Question

which of newton's laws (1, 2, or 3)are used in the following:
1) spaceship reaches the speed for orbit around the earth,
2) pushing the shuttle forward in space
3) the force needed to escape earth's atmosphere

Answer 1

1) F = m a #2

G m Me/r^2 = m v^2/r specifically

2) conservation of momentum #1
specifically:
mass remaining on craft * speed of craft + mass of exhaust * speed of exhaust (which is negative) = original mass of craft* original speed of craft
BUT
You can also say action = reaction
force of exhaust on rocket = force of rocket on exhaust - #3

3) well the important thing is law of gravity, but at every altitude F = m a