Answer: Half as large
Explanation:
Newton's law of universal gravitation for Moon 1 is:
[tex]F_{1}=G\frac{Mm}{r^{2}}[/tex] (1)
And for Moon 2:
[tex]F_{2}=G\frac{Mm}{(2r)^{2}}[/tex] (2)
Taking into account the mass of Moon 1 is equal to the mass of Moon 2
Where:
[tex]F_{1}[/tex] is the gravitational force exerted by the planet on Moon 1
[tex]F_{2}[/tex] is the gravitational force exerted by the planet on Moon 2
[tex]G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}[/tex] is the Gravitational Constant
[tex]M[/tex] is the mass of the planet
[tex]m[/tex] is the mass of each Moon
[tex]r[/tex] is the distance between the planet and Moon 1
[tex]2r[/tex] is the distance between the planet and Moon 2
Dividing (2) by (1):
[tex]\frac{F_{2}}{F_{1}}=\frac{G\frac{Mm}{(2r)^{2}}}{G\frac{Mm}{(r)^{2}}}[/tex]
[tex]\frac{F_{2}}{F_{1}}=\frac{1}{2}[/tex]
Isolating [tex]F_{2}[/tex]:
[tex]F_{2}=\frac{1}(2) F_{1}[/tex]
