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Thu 1 Dec, 2005 12:11 pm
If the distance between an artificial satellite and a planet's center increases by a factor of 4, then the attraction between the satellite and planet changes to a factor of
a) 1/2
b) 1/4
c) 1/8
d) 1/16
Do I use the formula (mv^2)/r and put 4 in place of r? Then the answer would be 1/4?
You are looking for the formula for the attraction due to gravity since that is what the "attraction between a satellite and a planet" is. Find that and you will have the answer.
I think I figured it out. The acceleration due to gravity is proportional to 1/r^2. Therefore, if it is 4 times greater a distance 4^2 is 16. This would make the answer 1/16. I hope I'm right. Thanks for the hint!
The concept of "acceleration" is secondary to the concept of "force".
Gravitational Force is directly proportional to the product of the masses and inversely proportional to the square of the distance.
Since the masses remain constant. F alters by 1/4sqd.
Acceleration comes in as a secondary concept from Newtons laws.
Force =Rate of Change of Momentum
= (mv-mu)/t
= m(v-u)/t
= ma
Yep, I believe you are correct.
Using Newtons universal law of gravitation we say F = G.m.m/r^2
The new Force is simply F = 1/r^2
r is now = 4 therfore F = 1/16
Of cource the Gravitational force, and both the masses cancel out because they are contant and do not change.
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