Question

If the earth were twice the distance from the sun that it is now, the gravitational force exerted on it by the sun would be: a) 1/4 what it is now

b) /2 what it is now
c) twice what it is now
d) 4 times what it is now

Answer 1

a) 1/4 what it is now

Step-by-step explanation:

As we know that force of gravitation between two planets at some distance "r" from each other is given as

`F_g = (Gm_1m_2)/(r^2)`

now since we know that if the distance between Earth and Sun is changed

So the force of gravity will be given as

`(F_g')/(F_g) = (r_1^2)/(r_2^2)`

now we know that the distance between sun and earth is changed to twice the initial distance between them

so we have

`r_2 = 2r_1`

so new gravitational force between sun and earth is given as

`F_g' = (r_1^2)/((2r_1)^2)F_g`

`F_g' = (1)/(4)F_g`