Barstro wrote:Thanks for pointing out my error in logic before. Can I get another quick lesson?
Why would hitting a single golf ball from a ship in orbit not be enough to get it to the moon (eventually)?
If it's at a perfect orbit and I am able, despite how little the change is, to decrease the mass of the ship by one unit of golf-ball (which I think is irrelevant), and increase the velocity by just a bit, then isn't the ship now going too fast for its orbit and it escapes until it hits the moon?
For circular orbits, the orbital speed decreases as the radius increases, so, yes, if you speed the ship up, it will then be moving too fast for its current orbit and any circular orbit with a greater radius. However, as the ship moves away from Earth, it'll slow down until it's moving too slowly for a circular orbit (and in the wrong direction) and slow still more until it's moving in the right direction for a circular orbit, but too slowly for an orbit at that distance. From there, it'll fall back, speeding up until it's moving too fast for a circular orbit, and, eventually, moving in the right direction but too fast - under Newtonian mechanics and ignoring the existence of everything other than the ship and the Earth, it'll be exactly where it started.
In general, under Newtonian mechanics, as one of only two bodies in the universe, you have three options for a free-fall trajectory - a closed ellipse, an ellipse that intersects the other body, or a hyperbola that escapes (there's a limiting case of a parabola that only just fails to return). Accelerating at periapsis (the lowest point of your orbit) means your orbit becomes more eccentric (less circular) and raises your apoapsis (highest point), and, if you do it enough, eventually you reach escape velocity and your apoapsis reaches infinity. If you don't escape to infinity or collide, then you will always return to the same point.
A standard Hohmann transfer orbit moves you from one circular orbit to another by accelerating in the lower orbit to turn it into an ellipse tangent to both circles, and accelerating again when you reach the higher orbit to turn the ellipse back into a circle.
It may be easier to think of things in terms of orbital energy rather than speeds, directions and distances - an object in low earth orbit has higher kinetic energy but significantly lower gravitational potential energy than the same object in geostationary orbit, which, in turn, is lower than the energy of an orbit at the distance of the Moon. Hitting the golf ball increases the energy of the orbit, but not by very much, so your orbit is still trapped fairly close to Earth...