Throwing a baseball from orbit to the earth

Question

I just read a thought piece about what a war in space may look like, and it changed my thoughts on what orbit actually is. From what I read about orbits, it sounds like going faster in the velocity direction will cause you to get to a lower altitude, and going slower will cause you to get to a higher altitude orbit. This feels completely backwards to me, so I tried a thought experiment, but it led me to the questions below.

I'm standing on satellite in a circular low earth orbit, and I want to make my (indestructible) baseball go to the ground without waiting for months or years to de-orbit. If I threw the baseball in the velocity direction, I don't think I could cause enough delta V to make it go fast enough that it would go to a significantly lower orbit. Is that correct?

So instead of throwing it in the velocity direction, if I threw it straight at the earth (nadir), would it continue to go towards the earth, or would that just modify the baseball's orbit similar to throwing it in the velocity direction? I remember hearing about something "bouncing off the atmosphere". That wouldn't come into play with my baseball would it?

If I threw the baseball in the wake direction to try to take a bit of my orbital speed off of it, would it truly get to a higher orbit? Why wouldn't it just fall to the ground?

Bonus question: if I threw it anti-nadir, what happens?

Answer 1

Orbits are all ellipses, so when you throw a baseball you change the orbit of the base ball from your circular ellipse to another ellipse.

If you throw it prograde (in the velocity direction), then you baseball will have an elliptical orbit. It will be closest to the Earth at the point at which you threw it, and furthest from the Earth (and higher than the circular orbit) at 180 degrees. So throwing prograde will never make the baseball deorbit. The speed of the baseball will now not be constant. It will be faster than the circular orbit speed at the lowest point in the orbit, but slower than the circular orbit speed at the highest point.

This is your misconception: Adding velocity doesn't make the ball to a lower orbit. Instead, adding velocity makes the ball go to a higher orbit, which in turn reduces the speed of the ball.

Throwing retrograde (wake direction) has the opposite effect. The baseball will enter an elliptical orbit that is close to the Earth at 180 degree from the point at which you threw and is, on average at a higher speed. If you throw retrograde hard enough you can reduce the height at 180 degrees to less than 0, ie the baseball hits the ground. But you have to throw far far harder than is physically possible, because you and the baseball start out at orbital speeds, about 7km/s so throwing at 10m/s won't be enough to deorbit.

Throwing at the nadir would also just change the baseball's orbit into an elliptical orbit. The baseball would initially approach the Earth, but as it did it would gain speed and then move away from the Earth in an ellipse. The closest point would be at about 90 degrees ahead of the throwing point. This is actually not a very effective way of deorbiting. It takes a lot harder throw to reduce the height by the same amount that throwing retrograde would. As with the other throws, the ball will pass through the throwing point after going all around the Earth. But you won't be at the same point again because your orbital period will be different to that of the ball.

Throwing anti-nadir has a similar effect, except now the furthest point is at about 90 degrees, and the ball falls to the closest point at 270 degrees. It is equally ineffective at de-orbiting or gaining height. This is why nearly all spacecraft manoeuvres happen either in the prograde direction (to add height) or retrograde (to reduce height)

"Bouncing off the atmosphere" is a practical problem not directly connected to orbits. If you enter the atmosphere at the wrong angle, you can actually start to fly and so gain altitude. That's not really connected to the orbital manoeuvres here