It may seem a little daunting, it is rocket science after all, but understanding all of the terms that are used when talking about space travel isn't hard at all. So let's break down all the different terms that get thrown around when talking about space. This is not a complete list of every term used in space travel to describe orbits of objects, but it is a good primer to explain the basic principles of space travel.
Apoapsis refers to the highest point in an orbit, where the object is as far away from the point it's orbiting. Periapsis on the other hand is the lowest point in an orbit, the point where the object is closest to the center of it's orbit. The prefixes apo- and peri- are often added to the name of whatever an object is orbiting. For example, an object orbiting the moon it's apoapsis and periapsis might be named apolune and perilune.
Somewhat related to apoapsis and periapsis is the semi major axis. Before getting into what a semi major axis is we have to get into the geometry of what every orbit is. All orbits take the form of ellipses. Every ellipse has a major axis, which is the longest line you can draw from one edge of an ellipse to the other. The major axis is the line between the Apoapsis and periapsis. The prefix semi literally means half, so the semi major axis is simply half the major axis, or half the distance between the periapsis and Apoapsis. This is practically equal to the average height of your orbit. Note that this is the height from the center of your orbit, NOT the altitude of an object over the surface of the main object it's orbiting.
The next important value in orbital mechanics we need to discuss is inclination. Inclination is far less complicated than the semi major axis. Imagine a line along the equator, now imagine your orbit and it's line as it crosses over the equator. The angle that your orbit makes with the equator is your orbits inclination. If you had a satellite orbiting directly over the Earth's equator it would have an inclination of 0 degrees, and if you had an orbit that went directly over the north and south poles it would have an inclination of 90 degrees.
Closely related to inclination are Ascending and Descending Nodes. These nodes are the points where your orbit crosses the equator of the planet it's orbiting. The ascending nodes is the point where an object crosses the equator heading north, or up, and the descending Nodes is the point where an object crosses the equator heading south. These are extremely important when trying to change your inclination relative to a planet.
Orbital plane is an imaginary disc that the orbiting object sits on. Obviously everything in our universe moves in three dimensions, but the orbital plane allows us to look at an orbit in 2D, which makes it simpler to deal with mentally.
The reference plane is the plane that we consider to be at 0 degrees for any system, and in space travel the reference plane is almost always the equitorial plane of the parent object. The reference plane for earth is it's equator, while the reference plane for the solar system is called the invariable plane, which is roughly the average of all the orbital planes of the planets orbiting the sun. The reference plane for the milky way Galaxy is likewise, the average of all the stars orbital planes in the galaxy.
Eccentricity is much more complex and there's a number of complicated mathematical formulas regarding conic sections, ellipse, circles , parabolas, and hyperbolas, that all go into defining what eccentricity is, and all of that is beyond the scope of what we're going to talk now. The simple definition of eccentricity is how far your orbit is from being circular. A perfectly circular orbit has an eccentricity of 0, an elliptical orbit has an eccentricity between 0 and 1, and a parabolic orbit (like an escape trajectory) has an eccentricity greater than 1.
Orbital speed is the velocity at which an object orbits it's parent body. Orbital speed changes with altitude and eccentricity, and it can refer to two different speeds, the average or mean orbital speed for an object around it's entire orbit, or the speed of the object at any particular point.
Next up are the different types of periods. Sidereal and synodic. A sidereal period is the time it takes for an object to complete it's orbit relative to the stars (not the surface of the object it's orbiting). A synodic period is the time it takes for an object to complete an orbit relative to the surface of the planet it's orbiting. When we talk about periods we are almost always talking about sidereal periods as they are the least ambiguous, but synodic periods are very important too. For instance, a geosynchronous orbit is one where the sidereal period of the orbiting object is equal to the rotational period of the object it's orbiting. A satellite orbiting the earth with a sidereal period of 24 hours will orbit the earth as fast as the earth rotates, this means that relative to the surface of the earth, it's not moving at all. It's sidereal period would be 24 hours but it's synodic period would be infinite, since it would take infinitely long to orbit the surface of the earth.
Now that you understand some of the basic terminology for orbits, you can better understand how they work, and how to use them in space missions!
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