Why does centripetal force not apply in gravitation problem?

1. Apr 28, 2016

Dennis Heerlein

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
Fc = mv^2/r
Fg = Gm1m2/r^2

3. 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)
[m(v1)^2]/R2(10)
----------------------- = 1/10
[m(v1x10)^2]/R2

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

2. Apr 28, 2016

Ken G

The centripetal force formula you are using only applies to circular motion, not to ellipses. Indeed, you could say that because the gravity at closest approach is less then the centripetal force requirement, this is the reason the orbit is swings out into a wide ellipse instead of staying in a tight circle.

3. Apr 28, 2016

Dennis Heerlein

That makes sense. Thanks a bunch, I appreciate it.