Question

1: The separation between two 1 kg masses is (a) decreased by 2/3, and (b) increased by a factor of 3. How is the mutual gravitational force affected in each case?

2: The Earth, in a slightly elliptical orbit around the Sun, travels at 3.04x104m/s at perihelion (the point of closest approach, Jan.3), at a distance of 147.3 million kilometers. At aphelion (the farthest distance, around July 3), 152.3 million km from the Sun, how fast is the Earth moving?

Answer 1

1)

Let the initial force be F

the problem can be solved based on the fact that the mutual gravitational force between two masses is inversely proportional to square of distance between the objects

a) when the distnace is decreased by a factor of 2/3, the separation becomes 1/3 of the initial separation

therefore, final force = F/(1/3)² = 9F

therefore, the force becomes 9 times the initial force

b) incrased by a factor of 3

new force = F/3²=F/9

Therefore, the force becomes (1/9) the initial force