Calculate Newton's Law Force to Keep Moon in Orbit

[etSahcs12]

Homework Statement

The mass of the moon is 7.35 x 10^22 kg and its distance from the Earth is 3.84 x 10^5 km. Taking Earth's mass to be 5.98 x 10^24, calculate what Newton called "the force resquisite to keep the moon in her orb."

mass of moon = 7.35 x 10^22 kg
distance from earth= 3.84 x 10^5 km
Earth's mass = 5.98 x 10^24

The Attempt at a Solution

First of all, i would like to know what Newton called "the force resquisite to keep the moon in her orb." means. Then maybe i will be able to figure out what the question is asking.

 

[Bob Loblaw]

Force=Gravitational constant*mass of the Earth*Mass of the moon/distance between them, squared.

I think this is the force in question.

 

[m2003]

Newton's Law of Universal Gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This force is known as the gravitational force.

In this case, the force required to keep the moon in its orbit around the Earth is the centripetal force, which is the force directed towards the center of the orbit that keeps the moon moving in a circular path. This force is equal to the gravitational force between the Earth and the moon.

Using the given values, we can calculate the gravitational force between the Earth and the moon using the formula F = G(m1m2)/d^2, where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), m1 is the mass of the Earth, m2 is the mass of the moon, and d is the distance between them.

Plugging in the values, we get:

F = (6.67 x 10^-11 Nm^2/kg^2)(5.98 x 10^24 kg)(7.35 x 10^22 kg)/(3.84 x 10^5 km)^2

Converting the distance from kilometers to meters (1 km = 1000 m), we get:

F = (6.67 x 10^-11 Nm^2/kg^2)(5.98 x 10^24 kg)(7.35 x 10^22 kg)/(3.84 x 10^8 m)^2

Solving this equation, we get a force of approximately 2.01 x 10^20 N.

This is the force required to keep the moon in its orbit around the Earth, and it is equivalent to the force that the Earth exerts on the moon. Therefore, this is the force that Newton would have called "the force resquisite to keep the moon in her orb."