Since ancient times, star gauges have known that planets are different from stars. While the stars always appear in the same place in the night sky, the planets change their positions from night to night. They seem to be moving against the background of the stars. Sometimes it even seemed that the planets were moving backwards. (This behavior is known as retrograde motion.) Such strange movements in the sky were difficult to explain.
Then, in the 1600s, Johannes Kepler identified mathematical models in the motions of the planets. Astronomers before him knew that planets orbited or moved around the sun. But Kepler was the first to describe these orbits – correctly – with mathematics. As if putting together a puzzle, Kepler saw the pieces of data fit together. He summarized the mathematics of orbital motion with three laws:
- The path the planet takes around the sun is an ellipse, not a circle. The ellipse is oval in shape. This means that sometimes a planet is closer to the sun than at other times.
- The speed of the planet changes as it moves along this path. The planet accelerates when it passes closest to the sun and slows when it moves away from the sun.
- Each planet orbits the sun at different speeds. The more distant ones move slower than the ones closer to the star.
Kepler still couldn’t explain why the planets followed elliptical paths instead of circular ones. But his laws can predict the positions of the planets with incredible accuracy. Then, about 50 years later, physicist Isaac Newton explained the mechanism why Kepler’s laws worked: gravity. The force of gravity attracts objects in space to each other – causing the movement of one object to constantly bend to another.
Throughout the cosmos, all kinds of celestial objects orbit each other. Moons and spaceships orbit the planets. Comets and asteroids orbit the sun – even other planets. Our sun orbits the center of our galaxy, the Milky Way. Galaxies also orbit each other. Kepler’s laws describing orbits apply to all these objects in the universe.
Let’s look at each of Kepler’s laws in more detail.
Orbits, orbits everywhere. This image shows the orbits of 2,200 potentially dangerous asteroids orbiting the sun. The orbit of the binary asteroid Didymus is shown with a thin white oval, and the orbit of the Earth is the thick white path. The orbits of Mercury, Venus and Mars are also marked. Center for Near-Earth Research, NASA / JPL-Caltech
Kepler’s first law: Ellipses
To describe how oval an ellipse is, scientists use the word eccentricity (Ek-sen-TRIS-sih-tee). This 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 ovals.
The Moon’s orbit around the Earth has an eccentricity of 0.055. This is an almost perfect circle. Comets have many eccentric orbits. Halley’s Comet, which orbits the Earth every 75 years, has an orbital eccentricity of 0.967.
(It is possible that the motion of an object has an eccentricity greater than 1. But such a high eccentricity describes an object that rotates around another in a wide U-shape – never to return. So, strictly speaking, it will not wandering around the site his path was winding.)
This animation shows how the speed of an object is related to how oval its orbit is. Phoenix7777 / Wikimedia Commons (CC BY-SA 4.0)
Ellipses are very important for planning the orbit of a spacecraft. If you want to send a spaceship to Mars, you have to remember that the spaceship starts from Earth. This may sound silly at first. But when you launch a rocket, it will naturally follow the ellipse of the Earth’s orbit around the sun. To reach Mars, the elliptical path of the spacecraft around the sun will have to change to match the orbit of Mars.
With some very complex mathematics – this famous “rocket science” – scientists can plan how fast and how high a rocket takes to launch a spaceship. Once the spacecraft is in orbit around the Earth, a separate set of smaller engines is slowly expanding the spacecraft’s orbit around the sun. With careful planning, the spacecraft’s new orbital ellipse will coincide with Mars at the right time. This allows the spacecraft to reach the Red Planet.
When a spacecraft changes its orbit – for example, when it moves from one around the Earth to one that will take it around Mars (as in this illustration) – its engines must change the shape of their elliptical path. NASA / JPL
Kepler’s second law: Change of speed
The point at which the planet’s orbit comes closest to the sun is its perihelion. The term comes from the Greek peri, or near, and helios, or sun.
The earth reaches its perihelion in early January. (This may seem strange to people in the Northern Hemisphere who experience winter in January. But the distance of the Earth from the sun is not the cause of our seasons. This is due to the tilt of the Earth’s axis of rotation.) In perihelion the Earth moves most the 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 the Earth moves the slowest in its orbital path – about 29 kilometers (18 miles) per second.
Planets are not the only orbital objects that accelerate and decelerate in this way. Every time something in orbit approaches the object that is orbiting, it feels a stronger gravitational pull. As a result, it accelerates.
Scientists are trying to use this extra boost when launching a spacecraft to other planets. For example, a probe sent to Jupiter could fly past Mars along the way. As the spacecraft approaches Mars, the planet’s gravity causes the probe to accelerate. This gravitational gain throws the spacecraft toward Jupiter much faster than it would travel alone. This is called the slingshot effect. Using it can save a lot of fuel. Gravity does some of the work, so engines need to do less.
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Kepler’s third law: Distance and velocity
At an average distance of 4.5 billion kilometers (2.8 billion miles), the gravitational pull of the sun on Neptune is strong enough to keep the planet in orbit. But it is much weaker than pulling the sun on the Earth, which is only 150 million kilometers (93 million miles) from the sun. So Neptune travels in its orbit slower than Earth. It orbits the sun at about 5 kilometers (3 miles) per second. The earth approaches the sun at about 30 kilometers (19 miles) per second.
As more distant planets travel more slowly around wider orbits, it takes them much longer to complete one orbit. This period of time is known as the year. On Neptune, it lasts about 60,000 Earth days. On Earth, far closer to the sun, a year is just over 365 days. And Mercury, the planet closest to the Sun, ends its year every 88 Earth days.
This relationship between the distance of the orbital object and its speed affects how fast satellites approach the Earth. Most satellites – including the International Space Station – orbit about 300 to 800 kilometers (200 to 500 miles) above the earth’s surface. These low-flying satellites complete one orbit every 90 minutes or so.
Some very high orbits – about 35,000 kilometers (20,000 miles) from the ground – make satellites move slower. In fact, these satellites move slowly enough to match the speed of the Earth’s rotation. These ships are in geosynchronous (Gee-oh-SIN-kron-ous) orbit. Because they appear to be stationary over a country or region, these satellites are often used to track weather conditions or relay communications.
In case of collisions and parking spaces
The space may be huge, but everything in it is always in motion. Sometimes two orbits intersect. And this can lead to clashes.
Some places are full of objects in cross orbits. Think of all the space debris that orbits the Earth. These pieces of debris are constantly colliding with each other – and sometimes with important spaceships. Predicting where potentially dangerous debris is directed in this swarm can be quite complicated. But it’s worth it if scientists can predict a collision and move a spaceship off the road.
This diagram shows where all five Lagrange points are located for a spacecraft orbiting the Sun-Earth system. At each of these points, the spacecraft will remain in place without much need to start its engines. (The small white circle around the Earth is the moon in its orbit.) Note that the distances here are not to scale. NASA / WMAP Science Team
Sometimes the target of a potential collision may not be able to deviate. Think of a meteor or other cosmic rock whose orbit could put it in a collision with Earth. If we are lucky, this incoming rock will burn in the earth’s atmosphere. But if the stone is too big to disintegrate completely in its path in the air, it can break on Earth. And that could be catastrophic – just as it was for dinosaurs 66 million years ago. To prevent these problems, scientists are exploring how to deflect the orbit of incoming space rocks. This requires a particularly challenging number of orbital calculations.
Saving satellites – and possibly preventing an apocalypse – are not the only reasons to understand orbits.
In the 1700s, the mathematician Joseph-Louis Lagrange identified a special set of points in space around the sun and each planet. At these points, the gravitational pull of the sun and the planet strike a balance. As a result, a spaceship parked in this place can stay there without burning a lot of fuel. Today they are known as Lagrange points.
One of these points, known as L2, is especially useful for space telescopes, which must remain …
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