and the rest of the background is deep, dark space.

Astronauts and scientists living on the International Space Station are in orbit around Earth, while you, on Earth, are orbiting around the Sun. Phew! So many orbits! Credit: NASA

Satellites that stay above a location on Earth are in geosynchronous Earth orbit , or GEO . These satellites orbit about 23,000 miles above the equator and complete one revolution around Earth precisely every 24 hours. Geosynchronous orbits are also called geostationary .

A satellite in geostationary orbit around Earth. Credit: NASA

Any satellite with an orbital path going over or near the poles has a polar orbit. Polar orbits are usually low Earth orbits. Eventually, Earth's entire surface passes under a satellite in polar orbit.

Polar Orbit

Geostationary orbit, both orbits.

Discover how we launch satellites into space here ! And learn about what happens to old satellites here .

If you liked this, you may like:

Illustration of a game controller that links to the Space Place Games menu.

Space Station Orbit Tutorial

For the purposes of planning Earth observing photography or remote sensing, there are four important points about the orbits of the ISS. Particulars of the orbits depend on the exact altitude of the station, and the exact altitude depends on the frequency that the station is reboosted to a higher orbit.

NASA meatball logo

An orbit is a regular, repeating path that one object takes around another object or center of gravity. Orbiting objects, which are called satellites, include planets, moons, asteroids, and artificial devices.

Astronomy, Geography, Physics

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Morgan Stanley

An orbit is a regular, repeating path that one object takes around another object or center of gravity . Orbiting objects, which are called satellites , include planets , moons , asteroids , and artificial devices. Objects orbit each other because of gravity. Gravity is the force that exists between any two objects with mass . Every object, from the smallest subatomic particle to the largest star , has mass. The more massive the object, the larger its gravitational pull . Gravitational pull is the amount of force one object exerts on another object. The sun is the most massive object in our solar system . All other objects in the solar system are subject to the gravitational pull of the sun. Many satellites orbit on orbital planes . An orbital plane is a flat, disk-shaped space that connects the center of the object being orbited with the center of orbiting objects. Because all planets in our solar system share a similar orbital plane, planets don't collide. All the planets in our solar system line up with each other on the same general orbital plane. However, sometimes orbital paths of other objects in the solar system intersect , and the objects can collide. Comet Tempel-Tuttle , for instance, passes through Earth's orbit. The debris from the tail of this comet passes through Earth's atmosphere as meteors , or falling stars, at a specific time every year. The debris from the comet's orbit is called the Leonid meteor shower . The time it takes for an object to orbit around another object is called its orbital period . Earth's orbital period around the sun is complete in slighly over 365 days. The farther away a planet is from the sun, the longer its orbital period. The planet Neptune , for example, takes almost 165 years to orbit the sun. Each orbit has its own eccentricity . Eccentricity is the amount an orbit's path differs from a perfect circle. A perfect circle has an eccentricity of zero. Earth's eccentricity is 0.017. Mercury has the largest eccentricity of all the planets in the solar system, at 0.206. Types of Orbits Moons orbit planets, while planets orbit the sun. Our entire solar system orbits the black hole at the center of our galaxy , the Milky Way . There are three major types of orbits: galactocentric orbits , heliocentric orbits , and geocentric orbits. Galactocentric orbits circle the center of a galaxy. Our solar system orbits the Milky Way. Heliocentric orbits go around stars. All the planets in our solar system, along with all the asteroids in the Asteroid Belt and all comets, follow this kind of orbit. Each planet's orbit is regular: They follow certain paths and take a certain amount of time to make one complete orbit. The planet Mercury completes its short heliocentric orbit every 88 days. Comet Kohoutek may take 100,000 years to complete its heliocentric orbit. A geocentric orbit is one that goes around Earth. Our moon follows a geocentric orbit, and so do most artificial satellites. The moon is Earth's only natural satellite. It takes about 27 days for the moon to complete its orbital period around Earth. There are three major types of geocentric orbits: low-Earth orbit (LEO), medium-Earth orbit (MEO), and geostationary orbit . Low-Earth orbit exists between 160 kilometers (100 miles) and 2,000 kilometers (1,240 miles) above Earth's surface. Most artificial satellites with human crews are in low-Earth orbit. The orbital period for objects in LEO is about 90 minutes. Medium-Earth orbit exists between 2,000 kilometers (1,243 miles) and 36,000 kilometers (23,000 miles) above the Earth's surface. Satellites in MEO are at greater risk for damage, because they are exposed to powerful radiation from the sun. Satellites in MEO include global positioning system (GPS) and communication satellites . MEO satellites can orbit Earth in about two hours. Satellites in geostationary orbit circle Earth directly above the Equator . These satellites have geosynchronous orbits , or move at the same rotation of Earth. Therefore, the orbital period of geosynchronous satellites is 24 hours. Geostationary satellites are useful because they appear as a fixed point in the sky. Antennae pointed toward the geostationary satellite will have a clear signal unless objects in the atmosphere (such as storm clouds) between Earth and the satellite interfere. Most weather satellites are geostationary and provide images of Earth's atmosphere. Satellite Orbits Artificial satellites are sent to orbit Earth to collect information we can only assemble from above the atmosphere. The first artificial satellite, Sputnik , was launched by the Soviet Union in 1957. Today, thousands of satellites orbit Earth. Weather satellites provide images of weather patterns for meteorologists to study. Communication satellites connect cellphone users and GPS receivers . Military satellites track movement of weapons and troops from different countries. Sometimes, artificial satellites have people on them. The most famous artificial satellite is the International Space Station (ISS) . Astronauts from all over the world stay on the ISS for months at a time as it orbits Earth. Astronomers and stargazers can see the ISS and other satellites as they orbit through telescopes and even powerful binoculars. Not all artificial satellites orbit Earth. Some orbit other planets. The Cassini-Huygens mission, for instance, is studying the planet Saturn . The project has a spacecraft , Cassini, which orbited Saturn. Putting satellites into orbit is complex and costly. Few governments can afford large space programs. Artificial satellites from the United States are sent into orbit by the National Aeronautics and Space Administration, or NASA . The European Space Agency (ESA) launches satellites from countries in the European Union . The Russian Federal Space Agency (Roscosmos), the Japanese Space Agency (JSA), and the Iranian Space Agency (ISA) are some of the governments that have successfully put satellites into orbit. Satellites are put into orbit from spaceports , which are carefully constructed for that purpose. The Baikonur Cosmodrome in Kazakhstan and the Kennedy Space Center in the U.S. state of Florida are both well-known spaceports.

Clarke Orbit The idea for geostationary orbit was outlined in a 1945 paper by the scientist and science-fiction author Arthur C. Clarke. For this reason, geostationary orbit is sometimes called "Clarke orbit."

Edge of Orbit Voyager II is a spacecraft launched by the United States in 1977. Voyager II passed through the heliosheath, the edge of the sun's gravitational pull, in 2007. Voyager II is outside the sun's orbit.

Pluto Pluto, a dwarf planet on the edge of our solar system, takes a strange orbit around the sun. Pluto's eccentricity is also much higher than any planet in the solar system, at 0.249. This is partly why Pluto, an official planet until 2006, was downgraded to a dwarf planet.

Space Junk There are more pieces of space junk orbiting Earth than useful satellites. Space junk is material from satellites, rockets, or other spacecraft that no longer works.

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7.1 Kepler's Laws of Planetary Motion

Section learning objectives.

By the end of this section, you will be able to do the following:

  • Explain Kepler’s three laws of planetary motion
  • Apply Kepler’s laws to calculate characteristics of orbits

Teacher Support

The learning objectives in this section will help your students master the following standards:

  • (C) analyze and describe accelerated motion in two dimensions using equations, including projectile and circular examples.

In this section students will apply Kepler’s laws of planetary motion to objects in the solar system.

[BL] [OL] Discuss the historical setting in which Kepler worked. Most people still thought Earth was the center of the universe, and yet Kepler not only knew that the planets circled the sun, he found patterns in the paths they followed. What would it be like to be that far ahead of almost everyone? A fascinating description of this is given in the program Cosmos with Carl Sagan (Episode 3, Harmony of the Worlds).

[AL] Explain that Kepler’s laws were laws and not theories. Laws describe patterns in nature that always repeat themselves under the same set of conditions. Theories provide an explanation for the patterns. Kepler provided no explanation.

Section Key Terms

Concepts related to kepler’s laws of planetary motion.

Examples of orbits abound. Hundreds of artificial satellites orbit Earth together with thousands of pieces of debris. The moon’s orbit around Earth has intrigued humans from time immemorial. The orbits of planets, asteroids, meteors, and comets around the sun are no less interesting. If we look farther, we see almost unimaginable numbers of stars, galaxies, and other celestial objects orbiting one another and interacting through gravity.

All these motions are governed by gravitational force. The orbital motions of objects in our own solar system are simple enough to describe with a few fairly simple laws. The orbits of planets and moons satisfy the following two conditions:

  • The mass of the orbiting object, m , is small compared to the mass of the object it orbits, M .
  • The system is isolated from other massive objects.

[OL] Ask the students to explain the criteria to see if they understand relative mass and isolated systems.

Based on the motion of the planets about the sun, Kepler devised a set of three classical laws, called Kepler’s laws of planetary motion , that describe the orbits of all bodies satisfying these two conditions:

  • The orbit of each planet around the sun is an ellipse with the sun at one focus.
  • Each planet moves so that an imaginary line drawn from the sun to the planet sweeps out equal areas in equal times.
  • The ratio of the squares of the periods of any two planets about the sun is equal to the ratio of the cubes of their average distances from the sun.

These descriptive laws are named for the German astronomer Johannes Kepler (1571–1630). He devised them after careful study (over some 20 years) of a large amount of meticulously recorded observations of planetary motion done by Tycho Brahe (1546–1601). Such careful collection and detailed recording of methods and data are hallmarks of good science. Data constitute the evidence from which new interpretations and meanings can be constructed. Let’s look closer at each of these laws.

[BL] Relate orbit to year and rotation to day. Be sure that students know that an object rotates on its axis and revolves around a parent body as it follows its orbit.

[OL] See how many levels of orbital motion the students know and fill in the ones they don’t. For example, moons orbit around planets; planets around stars; stars around the center of the galaxy, etc.

[AL] From the point of view of Earth, which objects appear (incorrectly) to be orbiting Earth (stars, the sun, galaxies) and which can be seen to be orbiting parent bodies (the moon, moons of other planets, stars in other galaxies)?

Kepler’s First Law

The orbit of each planet about the sun is an ellipse with the sun at one focus, as shown in Figure 7.2 . The planet’s closest approach to the sun is called perihelion and its farthest distance from the sun is called aphelion .

[AL] Ask for a definition of planet. Prepare to discuss Pluto’s demotion if it comes up. Discuss the first criterion in terms of center of rotation of a moon-planet system. Explain that for all planet-moon systems in the solar system, the center of rotation is within the planet. This is not true for Pluto and its largest moon, Charon, because their masses are similar enough that they rotate around a point in space between them.

If you know the aphelion ( r a ) and perihelion ( r p ) distances, then you can calculate the semi-major axis ( a ) and semi-minor axis ( b ).

[AL] If any students are interested and proficient in algebra and geometry, ask them to derive a formula that relates the length of the string and the distance between pins to the major and minor axes of an ellipse. Explain that this is a real world problem for workers who design elliptical tabletops and mirrors.

[BL] [OL] Impress upon the students that Kepler had to crunch an enormous amount of data and that all his calculations had to be done by hand. Ask students to think of similar projects where scientists found order in a daunting amount of data (the periodic table, DNA structure, climate models, etc.).

Teacher Demonstration

Demonstrate the pins and string method of drawing an ellipse, as shown in Figure 7.3 , or have the students try it at home or in class.

Ask students: Why does the string and pin method create a shape that conforms to Kepler's second law? That is, why is the shape an ellipse?

Explain that the pins are the foci and explain what each of the three sections of string represents. Note that the pencil represents a planet and one of the pins represents the sun.

Kepler’s Second Law

Each planet moves so that an imaginary line drawn from the sun to the planet sweeps out equal areas in equal times, as shown in Figure 7.4 .

Ask the students to imagine how complicated it would be to describe the motion of the planets mathematically, if it is assumed that Earth is stationary. And yet, people tried to do this for hundreds of years, while overlooking the simple explanation that all planets circle the sun.

[OL] Ask students to use this figure to understand why planets and comets travel faster when they are closer to the sun. Explain that time intervals and areas are constant, but both velocity and distance from the sun vary.

Tips For Success

Note that while, for historical reasons, Kepler’s laws are stated for planets orbiting the sun, they are actually valid for all bodies satisfying the two previously stated conditions.

Kepler’s Third Law

The ratio of the periods squared of any two planets around the sun is equal to the ratio of their average distances from the sun cubed. In equation form, this is

where T is the period (time for one orbit) and r is the average distance (also called orbital radius). This equation is valid only for comparing two small masses orbiting a single large mass. Most importantly, this is only a descriptive equation; it gives no information about the cause of the equality.

[BL] See if students can rearrange this equation to solve for any one of the variables when the other three are known.

[AL] Show a solution for one of the periods T or radii r and ask students to interpret the fractional powers on the right hand side of the equation.

[OL] Emphasize that this approach only works for two satellites orbiting the same parent body. The parent body must be the same because r 2 / T 2 = G M / ( 4 π 2 ) r 2 / T 2 = G M / ( 4 π 2 ) and M is the mass of the parent body. If M changes, the ratio r 3 / T 2 also changes.

Links To Physics

History: ptolemy vs. copernicus.

Before the discoveries of Kepler, Copernicus, Galileo, Newton, and others, the solar system was thought to revolve around Earth as shown in Figure 7.5 (a) . This is called the Ptolemaic model , named for the Greek philosopher Ptolemy who lived in the second century AD. The Ptolemaic model is characterized by a list of facts for the motions of planets, with no explanation of cause and effect. There tended to be a different rule for each heavenly body and a general lack of simplicity.

Figure 7.5 (b) represents the modern or Copernican model . In this model, a small set of rules and a single underlying force explain not only all planetary motion in the solar system, but also all other situations involving gravity. The breadth and simplicity of the laws of physics are compelling.

Nicolaus Copernicus (1473–1543) first had the idea that the planets circle the sun, in about 1514. It took him almost 20 years to work out the mathematical details for his model. He waited another 10 years or so to publish his work. It is thought he hesitated because he was afraid people would make fun of his theory. Actually, the reaction of many people was more one of fear and anger. Many people felt the Copernican model threatened their basic belief system. About 100 years later, the astronomer Galileo was put under house arrest for providing evidence that planets, including Earth, orbited the sun. In all, it took almost 300 years for everyone to admit that Copernicus had been right all along.

Grasp Check

Explain why Earth does actually appear to be the center of the solar system.

  • Earth appears to be the center of the solar system because Earth is at the center of the universe, and everything revolves around it in a circular orbit.
  • Earth appears to be the center of the solar system because, in the reference frame of Earth, the sun, moon, and planets all appear to move across the sky as if they were circling Earth.
  • Earth appears to be at the center of the solar system because Earth is at the center of the solar system and all the heavenly bodies revolve around it.
  • Earth appears to be at the center of the solar system because Earth is located at one of the foci of the elliptical orbit of the sun, moon, and other planets.

Introduce the historical debate around the geocentric versus the heliocentric view of the universe. Stress how controversial this debate was at the time. Explain that this was important to people because their world view and cultural beliefs were at stake.

Virtual Physics

Acceleration.

This simulation allows you to create your own solar system so that you can see how changing distances and masses determines the orbits of planets. Click Help for instructions.

  • The orbiting object moves fastest when it is closest to the central object and slowest when it is farthest away.
  • The orbiting object moves slowest when it is closest to the central object and fastest when it is farthest away.
  • The orbiting object moves with the same speed at every point on the circumference of the elliptical orbit.
  • There is no relationship between the speed of the object and the location of the planet on the circumference of the orbit.

Give the students ample time to manipulate this animation. It may take some time to get the parameters adjusted so that they can see how mass and eccentricity affect the orbit. Initially, the planet is likely to disappear off the screen or crash into the sun.

Calculations Related to Kepler’s Laws of Planetary Motion

Refer back to Figure 7.2 (a) . Notice which distances are constant. The foci are fixed, so distance f 1 f 2 ¯ f 1 f 2 ¯ is a constant. The definition of an ellipse states that the sum of the distances f 1 m ¯ + m f 2 ¯ f 1 m ¯ + m f 2 ¯ is also constant. These two facts taken together mean that the perimeter of triangle Δ f 1 m f 2 Δ f 1 m f 2 must also be constant. Knowledge of these constants will help you determine positions and distances of objects in a system that includes one object orbiting another.

Refer back to Figure 7.4 . The second law says that the segments have equal area and that it takes equal time to sweep through each segment. That is, the time it takes to travel from A to B equals the time it takes to travel from C to D, and so forth. Velocity v equals distance d divided by time t : v = d / t v = d / t . Then, t = d / v t = d / v , so distance divided by velocity is also a constant. For example, if we know the average velocity of Earth on June 21 and December 21, we can compare the distance Earth travels on those days.

The degree of elongation of an elliptical orbit is called its eccentricity ( e ). Eccentricity is calculated by dividing the distance f from the center of an ellipse to one of the foci by half the long axis a .

When e = 0 e = 0 , the ellipse is a circle.

The area of an ellipse is given by A = π a b A = π a b , where b is half the short axis. If you know the axes of Earth’s orbit and the area Earth sweeps out in a given period of time, you can calculate the fraction of the year that has elapsed.

[OL] Review the definitions of major and minor axes, semi-major and semi-minor axes, and distance f . The major axis is the length of the ellipse and passes through both foci. The minor axis is the width of the ellipse and is perpendicular to the major axis. The semi-major and semi-minor axes are half of the major and minor axes, respectively.

Worked Example

At its closest approach, a moon comes within 200,000 km of the planet it orbits. At that point, the moon is 300,000 km from the other focus of its orbit, f 2 . The planet is focus f 1 of the moon’s elliptical orbit. How far is the moon from the planet when it is 260,000 km from f 2 ?

Show and label the ellipse that is the orbit in your solution. Picture the triangle f 1 m f 2 collapsed along the major axis and add up the lengths of the three sides. Find the length of the unknown side of the triangle when the moon is 260,000 km from f 2 .

Perimeter of f 1 m f 2 = 200 , 000 km + 100,000 km + 300,000 km = 600,000 km. f 1 m f 2 = 200 , 000 km + 100,000 km + 300,000 km = 600,000 km.

m f 1 = 600,000 km − ( 100,000 km + 260,000 km ) = 240,000 km. m f 1 = 600,000 km − ( 100,000 km + 260,000 km ) = 240,000 km.

The perimeter of triangle f 1 mf 2 must be constant because the distance between the foci does not change and Kepler’s first law says the orbit is an ellipse. For any ellipse, the sum of the two sides of the triangle, which are f 1 m and mf 2 , is constant.

Walk the students through the process of mentally collapsing the f 1 mf 2 at the end of the major axis to reveal what the three sides of the triangle f 1 mf 2 are equal to. Picture the sections of the string as the pencil approaches the major axis. This distance f 1 f 2 remains constant, f 1 m is the distance from f 1 to the end of the major axis, and mf 2 is f 1 m + f 1 f 2 .

[OL] Have students relate eccentricity, distance between foci, and shape of orbit.

[AL] Ask for examples of orbits with high eccentricity (comets, Pluto) and low eccentricity (moon, Earth).

Figure 7.6 shows the major and minor axes of an ellipse. The semi-major and semi-minor axes are half of these, respectively.

Earth’s orbit is very slightly elliptical, with a semi-major axis of 1.49598 × 10 8 km and a semi-minor axis of 1.49577 × 10 8 km. If Earth’s period is 365.26 days, what area does an Earth-to-sun line sweep past in one day?

Each day, Earth sweeps past an equal-sized area, so we divide the total area by the number of days in a year to find the area swept past in one day. For total area use A = π a b A = π a b . Calculate A , the area inside Earth’s orbit and divide by the number of days in a year (i.e., its period).

The area swept out in one day is thus 1.93 × 10 14 km 2 1.93 × 10 14 km 2 .

The answer is based on Kepler’s law, which states that a line from a planet to the sun sweeps out equal areas in equal times.

Explain that this formula is easy to remember because it is similar to A = π r 2 . A = π r 2 . Discuss Earth’s eccentricity. Compare it with that of other planets, asteroids, or comets to further emphasize what defines a planet. Note that Earth has one of the least eccentric orbits and Mercury has the most eccentric orbit of the planets.

[BL] Have the students memorized the value of π ? π ?

[OL] [AL] What is the formula when a = b ? Is the formula familiar?

[OL] Can the student verify this statement by rearranging the equation?

Kepler’s third law states that the ratio of the squares of the periods of any two planets ( T 1 , T 2 ) is equal to the ratio of the cubes of their average orbital distance from the sun ( r 1 , r 2 ). Mathematically, this is represented by

From this equation, it follows that the ratio r 3 /T 2 is the same for all planets in the solar system. Later we will see how the work of Newton leads to a value for this constant.

Given that the moon orbits Earth each 27.3 days and that it is an average distance of 3.84 × 10 8 m 3.84 × 10 8 m from the center of Earth, calculate the period of an artificial satellite orbiting at an average altitude of 1,500 km above Earth’s surface.

The period, or time for one orbit, is related to the radius of the orbit by Kepler’s third law, given in mathematical form by T 1 2 T 2 2 = r 1 3 r 2 3 T 1 2 T 2 2 = r 1 3 r 2 3 . Let us use the subscript 1 for the moon and the subscript 2 for the satellite. We are asked to find T 2 . The given information tells us that the orbital radius of the moon is r 1 = 3.84 × 10 8 m r 1 = 3.84 × 10 8 m , and that the period of the moon is T 1 = 27.3 days T 1 = 27.3 days . The height of the artificial satellite above Earth’s surface is given, so to get the distance r 2 from the center of Earth we must add the height to the radius of Earth (6380 km). This gives r 2 = 1500 km + 6380 km = 7880 km r 2 = 1500 km + 6380 km = 7880 km . Now all quantities are known, so T 2 can be found.

To solve for T 2 , we cross-multiply and take the square root, yielding

This is a reasonable period for a satellite in a fairly low orbit. It is interesting that any satellite at this altitude will complete one orbit in the same amount of time.

Remind the students that this only works when the satellites are small compared to the parent object and when both satellites orbit the same parent object.

Practice Problems

A planet with no axial tilt is located in another solar system. It circles its sun in a very elliptical orbit so that the temperature varies greatly throughout the year. If the year there has 612 days and the inhabitants celebrate the coldest day on day 1 of their calendar, when is the warmest day?

  • 2.75 × 10 3 km
  • 1.96 × 10 4 km
  • 1.40 × 10 5 km
  • 1.00 × 10 6 km

Check Your Understanding

  • Kepler’s laws are purely descriptive.
  • Kepler’s laws are purely causal.
  • Kepler’s laws are descriptive as well as causal.
  • Kepler’s laws are neither descriptive nor causal.

True or false—According to Kepler’s laws of planetary motion, a satellite increases its speed as it approaches its parent body and decreases its speed as it moves away from the parent body.

  • One focus is the parent body, and the other is located at the opposite end of the ellipse, at the same distance from the center as the parent body.
  • One focus is the parent body, and the other is located at the opposite end of the ellipse, at half the distance from the center as the parent body.
  • One focus is the parent body and the other is located outside of the elliptical orbit, on the line on which is the semi-major axis of the ellipse.
  • One focus is on the line containing the semi-major axis of the ellipse, and the other is located anywhere on the elliptical orbit of the satellite.

Use the Check Your Answers questions to assess whether students master the learning objectives for this section. If students are struggling with a specific objective, the Check Your Answers will help identify which objective is causing the problem and direct students to the relevant content.

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November 24, 2014

Earth's orbit around the sun

by Matt Williams, Universe Today

Earth’s Orbit Around The Sun

Ever since the 16th century when Nicolaus Copernicus demonstrated that the Earth revolved around in the Sun, scientists have worked tirelessly to understand the relationship in mathematical terms. If this bright celestial body – upon which depends the seasons, the diurnal cycle, and all life on Earth – does not revolve around us, then what exactly is the nature of our orbit around it?

For several centuries, astronomers have applied the scientific method to answer this question, and have determined that the Earth's orbit around the Sun has many fascinating characteristics.

First of all, the speed of the Earth's orbit around the Sun is 108,000 km/h, which means that our planet travels 940 million km during a single orbit. The Earth completes one orbit every 365.242199 mean solar days, a fact which goes a long way towards explaining why need an extra calendar day every four years (aka. during a leap year).

The planet's distance from the Sun also varies as it orbits. In fact, the Earth is never the same distance from the Sun from day to day. When the Earth is closest to the Sun, it is said to be at perihelion. This occurs around January 3rd each year, when the Earth is at a distance of about 147,098,074 km. When it is at its farthest distance from the Sun, Earth is said to be at aphelion – which happens around July 4th where the Earth reaches a distance of about 152,097,701 km. And those of you in the northern hemisphere will notice that "warm" or "cold" weather does not coincide with how close the Earth is to the Sun. That is determined by axial tilt, which we discuss below.

The average distance of the Earth from the aun is about 149.6 million km, which is also referred to as one astronomical unit (AU).

Next, there is the nature of the Earth's orbit. Rather than being a perfect circle, the Earth moves around the Sun in an extended circular or oval pattern. This is what is known as an "elliptical" orbit. This orbital pattern was first described by Johannes Kepler, a German mathematician and astronomer, in his seminal work Astronomia nova (New Astronomy).

After measuring the orbits of the Earth and Mars, he noticed that at times, the orbits of both planets appeared to be speeding up or slowing down. This coincided directly with the planets' aphelion and perihelion, meaning that the planets' distance from the Sun bore a direct relationship to the speed of their orbits. It also meant that both Earth and Mars did not orbit the Sun in perfectly circular patterns.

Earth’s Orbit Around The Sun

In describing the nature of elliptical orbits, scientists use a factor known as "eccentricity", which is expressed in the form of a number between zero and one. If a planet's eccentricity is close to zero, then the ellipse is nearly a circle. If it is close to one, the ellipse is long and slender.

Earth's orbit has an eccentricity of less than 0.02, which means that it is very close to being circular. That is why the difference between the Earth's distance from the Sun at perihelion and aphelion is very little – less than 5 million km.

Third, there is the role Earth's orbit plays in the seasons, which we referred to above. The four seasons are determined by the fact that the Earth is tilted 23.4° on its vertical axis, which is referred to as "axial tilt." This quirk in our orbit determines the solstices – the point in the orbit of maximum axial tilt toward or away from the Sun – and the equinoxes, when the direction of the tilt and the direction to the Sun are perpendicular.

In short, when the northern hemisphere is tilted away from the Sun, it experiences winter while the southern hemisphere experiences summer. Six months later, when the northern hemisphere is tilted towards the Sun, the seasonal order is reversed.

In the northern hemisphere, winter solstice occurs around December 21st, summer solstice is near June 21st, spring equinox is around March 20th and autumnal equinox is about September 23rd. The axial tilt in the southern hemisphere is exactly the opposite of the direction in the northern hemisphere. Thus the seasonal effects in the south are reversed.

While it is true that Earth does have a perihelion, or point at which it is closest to the sun , and an aphelion, its farthest point from the Sun, the difference between these distances is too minimal to have any significant impact on the Earth's seasons and climate.

Earth’s Orbit Around The Sun

Another interesting characteristic of the Earth's orbit around the Sun has to do with Lagrange Points. These are the five positions in Earth's orbital configuration around the Sun where the combined gravitational pull of the Earth and the Sun provides precisely the centripetal force required to orbit with them.

The five Lagrange Points between the Earth are labelled (somewhat unimaginatively) L1 to L5. L1, L2, and L3 sit along a straight line that goes through the Earth and Sun. L1 sits between them, L3 is on the opposite side of the Sun from the Earth, and L2 is on the opposite side of the Earth from L1. These three Lagrange points are unstable, which means that a satellite placed at any one of them will move off course if disturbed in the slightest.

The L4 and L5 points lie at the tips of the two equilateral triangles where the Sun and Earth constitute the two lower points. These points liem along Earth's orbit, with L4 60° behind it and L5 60° ahead. These two Lagrange Points are stable, hence why they are popular destinations for satellites and space telescopes.

Earth’s Orbit Around The Sun

The study of Earth's orbit around the Sun has taught scientists much about other planets as well. Knowing where a planet sits in relation to its parent star, its orbital period, its axial tilt , and a host of other factors are all central to determining whether or not life may exist on one, and whether or not human beings could one day live there.

We have many more articles about the Earth's orbit , including 10 interesting facts about Earth. To learn more, check out this article on elliptical orbitsor check out NASA's Earth: Overview. Astronomy Cast also has a good episode on the subject entitled "Black black holes, Unbalancing the Earth, and Space Pollution."

Provided by Universe Today

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Orbits and Kepler’s Laws

Orange sun with colorful planets trailing out to one side.

Kepler's Laws of Planetary Motion

The story of how we understand planetary motion could not be told if it were not for the work of a German mathematician named Johannes Kepler. 

Kepler's three laws describe how planets orbit the Sun. They describe how (1) planets move in elliptical orbits with the Sun as a focus, (2) a planet covers the same area of space in the same amount of time no matter where it is in its orbit, and (3) a planet’s orbital period is proportional to the size of its orbit.

Who Was Johannes Kepler?

Johannes Kepler was born on Dec. 27, 1571, in Weil der Stadt, Württemberg, which is now in the German state of Baden-Württemberg.

A black and white drawing of Johannes Kepler showing him with dark hair, a mustache and beard, and wearing a high collar shirt with lace around the edges.

As a rather frail young man, the exceptionally talented Kepler turned to mathematics and the study of the heavens early on. When he was six, his mother pointed out a comet visible in the night sky. When Kepler was nine, his father took him out one night under the stars to observe a lunar eclipse. These events both made a vivid impression on Kepler's youthful mind and turned him toward a life dedicated to astronomy.

Kepler lived and worked in Graz, Austria, during the tumultuous early 17th century. Due to religious and political difficulties common during that era, Kepler was banished from Graz on Aug. 2, 1600. 

Fortunately, he found work as an assistant to the famous Danish astronomer Tycho Brahe (usually referred to by his first name) in Prague. Kepler moved his family from Graz, 300 miles (480 kilometers) across the Danube River to Tycho's home.

Mars is a reddish brown in this image from a spacecraft. A deep gash is visible across the center of the planet.

Kepler and the Mars Problem

Tycho was a brilliant astronomer. He is credited with making the most accurate astronomical observations of his time, which he accomplished without the aid of a telescope. He had been impressed with Kepler’s studies in an earlier meeting. 

However, some historians think Tycho mistrusted Kepler, fearing that his bright young intern might eclipse him as the premier astronomer of his day. Because of this, he only let Kepler see part of his voluminous collection of planetary data.

Tycho assigned Kepler the task of understanding the orbit of the planet Mars. The movement of Mars was problematic – it didn’t quite fit the models as described by Greek philosopher and scientist Aristotle (384 to 322 B.C.E.) and Egyptian astronomer Claudius Ptolemy (about 100 C.E to 170 C.E.). Aristotle thought Earth was the center of the universe, and that the Sun, Moon, planets, and stars revolved around it. Ptolemy developed this concept into a standardized,  geocentric model (now known as the Ptolemaic system) based around Earth as a stationary object, at the center of the universe.

Historians think that part of Tycho’s motivation for giving the Mars problem to Kepler was Tycho's hope that it would keep Kepler occupied while Tycho worked to perfect his own theory of the solar system. That theory was based on a geocentric model, modified from Ptolemy's, in which the planets Mercury, Venus, Mars, Jupiter, and Saturn all orbit the Sun, which in turn orbits Earth. 

As it turned out, Kepler, unlike Tycho, believed firmly in a model of the solar system known as the heliocentric model, which correctly placed the Sun at its center. This is also known as the Copernican system, because it was developed by astronomer Nicolaus Copernicus (1473-1543). But the reason Mars' orbit was problematic was because the Copernican system incorrectly assumed the orbits of the planets to be circular.

Like many philosophers of his era, Kepler had a mystical belief that the circle was the universe’s perfect shape, so he also thought the planets’ orbits must be circular. For many years, he struggled to make Tycho’s observations of the motions of Mars match up with a circular orbit.

Kepler eventually realized that the orbits of the planets are not perfect circles. His brilliant insight was that planets move in elongated, or flattened, circles called ellipses. 

The particular difficulties Tycho had with the movement of Mars were due to the fact that its orbit was the most elliptical of the planets for which he had extensive data. Thus, in a twist of irony, Tycho unwittingly gave Kepler the very part of his data that would enable his assistant to formulate the correct theory of the solar system.

Basic Properties of Ellipses

Since the orbits of the planets are ellipses, it might be helpful to review three basic properties of an ellipse:

  • An ellipse is defined by two points, each called a focus, and together called foci. The sum of the distances to the foci from any point on the ellipse is always a constant. 
  • The amount of flattening of the ellipse is called the eccentricity. The flatter the ellipse, the more eccentric it is. Each ellipse has an eccentricity with a value between zero (a circle), and one (essentially a flat line, technically called a parabola).
  • The longest axis of the ellipse is called the major axis, while the shortest axis is called the minor axis. Half of the major axis is termed a semi-major axis. 

After determining that the orbits of the planets are elliptical, Kepler formulated three laws of planetary motion, which accurately described the motion of comets as well.

Kepler's Laws

In 1609 Kepler published “Astronomia Nova,” which explained what are now called Kepler's first two laws of planetary motion. Kepler had noticed that an imaginary line drawn from a planet to the Sun swept out an equal area of space in equal times, regardless of where the planet was in its orbit. If you draw a triangle from the Sun to a planet’s position at one point in time and its position at a fixed time later, the area of that triangle is always the same, anywhere in the orbit. 

For all these triangles to have the same area, the planet must move more quickly when it’s near the Sun, but more slowly when it is farther from the Sun. This discovery became Kepler’s second law of orbital motion, and led to the realization of what became Kepler’s first law: that the planets move in an ellipse with the Sun at one focus point, offset from the center. 

In 1619, Kepler published “Harmonices Mundi,” in which he describes his "third law." The third law shows that there is a precise mathematical relationship between a planet’s distance from the Sun and the amount of time it takes revolve around the Sun.

Here are Kepler’s Three Laws:

Kepler's First Law : Each planet's orbit about the Sun is an ellipse. The Sun's center is always located at one focus of the ellipse. The planet follows the ellipse in its orbit, meaning that the planet-to-Sun distance is constantly changing as the planet goes around its orbit.

Kepler's Second Law: The imaginary line joining a planet and the Sun sweeps out – or covers – equal areas of space during equal time intervals as the planet orbits. Basically, the planets do not move with constant speed along their orbits. Instead, their speed varies so that the line joining the centers of the Sun and the planet covers an equal area in equal amounts of time. The point of nearest approach of the planet to the Sun is called perihelion. The point of greatest separation is aphelion, hence by Kepler's second law, a planet is moving fastest when it is at perihelion and slowest at aphelion.

Kepler's Third Law: The orbital period of a planet, squared, is directly proportional to the semi-major axes of its orbit, cubed. This is written in equation form as p 2 =a 3 . Kepler's third law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit. Mercury, the innermost planet, takes only 88 days to orbit the Sun. Earth takes 365 days, while distant Saturn requires 10,759 days to do the same.  

How We Use Kepler’s Laws Today

Kepler didn’t know about gravity, which is responsible for holding the planets in their orbits around the Sun, when he came up with his three laws. But Kepler’s laws were instrumental in Isaac Newton’s development of his theory of universal gravitation, which explained the unknown force behind Kepler's third law. Kepler and his theories were crucial in the understanding of solar system dynamics and as a springboard to newer theories that more accurately approximate planetary orbits. However, his third law only applies to objects in our own solar system. 

Newton’s version of Kepler’s third law allows us to calculate the masses of any two objects in space if we know the distance between them and how long they take to orbit each other (their orbital period). What Newton realized was that the orbits of objects in space depend on their masses, which led him to discover gravity.

Newton’s generalized version of Kepler’s third law is the basis of most measurements we can make of the masses of distant objects in space today. These applications include determining the masses of moons orbiting the planets, stars that orbit each other, the masses of black holes (using nearby stars affected by their gravity), the masses of exoplanets (planets orbiting stars other than our Sun), and the existence of mysterious dark matter in our galaxy and others.

In planning trajectories (or flight plans) for spacecraft, and in making measurements of the masses of the moons and planets, modern scientists often go a step beyond Newton. They account for factors related to Albert Einstein’s theory of relativity, which is necessary to achieve the precision required by modern science measurements and spaceflight. 

However, Newton’s laws are still accurate enough for many applications, and Kepler’s laws remain an excellent guide for understanding how the planets move in our solar system.

Illustration of NASA's Kepler space telescope

Johannes Kepler died Nov. 15, 1630, at age 58. NASA's Kepler space telescope was named for him. The spacecraft launched March 6, 2009, and spent nine years searching for Earth-like planets orbiting other stars in our region of the Milky Way. The Kepler space telescope left a legacy of more than 2,600 planet discoveries from outside our solar system, many of which could be promising places for life.

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Explore Johannes Kepler's Laws of Motion

  • An Introduction to Astronomy
  • Important Astronomers
  • Solar System
  • Stars, Planets, and Galaxies
  • Space Exploration
  • Weather & Climate

Everything in the universe is in motion. Moons orbit planets, which in turn orbit stars. Galaxies have millions and millions of stars orbiting within them, and across very large scales, galaxies orbit in giant clusters. On a solar system scale, we notice that most orbits are largely elliptical (a sort of flattened circle). Objects closer to their stars and planets have faster orbits, while more distant ones have longer orbits.

It took a long time for sky observers to figure these motions out, and we know about them thanks to the work of a Renaissance genius named Johannes Kepler (who lived from 1571 to 1630). He looked at the sky with great curiosity and a burning need to explain the motions of the planets as they seemed to wander across the sky.

Who Was Kepler?

Kepler was a German astronomer and mathematician whose ideas fundamentally altered our understanding of planetary motion. His best-known work stems from his employment by Danish astronomer Tycho Brahe (1546-1601). He settled in Prague in 1599 (then the site of the court of the German emperor Rudolf) and became court astronomer. There, he hired Kepler, who was a mathematical genius, to carry out his calculations.

Kepler had studied astronomy long before he met Tycho; he favored the Copernican world-view that said the planets orbited the Sun. Kepler also corresponded with Galileo about his observations and conclusions.

Eventually, based on his work, Kepler wrote several works about astronomy, including Astronomia Nova , Harmonices Mundi , and Epitome of Copernican Astronomy . His observations and calculations inspired later generations of astronomers to build on his theories. He also worked on problems in optics, and in particular, invented a better version of the refracting telescope. Kepler was a deeply religious man and also believed in some tenets of astrology for a period during his life. 

Kepler's Laborious Task

Kepler was assigned by Tycho Brahe the job of analyzing the observations that Tycho had made of the planet Mars. Those observations included some very accurate measurements of the position of the planet which did not agree with either Ptolemy's measurements or Copernicus's findings. Of all the planets, the predicted position of Mars had the largest errors and therefore posed the greatest problem. Tycho's data were the best available before the invention of the telescope. While paying Kepler for his assistance, Brahe guarded his data jealously and Kepler often struggled to get the figures he needed to do his job.

Accurate Data

When Tycho died, Kepler was able to obtain Brahe's observational data and attempted to puzzle out what they meant. In 1609, the same year that Galileo Galilei first turned his telescope towards the heavens, Kepler caught a glimpse of what he thought might be the answer. The accuracy of Tycho's observations was good enough for Kepler to show that Mars' orbit would precisely fit the shape of an ellipse (an elongated, almost egg-shaped, form of the circle).

Shape of the Path

His discovery made Johannes Kepler the first to understand that the planets in our solar system moved in ellipses, not circles. He continued his investigations, finally developing three principles of planetary motion. These became known as Kepler's Laws and they revolutionized planetary astronomy. Many years after Kepler, Sir Isaac Newton proved that all three of Kepler's Laws are a direct result of the laws of gravitation and physics which govern the forces at work between various massive bodies. So, what are Kepler's Laws? Here is a quick look at them, using the terminology that scientists use to describe orbital motions.

Kepler's First Law

Kepler's first law states that "all planets move in elliptical orbits with the Sun at one focus and the other focus empty." This is also true of comets that orbit the Sun. Applied to Earth satellites, the center of Earth becomes one focus, with the other focus empty.

Kepler's Second Law

Kepler's second law is called the law of areas. This law states that "the line joining the planet to the Sun sweeps over equal areas in equal time intervals." To understand law, think about when a satellite orbits. An imaginary line joining it to Earth sweeps over equal areas in equal periods of time. Segments AB and CD take equal times to cover. Therefore, the speed of the satellite changes, depending on its distance from the center of the Earth. Speed is greatest at the point in the orbit closest to the Earth, called perigee, and is slowest at the point farthest from the Earth, called apogee. It is important to note that the orbit followed by a satellite is not dependent on its mass.

Kepler's Third Law

Kepler's 3rd law is called the law of periods. This law relates time required for a planet to make one complete trip around the Sun to its mean distance from the Sun. The law states that "for any planet, the square of its period of revolution is directly proportional to the cube of its mean distance from the Sun." Applied to Earth satellites, Kepler's 3rd law explains that the farther a satellite is from Earth, the longer it will take to complete an orbit, the greater the distance it will travel to complete an orbit, and the slower its average speed will be. Another way to think of this is that the satellite moves fastest when it's closest to Earth and slower when it's farther away.

Edited by Carolyn Collins Petersen .

  • A Short History of the Scientific Revolution
  • Profile of Tycho Brahe, Danish Astronomer
  • The Story of Earth's Orbit Around the Sun
  • Biography of Johannes Kepler, Pioneering German Astronomer
  • What Is Astronomy and Who Does It?
  • Claudius Ptolemy: Astronomer and Geographer from Ancient Egypt
  • Biography of Isaac Newton, Mathematician and Scientist
  • Journey Through the Solar System: Planets, Moons, Rings and More
  • Understanding Cosmology and Its Impact
  • The Inventions of Galileo Galilei
  • A Historical Timeline of Rockets
  • Biography of Galileo Galilei, Renaissance Philosopher and Inventor
  • Newton's Law of Gravity
  • Astronomy: The Science of the Cosmos
  • Saturn: Sixth Planet from the Sun
  • Journey Through the Solar System: Planet Neptune

Universe Today

Universe Today

Space and astronomy news

one complete trip along an orbit

The Orbit of Earth. How Long is a Year on Earth?

Ever since the 16th century when Nicolaus Copernicus demonstrated that the Earth revolved around in the Sun, scientists have worked tirelessly to understand the relationship in mathematical terms. If this bright celestial body – upon which depends the seasons, the diurnal cycle, and all life on Earth – does not revolve around us, then what exactly is the nature of our orbit around it?

For several centuries, astronomers have applied the scientific method to answer this question, and have determined that the Earth’s orbit around the Sun has many fascinating characteristics. And what they have found has helped us to understanding why we measure time the way we do.

Orbital Characteristics:

First of all, the speed of the Earth’s orbit around the Sun is 108,000 km/h, which means that our planet travels 940 million km during a single orbit. The Earth completes one orbit every 365.242199 mean solar days, a fact which goes a long way towards explaining why need an extra calendar day every four years (aka. during a leap year).

The planet’s distance from the Sun varies as it orbits. In fact, the Earth is never the same distance from the Sun from day to day. When the Earth is closest to the Sun, it is said to be at perihelion. This occurs around January 3rd each year, when the Earth is at a distance of about 147,098,074 km.

The average distance of the Earth from the Sun is about 149.6 million km, which is also referred to as one astronomical unit (AU). When it is at its farthest distance from the Sun, Earth is said to be at aphelion – which happens around July 4th where the Earth reaches a distance of about 152,097,701 km.

And those of you in the northern hemisphere will notice that “warm” or “cold” weather does not coincide with how close the Earth is to the Sun. That is determined by axial tilt (see below).

Elliptical Orbit:

Next, there is the nature of the Earth’s orbit. Rather than being a perfect circle, the Earth moves around the Sun in an extended circular or oval pattern. This is what is known as an “elliptical” orbit. This orbital pattern was first described by Johannes Kepler, a German mathematician and astronomer, in his seminal work Astronomia nova (New Astronomy).

After measuring the orbits of the Earth and Mars, he noticed that at times, the orbits of both planets appeared to be speeding up or slowing down. This coincided directly with the planets’ aphelion and perihelion, meaning that the planets’ distance from the Sun bore a direct relationship to the speed of their orbits. It also meant that both Earth and Mars did not orbit the Sun in perfectly circular patterns.

In describing the nature of elliptical orbits, scientists use a factor known as “eccentricity”, which is expressed in the form of a number between zero and one. If a planet’s eccentricity is close to zero, then the ellipse is nearly a circle. If it is close to one, the ellipse is long and slender.

Earth’s orbit has an eccentricity of less than 0.02, which means that it is very close to being circular. That is why the difference between the Earth’s distance from the Sun at perihelion and aphelion is very little – less than 5 million km.

Seasonal Change:

Third, there is the role Earth’s orbit plays in the seasons, which we referred to above. The four seasons are determined by the fact that the Earth is tilted 23.4° on its vertical axis, which is referred to as “axial tilt.” This quirk in our orbit determines the solstices – the point in the orbit of maximum axial tilt toward or away from the Sun – and the equinoxes, when the direction of the tilt and the direction to the Sun are perpendicular.

Over the course of a year the orientation of the axis remains fixed in space, producing changes in the distribution of solar radiation. These changes in the pattern of radiation reaching earth’s surface cause the succession of the seasons. Credit: NOAA/Thomas G. Andrews

In short, when the northern hemisphere is tilted away from the Sun, it experiences winter while the southern hemisphere experiences summer. Six months later, when the northern hemisphere is tilted towards the Sun, the seasonal order is reversed.

In the northern hemisphere, winter solstice occurs around December 21st, summer solstice is near June 21st, spring equinox is around March 20th and autumnal equinox is about September 23rd. The axial tilt in the southern hemisphere is exactly the opposite of the direction in the northern hemisphere. Thus the seasonal effects in the south are reversed.

While it is true that Earth does have a perihelion, or point at which it is closest to the sun, and an aphelion, its farthest point from the Sun, the difference between these distances is too minimal to have any significant impact on the Earth’s seasons and climate.

Lagrange Points:

Another interesting characteristic of the Earth’s orbit around the Sun has to do with Lagrange Points . These are the five positions in Earth’s orbital configuration around the Sun where where the combined gravitational pull of the Earth and the Sun provides precisely the centripetal force required to orbit with them.

The five Lagrange Points between the Earth are labelled (somewhat unimaginatively) L1 to L5. L1, L2, and L3 sit along a straight line that goes through the Earth and Sun. L1 sits between them, L3 is on the opposite side of the Sun from the Earth, and L2 is on the opposite side of the Earth from L1. These three Lagrange points are unstable,  which means that a satellite placed at any one of them will move off course if disturbed in the slightest.

The L4 and L5 points lie at the tips of the two equilateral triangles where the Sun and Earth constitute the two lower points. These points liem along along Earth’s orbit, with L4 60° behind it and L5 60° ahead.  These two Lagrange Points are stable, hence why they are popular destinations for satellites and space telescopes.

The study of Earth’s orbit around the Sun has taught scientists much about other planets as well. Knowing where a planet sits in relation to its parent star, its orbital period, its axial tilt, and a host of other factors are all central to determining whether or not life may exist on one, and whether or not human beings could one day live there.

We have written many interesting articles about the Earth’s orbit here at Universe Today. Here’s 10 Interesting Facts About Earth , How Far is Earth from the Sun? , What is the Rotation of the Earth? , Why are there Seasons? , and What is Earth’s Axial Tilt?

For more information, check out this article on NASA- Window’s to the Universe article on elliptical orbits or check out NASA’s Earth: Overview .

Astronomy Cast also espidoes that are relevant to the subject. Here’s BQuestions Show: Black black holes, Unbalancing the Earth, and Space Pollution .

  • Wikipedia – Earth’s Orbit
  • NASA: Windows to the Universe – The Earth’s Orbit
  • NASA: Ask an Astrophysicist – Speed of the Earth’s Rotation

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5 Replies to “The Orbit of Earth. How Long is a Year on Earth?”

Matt, Are you sure about L4 and L5 being “more stable” than L2? As far as I know, the James Webb Space Telescope, Gaia, and I presume also some other satellites are all already in L2 or scheduled to fly to L2. Which satellite is parked in L4 or L5 and why there instead of L2? Thanks

The attraction of L2 is that it is behind the Earth, so that the Sun is eclipsed. This has the benefit of keeping sunlight out of the telescope, and keeping it nice and cool. But because L2 is not stable, the telescope needs to maintain its position there with course correction maneuvers.

mewo, L2 is 1.5 million km (or approx. 1 milliom miles, or 1% AU) from the Earth. At that distance, the Earth is too small to eclipse the Sun. According to wiki ( http://en.wikipedia.org/wiki/Lagrangian_point#cite_ref-14 ), the angular size of the Sun at 1 AU + 930000 miles is 31.6′, whereas the angular size of the Earth at 930000 miles is only 29.3′. Also, Wikipedia mentions that sattelite controllers even attempt to orbit the L-points at orbits as large as possible, in order to get even more sunshine on the solar batteries of the satellite in order to power it. The James Webb Space Telescope is designed with a solar battery so it does need the Sun. Yes, L1-L3 are somewhat more unstable, but a look at the L-points pic http://en.wikipedia.org/wiki/File:Lagrangian_points_equipotential.jpg shows them all somewhat on a top of a gravitational “ridge”. The JWST is scheduled to fly to L2 and I know of no satellites in L4 or L5. Wiki lists missions to L-points here: http://en.wikipedia.org/wiki/Lagrangian_point and no missions for L4 or L5 are mentioned.

The Lagrange point I find most interesting is L3. Would that there were an ETI here to monitor humanity’s climb to the stars, wouldn’t that be the best place to put a base or otherwise ‘hide out’?

I believe Irwin Allen used the premise of an “alternate Earth” at the L3 point (and sub-orbital space tourism) for the production of the TV show “Land Of The Giants” back in the late ’60’s … with mixed results

http://youtu.be/d4vsbOMdxPg

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Space Facts

Space Facts

Orbital Periods of the Planets

Orbital Periods of the Planets

How long are years on other planets?

A year is defined as the time it takes a planet to complete one revolution of the Sun, for Earth this is just over 365 days. This is also known as the orbital period. Unsurprisingly the the length of each planet’s year correlates with its distance from the Sun as seen in the graph above. The precise amount of time in Earth days it takes for each planet to complete its orbit can be seen below.

Mercury: 87.97 days (0.2 years) Venus : 224.70 days (0.6 years) Earth: 365.26 days(1 year) Mars: 686.98 days(1.9 years) Jupiter: 4,332.82 days (11.9 years) Saturn: 10,755.70 days (29.5 years) Uranus: 30,687.15 days (84 years) Neptune: 60,190.03 days (164.8 years)

Related space facts:

61 comments.

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I still treat Pluto as a planet and I’m sure many others do , I’d like to see this in your list. Hopefully it still takes approximately 248 years to orbit the Sun or have the scientists moved the goalposts on this as well?

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this does not show each planets length of orbit, in a year as we know them

Ricky, for more in depth factoids about space it’s best to have many sources of reference, then do some cross research try this site http://www.org.northern.edu>uss>docs . Have fun .

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please tell us how long it takes each planet to orbit the sun

From up above (that is, if you will scroll up to just above this bunch/list of comments) you should see the duration of years for each planet. I copied and pasted it here. So, after the colon, on what should be the next line is not my writing and I cannot and will not take any credit for it. I hope this helps you: “A year is defined as the time it takes a planet to complete one revolution of the Sun, for Earth this is just over 365 days. This is also known as the orbital period. Unsurprisingly the the length of each planet’s year correlates with its distance from the Sun as seen in the graph above. The precise amount of time in Earth days it takes for each planet to complete its orbit can be seen below.

Mercury: 87.97 days (0.2 years) Venus : 224.70 days (0.6 years) Earth: 365.26 days(1 year) Mars: 686.98 days(1.9 years) Jupiter: 4,332.82 days (11.9 years) Saturn: 10,755.70 days (29.5 years) Uranus: 30,687.15 days (84 years) Neptune: 60,190.03 days (164.8 years)”

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HONORABLE MENTION: Pluto’s orbital period: 248 years

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What about Sedna?

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about 100 thousand million stars

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The interesting thing is that tomorrow, 12/31, is my 84th birthday and the planet Uranus is finally back to where it was on the day I was born. One orbit for Uranus, 84 years for me!

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