Orbital mechanics

**Orbital mechanics** refer to the laws which govern objects undergoing free-falling trajectories in the influence of a gravitational field, and the ways in which spacecraft can use them to reach a desired location.

## Down Here Versus Up There

When people think of spaceflight, they may think of it as a natural extension of terrestial locomotion, where to go from one place to another you simply point yourself in the direction you want to travel in, and off you go! In reality however, astronautics is as different from aeronautics as aeronautics is from automotive mechanics. In the same way you won't call a plane a "special type of car" because it spends some of its operation time on the runway, it is unfair to call a rocket "a special type of plane" and view rocketry as an extension of aviation just because the rocket spends some of its life beneath the Kármán line of 100 kilometers (54 nautical miles, 62 statue miles).

To design a successful rocket there are many features which need to be taken into consideration that are not in aviation. This just as dramatically affects orbital mechanics, or the physics by which things orbit - but what is an orbit?

## Orbit

An orbit is the path of an object through a gravitational field. While the first thing that may come to mind when you read "orbit" is of a perfectly circular orbit of one body around another, this is a mathematical idealization that does not exist in physical reality. For reasons which go beyond this article to fully explore, any bound orbit of two objects will end up decaying due to the release of gravitational waves as predicted by Albert Einstein's theory of general relativity. Thus there exists no perfect two-body systems of orbit. Even the seemingly stable ones such as the moon Luna's orbit around Earth or Earth's orbit around the sun are in elliptical shapes and often skewed slightly away from the equatorial plane of the sun's rotation. It is only due to the extreme longevity and predictability of these orbits that they are called "stable." In a universe of hundreds of billions of stars, stability is a fleeting illusion.

In the age of space, humans have launched many vehicles capable of crossing the most commonly accepted threshold of space called the Kármán line at 100 km, and have successfully launched vehicles which can orbit multiple times around Earth. To achieve this, a spacecraft must ensure two things:

* The vertical distance from the ground must be high enough to avoid drag with the atmosphere. This will pull the spacecraft back down unless thrust is applied to keep the spacecraft orbiting, which isn't desirable if you're seeking to minimize the weight of the craft.
* The lateral speed must be no less than 28,000 km/hr (17,500 mph) to achieve a Low Earth Orbit (LEO) of 325 km (175 nautical miles, 200 statue miles). By comparison the Russian probe Sputnik-1 was launched to a height of 215 km. Orbits at 200 km require less than this 28,000 km/hr figure, though orbits with periapsis less than 300 km will suffer from atmospheric drag effects that once more bring the craft down.

Orbiting the Earth in this way may seem incredible, but it is a consequence of Earth's curved shape. One travelling in a straight line tangent to the ground at a given location will eventually find the ground dropping away beneath them due to the curvature of Earth. This happens at a rate of 8 inches per mile squared, so one miles away should be 2/3rds of a foot lower, and two miles away should be 2.5 feet lower. Now, every object launched follows a trajectory that will also tend to curve past the highest point back down. If the rate that an object falls is carefully matched to the rate that the Earth's surface drops off, then an object can be at a constant height relative to the Earth's surface and yet maintain its lateral or surface-tangential speed. Objects in orbit are in free fall, and hence feel no gravitational influence through Einstein's equivalence principle. In LEO however Earth's gravity is still 90% of its standard value, and so it is not true there is "zero-gravity." In addition to Earth's gravity facilitating the orbit in the first place, there is also the very small gravity of the spacecraft, which is why astronauts in space are said to be in a microgravity environment.

## Basic Terms

### Points

**Apoapsis:** The point of an orbit's trajectory farthest from the parent body.
**Aphelion:** The point of a planet or other celestial body's farthest approach to the sun within a closed orbit.
**Periapsis:** The point of an orbit's trajectory closest to the parent body.
**Perihelion:** The point of a planet or other celestial body's closest approach to the sun within a closed orbit.
### Directions

**Radial-In/Out:** Directions directed *towards* and *away* the center of mass of a spherical body respectively. Increasing your radial-out distance from Earth means increasing your distance from Earth's core, or going 'straight up.'
**Normal/Antinormal** Directions perpendicular to the orbital plane.
**Prograde/Retrograde:** Directions that go *with* or *opposite* the direction of rotation of the parent object.