Question

A spacecraft is on a journey to the moon. At what point, as measured from the center of the earth, does the gravitational force exerted on the spacecraft by the earth balance that exerted by the moon? This point lies on a line between the centers of the earth and the moon. The distance between the earth and the moon is 3.85 108 m, and the mass of the earth is 81.4 times as great as that of the moon.

Answer 1

If the forces balance, they must be equal so

Canceling common terms G and MShip

Now we must solve for r

Take square root of both sides

Now solve for r

Use the mass of Earth is 84.1 times mass of Moon.

If the forces balance, they must be equal so

Canceling common terms G and MShip

Now we must solve for r

Take square root of both sides

Now solve for r

Use the mass of Earth is 84.1 times mass of Moon.

If the forces balance, they must be equal so

Canceling common terms G and MShip

Now we must solve for r

Take square root of both sides

Now solve for r

Use the mass of Earth is 84.1 times mass of Moon.

If the forces balance, they must be equal so

Canceling common terms G and MShip

Now we must solve for r

Take square root of both sides

Now solve for r

Use the mass of Earth is 84.1 times mass of Moon.