The elliptical orbit of a comet is shown above (hidden document I apologize but easy to picture). Positions 1 and 2 are, respectively, the farthest and nearest positions to the Sun, and at position 1 the distance from the comet to the Sun is 10 times that at position 2.
What is the ratio v1/v2 of the speed of the comet at position 1 to the speed at position 2? What is the ratio F1/F2 of the force on the comet at position 1 to the force on the comet at position 2?
Fc = mv^2/r
Fg = Gm1m2/r^2
The Attempt at a Solution
I used IW = IW to solve that the ratio v1/v2 is 1/10. Then, for the force equations, I divided centripetal force of v1 by centripetal force of v2, making substitutions, like this (the line of dashes representing division)
----------------------- = 1/10
The answer is 1/100, which is found if Fg is used, as the only difference in Fg is the radius substitution of (10xR2)^2