Starting from newton’s law of universal gravitation, show how to find the speed of the moon in its orbit from the earth-moon distance of 3.9 × 108 m and the earth’s mass. assume the orbit is a circle.

1010.92 m/s

Explanation:

According to Newton's law of universal gravitation:

(1)

Where:

is the gravitational force between Earth and Moon

is the Gravitational Constant  

is the mass of the Earth

is the mass of the Moon

is the distance between the Earth and Moon

Asuming the orbit of the Moon around the Earth is a circular orbit, the Earth exerts a centripetal force on the moon, which is equal to :

(2)

Where is the centripetal acceleration given by:

(3)  

Being the orbital velocity of the moon

Making (1)=(2):

(4)

Simplifying:

(5)

Making (5)=(3):

(6)  

Finding :

(7)

(8)

Finally:

the independent variable, or the one that is intentionally manipulated is the speed.