Question

The sun’s mass is about 2.7 x 107 times greater than the moon’s mass. The sun is about 400 times farther from Earth than the moon. How does the gravitational force exerted on Earth by the sun compare with the gravitational force exerted on Earth by the moon?

Answer 1

start with Newton's Law of gravitation:
\[F = \frac{G \ M \ m }{r^2}\]
and compare ratios:
\[\frac{F_{es}}{F_{em}} = \frac{\frac{G \ M_e \ m_s }{r_{es}^2}}{\frac{G \ M_e \ m_m }{r_{em}^2}}\]
simplify eg G, Me cancel out