The force of gravity from the sun will be weaker

[ritwik06]

Nature decides that instead of inverse square law for gravitational forces the law will be inverse cube law. In that case what among the following will be true?
a) The force of gravity from the sun will be weaker
b) The period of the planet will be proportional to the square of the distance
c)the length of the year will decrase.
d) The rotaion speed of Earth will decrease?

 

[ranger]

What do you think?

 

[rbj]

(d) depends on what the speed of rotation is to begin with.

(a) and (c) end up depending on what the new value of G is (given a fixed set of units, before and after Nature changes her mind) since it would have to be a different value with different dimensional. if the new G was just right, and the Earth was in a circular orbit, it's possible that the graviational force from the sun and the length of year could remain unchanged.

but i am not sure that the orbit (or any orbit) would be stable. particularly an elliptal orbit.

 

[Ja4Coltrane]

This question is annoying because it's so made up, but I don't really think that the new dimensions of G would pose a problem. I also think that orbits would be stable (including eliptical orbits). It would just be easier to escape (and therefore the orbits could not be as eliptical). Now part B is easy to solve--just figure it out by assuming a circular orbit, and set gravitational force equal to centripetal force.