Question

If Earth had twice the mass it has now, how would the gravitational force between it and the Sun change?

Answer 1

Answer:

a)The gravitational force would be twice as much as it is now

Explanation:

If the earth had twice its mass as it is now, the gravitational force between the sun and the earth would be twice as much as it is now.

According to Newton's law of universal gravitation "the gravitational force of attraction between bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them".

       F$_{g}$   = $\frac{G m _{e} m _{s} }{r^{2} }$

G is the universal gravitation constant

m is the mass

r is the distance

let mass of sun  = s

     mass of earth  = e

 new mass of sun  = s

 new mass of sun  = 2e

input variables;

    F  = $\frac{Gx e x s}{r^{2} }$    ------ i

   F = $\frac{G x s x 2e}{r^{2} }$    ------- ii

From the second equation;

      2F  = $\frac{Gx e x s}{r^{2} }$

      2F  = F

Therefore, the force will double.