phillip1882

i also wanted to add, if you spin  the ship fast enough, you stick to the walls

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Do astronauts in the ISS feel themselves thrown to the side of the station?

no, but that's because gravity counter  acts the effect.

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You are still confusing force with expenditure of energy. A rock on the ground exerts a force on it but no energy is expended. Think about that.

yeah i understand, i was wrong, force doesn't necessarily require energy, but we should clearly indicate when force is being applied

no its velocity, you can experience this with your car, when you turn your thrown to the side some. clearly force is being applied.

so, i used to have a beef with newton. i thought that an orbiting body should require the expenditure of anergy.

with the strong nonclear force i can understand not requiring energy,

there's no motion and therefore no change in velocity and therefore no acceleration and therefore no force.

but with an orbiting body there's change in velocity, a change in direction,

therefore force, and force should require the expenditure of energy.

but then i envisioned a pole with one end of rope tied to a pole and the other end tied to a rock,

if you put the rock "into orbit" around the pole, yes the rope is applying force, but i see no reason discounting friction it can't obit indefinitely.

clearly not all force requires energy expenditure.

hmmm. lets say n is 7, 

 72 × 1 + 36, = 108

72 × 2 + 36 = 180

72 × 3 +36 =252

72 x 4 +36 = 324

72 x 5 +36 = 396

72 x 6 +36 =468

72 x 7 +36 =540

adding all of them together,  i get 2268. I'm not sure where the +35 is coming from, but lets add that as well, 2303

from here, how would you determine p and q?