SpaceProf.xyz || Nibbles in Space: 000316

What's an orbit?

September 2020 || 000316

2 - 3 minute read

Title image is Earth as seen by the Apollo 17 crew on 7 December 1972, traveling towards the moon. This was the first time the Apollo trajectory made it possible to photograph the south polar ice cap, and this image is the original from which The Blue Marble image was produced. Image credit: NASA

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A satellite is an object that orbits something else, satellites can be natural, like the Moon, or artificial, like a spacecraft. But. What’s an orbit? The Ancient Greek philosopher and polymath Aristotle thought that circular motion was the only perfect motion. It followed that this must be the motion of all ‘heavenly’ bodies. However, over 400 years ago, the work of a Danish nobleman, Tycho Brahe and his assistant, the prematurely born son of a mercenary, and a healer later tried for witchcraft, changed our thinking forever.

Brahe made the most accurate astronomical observations of his time, and from these his assistant developed his own theories of ‘heavenly’ motion. In 1609, Brahe’s assistant published his first two laws of planetary motion. A third followed in 1619. And, with this Johannes Kepler had his three laws of planetary motion. But, Kepler’s laws only describe the motion, they are not an explanation.

Providing the explanation, Isaac Newton introduced his three laws of motion in his 1687 manuscript, Principia, alongside his law of universal gravitation. Newton’s law of universal gravitation has itself been superseded in many ways by Albert Einstein's theory of general relativity, attributing gravity to curved spacetime instead of a force between two objects. But, Newton’s laws provide a good approximation, and often, as engineers, that is what we want.

So, what is an orbit? Well, Newton himself introduced a thought experiment to explain this. If we ignore the effect of the Earth’s atmosphere and other so-called disturbing forces on the motion of a cannonball, then when it is fired it will follow an arc until it hits the ground. If the cannon is fired faster it will fly further, before hitting the ground.

If the cannon is fired faster, and faster, at some point it will get so fast it will follow an arc that has the same curvature as the Earth, and it will never hit the ground. Instead, it will return to the exact point it was fired from, either hitting the back of the cannon or, if you’ve moved your cannon it will continue onwards around the Earth again.

Therefore, an object in orbit is in continual freefall, moving forward so fast it never hits the ground.

Firing our cannonball faster still, it now follows an arc that is less curved than the Earth. As the cannonball moves away from Earth it will slow down, before Earth’s gravity pulls it back. Once again, it will return to pass through the exact point it was fired from. This is termed an eccentric orbit. All orbits are eccentric. Some orbits are more eccentric than others.

The closest point of an orbit to Earth is termed perigee, and the furthest point is apogee. From περί or peri, meaning near, and ἀπό or apo, meaning away from, which is adjoined to the body being orbited, so -gee for Earth from Ancient Greek Γῆ or Gē, meaning land or Earth. This means similar terms can be constructed for orbits around most things in the solar system. The line connecting perigee and apogee is the major axis. The size of an orbit is given by half of this distance, termed the semi-major axis.

Firing our cannonball even faster, it will no longer be slowed down enough by Earth’s gravity. Instead it will continue onwards on an escape trajectory into the solar system. This is how we send spacecraft to other planets.

So, an orbit is the path around another object in space. The path is curved. The amount of curve depends on the relative size and speed of the two objects. The path can be open or closed, that is, a curve or an oval. No real orbit is a perfect circle.

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