# Do all orbits have a perigee and an apogee?

I'm taking an astronomy class and are stuck on a few questions. Mainly, this one about apogee.

It's asking: The apogee of a(n) ______ orbit does not exist? The choices are parabolic, geosynchronous, or all orbits have both a perigee and an apogee.

The question originally had 5 options, but I already canceled out 2 of them. I don't just want an answer. I'm also looking for an explanation. I've looked all over the book, and even online, and can't seem to figure it out.

Geosynchronous orbits are fixed, and I would think have the same perigee and apogee. Parabolic basically moves away from the earth. Then, I'm not sure if it's the last choice.

Any help in this will be greatly appreciated! Thank you!

Relevance

The only orbit which has both a perigee and an apogee is an elliptical orbit. In a circular orbit, the perigee and apogee are undefined because the object is always at the same distance. Parabolic and hyperbolic orbits are open-ended, so the object can pass perigee but will never reach apogee because it will always be moving away. A geosynchronous orbit has a period of one day, but there's no reason why it can't be elliptical. A geostationary orbit is a special case of a geosynchronous orbit, where the object sits above the same point on the Earth's equator, but in practice, even these orbits deviate from exact circles by a small amount.

• Orbits that are closed loops all have at least a perigee and an apogee.

Since it is possible to derive a formula that links eccentricity to the difference (in distance) between perigee and apogee, then the perfect circle (e = 0) has the same perigee and apogee distance (difference = 0). You cannot distinguish the perigee from the apogee (or, if you prefer, every single point on the orbit is simultaneously a perigee and an apogee).

This leaves open orbits: parabolic and hyperbolic.

The both have a perigee but no apogee (the distance is boundless). Whatever distance you try to set as that of apogee, you can show that the orbit can go further out.

The open orbits definitely do not have an apogee.

For the circular orbit, the answer could be ambiguous.

The circular orbit does not have a distinct apogee. If the definition of apogee requires you to identify a point as distinct from the perigee, then the circular orbit does not have one. If the definition is simply the furthest point, then the entire orbit is the apogee.

• I agree with the others that a parabolic orbit has no apogee, because if it did, that point would be at infinity, (which is just an abstraction). I must also point out that there is no such thing as a perfectly circular orbit in the real world. The concept of "circle" is a mathematical abstraction that can be approached to any level of accuracy, but can never be achieved in reality, sort of like absolute zero. Furthermore, the term "orbit" comes from the Greek, meaning "circle", so technically, a parabolic "orbit" is really not an orbit but simply a trajectory. Also, to get REALLY pedantic, "apogee" means the highest point from the EARTH, so orbits around the Sun for instance have no "apogee" but rather a "perihelion" and an "aphelion". Oh well, it's fun to talk about these things, don't you agree?

• Just to recap, the apogee is the farthest point of the orbit and the perigee is the closest point. The only orbits that don't have those are orbits that are perfectly circular, so each and every point is exactly the same distance away. Those almost never happen in nature, btw. In a geosynchronous orbit, the satellite stays exactly above the same spot on the earth all the time. A satellite can only do that if it maintains a perfectly circular orbit, so that must be the answer.

• Anonymous

A parabolic or hyperbolic Orbit has no apogee, as it is not a closed line and reaches infinity, when true anomaly approaches 180° (TA = 180° -> Apogee). Circular orbits exist only in theory, just like parabolic orbits - small differences in velocity make eccentricity unequal 0 (circular) or 1 (parabolic).

A geostationary thus still has apogee and perigee, but the difference in so small, that you can practically assume a circular orbit for calculations.

• Anonymous
5 years ago

The satellite at apogee of the elliptical orbit is moving slower than the satellite in the circular orbit. That's why it falls in to the perigee point. If you speed it up slightly, then the perigee moves further out. Speed it up just enough, and you have a circular orbit.

• Perigee, apogee are the same for a perfectly circular orbit. Most orbits are eliptical

• Well to be precise, any orbit that isn't around the Earth has no apogee or perigee, as these terms are specific to the Earth. The generic terms are apoapsis and periapsis. Around the sun, it's aphelion and perihelion, around the moon its apislune and perislune, jupiter is apojove, perijove etc and so on.