The gravitational attraction between planetary bodies

The precise value of the gravitational force the Sun exerts on the Moon and the Earth exerts on the Moon can be calculated using Newton's law of universal gravitation :

Where

- F represents the gravitational force between the masses (in this case, the masses are the Sun and the Moon)

- G represents the gravitational constant 6.674*10^-11 N(m/kg)^2

- M1 is the first mass (mass of the sun)

- M2 is the second mass (mass of the moon)

- r is the distance between the points at the centre of the masses in metres

Therefore, using simple math, we can calculate F (force, more specifically attraction, between the Sun and the Moon) :

The value for gravitational force = 6.74 N 

Note that the value for r was the average distance between the two masses, which ranges from 147000000000 m to 152000000000 km.

The value for F turns out to be 4.363 * 10^26 N

The force between the Earth and the Moon can be calculated as well : 

The value of gravitational force = 1.986*10^20 N

Therefore, it is apparent that the gravitational force between the Earth and the Moon is larger by a factor of approximately 2.946*10^19. Due to Newton's law of universal gravitation, the Moon orbits the Earth rather than the sun