I’ve lately come to realize that I don’t really understand orbits all that well. The very basics I get - falling around the planet, cannon on mountain, etc. Where my understanding breaks down is with what happens next, and Wikipedia is a little too formula-laden for me to even figure out where I should be looking.
So: suppose I’m orbiting the earth, in the space shuttle. I have a penny. If I exert a force on it parallel to the orbit, it’s going to go up (if I push it forwards) or down (backwards), yes? But - what happens if I push it up or down?
I have a vague notion that it takes a fair amount of energy to come out of an orbit and land on a planet, but I’m not sure if that’s just the case if you want to land in one piece, and smacking the earth at however many miles an hour is easy, or if the penny will just end up in another orbit if I don’t slow it down.
Finally, I’m completely in the dark about how elliptical orbits work. Say I wanted to change my nice, circular orbit into an elliptical one. How would I go about doing that? What about if I want to switch back? My ignorance needs a whoopin’.
The penny you throw towards the middle of the earth from your orbit would take on an elliptical orbit. If you could throw it with precise accurately from a hatch in the bottom center of the ship after 90 degrees of orbiting around the planet the penny would bounce off the bottom of your ship with the same force you used to throw it.
Assuming a circular orbit:
Forces in two dimensions (towards/away from the earth and with/against the normal of your orbit) will push your ship into a slightly less circular (elliptical) orbit.
Forces in the third dimension (perpendicular to the other two) would rotate your orbit around the planet slightly and also make your orbit a tiny bit more elliptical.
If you’re in the Space Shuttle and you throw a penny in the direction you’re travelling, here’s what will happen. The penny will start moving away from you. As you travel in a circular orbit, the penny’s extra energy will carry it a little higher. As it gains height, it will start to slow down. (Trading kinetic energy for potential energy, like rolling a ball uphill.) Exactly halfway around the Earth, it will be as high and as slow as it’s going to get. It will be going too slow to maintain that altitude, so it will start coming back down and gaining speed. The penny will return to exactly the point where you released it! (It may not look like it, because the Earth rotates, so the same point in space is not over the same point on land.) The energy you gave the penny by throwing it moves it from the original circular orbit to a slightly elliptical orbit.
Read that underlined sentence again. Anything in orbit comes back to where it started, and the path that it follows is an ellipse. (A circle is a special case of an ellipse, just like a square is a special case of a rectangle.) Remember the thought experiment with the cannonballs? The first cannonballs, before we built the super-duper cannon, hit the ground. Suppose we ignore that for the moment. We fire the cannon, the cannonball comes out and starts curving downwards; if it could pass through the ground, what path would it take? It would keep going faster and faster, but not directly at the center of the Earth, because we fired it sideways. It would whip around the core and that speed would start to carry it upwards. It would return to exactly where it left the muzzle of the cannon. (I’m leaving out a huge complication. The point is that even a cannonball that hits the ground is following an orbital path, it just doesn’t get to complete it.)
Let me know if all that makes sense, and I can try to answer the rest of the questions.
This description ignores the sun, the moon, drag, precession, and a whole lot of other stuff that would intrude on an ideal orbit. I’m not a rocket scientist; and the solar system is a complicated place. Be sure to comply with all local zoning regulations before attempting to place an object in orbit.
Also, by throwing the penny ahead of your own mass, you slow yourself (and the shuttle) down by an infinitesimal degree, and push yourself into a lower (elliptical) orbit as well.
For a real life application of this, we have an empty ammonia tank which was purposefully thrown away from the International Space Station by an astronaut during a spacewalk.
Ok, so if I just lob my penny straight down, it’s coming back to me. What does that look like? I mean, I’d imagine that putting it into a lower orbit (or, I guess, a lower part of an elliptical orbit?) would mean it would, from my point of view, sort of curve down and forward? And then eventually curve back and up to meet me? How fast is that? Is there a generalized formula for that? I’d imagine that, since it’s gravity based, it’s gonna be mass-independent, but does it depend on your initial orbit?
Also, Chronos, you mention that a 93 MPH pitch will drop a baseball by 145 kilometers (at perigee). That’s actually a lot more of a change than I’d have expected. What does the graph of initial speed vs perigee change look like? If I could get something going three times that fast, would it then be in an orbit to intersect the ground? I was under the impression that it took a fair bit of energy to deorbit something, so that seems too easy - but I’m obviously no rocket scientist.
