Reddit mentions of Orbital Mechanics for Engineering Students (Aerospace Engineering)

There are several courses that ARO (usually) has, but ME exclusive program doesn't, such as Gas Dynamics, Low/High Speed Aerodynamics, Orbital Mechanics, Aircraft Stability, and Jet Propulsion. I based this statement from the school (CalPoly Pomona) that I went to. YMMV.

Book recommendations:

• Orbital Mechanics
  
• Gas Dynamics & High Speed Aerodynamics
  
• Flight Mechanics
  
• Jet Propulsion
  
• Spacecraft Design
  
• Rocket Propulsion
  
  Aerospace is broad subject, you haven't specified whether you're interested in structures, aerodynamics, flight mechanics, or propulsion. I gave you a broad list of selection to reflect that, although I assume you are more inclined toward Astronautics (Space) part of Aerospace instead of Aeronautics (Air); hence you posted your question in /r/space.

This was one of my favorite classes and I thought it was a rather good book to learn from. That being said you can probably find it cheaper than this.

http://www.amazon.com/Orbital-Mechanics-Engineering-Students-Aerospace/dp/0123747783/ref=sr_1_2?ie=UTF8&qid=1395292188&sr=8-2&keywords=orbital+mechanics+for+engineering+students

You will NEED to have a good grasp on the laws of motion and math/calculus. Otherwise you will just not be able to do this stuff.

If you are okay with Calculus, I really liked Curtis' Orbital mechanics book. Real eye opener. The satellite paradox is especially cool.

Orbital Mechanics for Engineering Students (Aerospace Engineering) https://www.amazon.com/dp/0123747783/ref=cm_sw_r_cp_apa_i_VEqXCbFAMVQ27

Haha... That applet is fun to play with!

First off, spiraling in or shooting way off are no the only options. You can orbit at many speeds and altitudes. In a perfect world, orbits are either ellipses with an eccentricity between 0 and 1, a parabola with a perfect eccentricity of 1, or a hyperbola with an eccentricity greater than 1. Wiki conic sections if you need more information of those shapes.

The ellipse is the orbit, obviously, and the Earth is at one of the focii? An ellipse will keep its shape without spiraling in. It will only stop unless near the perigee the distance between the orbit and focus is smaller than the radius of the earth (collision).

A parabola is the perfect eccentricity where the satellite will not come back, and basically will eventually fly away and stop somewhere, while a hyperbola will have some escape velocity that it will keep flying at.

The only problem with perfect conic section orbits are perturbations. One is atmospheric drag. Even at LEO orbits, drag affects orbits. The ISS falls a few feet a day, and requires frequent changes to keep it at altitude. Higher Geo-synchronous orbits have very negligible drag, but its affected by Moon's gravity more, as the moon has its own gravitational pull.

Humans cannot simply launch a perfect rocket from earth and have it just "land" in the perfect orbit that it was intended for (like shooting a 3 pointer from miles away). Until a satellite is where it needs to be, it requires small changes in direction and speed, but these usually aren't very large and usually take place when you get closer to the destination.

There are books and books of orbital equations. I am in my 2nd of 4 graduate level orbital determination classes, but a good starting point would be the wiki page on the vis-viva equation. Following Wiki around can give you a better understanding than I can in a comment.

If you really are fascinated by this information, and are a self learner, I would definitely go check out Orbital Mechanics. I used this book in my class and it explains it well enough to learn it without an instructor..