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

Answer:

a) 1/4 what it is now

Explanation:

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

$F_g = \frac{Gm_1m_2}{r^2}$

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

So the force of gravity will be given as

$\frac{F_g'}{F_g} = \frac{r_1^2}{r_2^2}$

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

$F_g' = \frac{r_1^2}{(2r_1)^2}F_g$

$F_g' = \frac{1}{4}F_g$