Question

In the apollo missions to the moon, astronauts reached a point where the gravitational pull from the moon became just as strong as the pull from the earth. the distance between the earth and the moon is 3.844×10⁸ m. the mass of the earth is 5.97 × 10²⁴ kg. the mass of the moon is 7.36 × 10²² kg.

(a) find the location of this point from the center of the earth.

Answer 1

To find the location where the gravitational pull from the moon becomes equal to the pull from the earth, we need to calculate the distance from the center of the earth to this point. The location of this point from the center of the earth is approximately 3.62 × 10^8 meters.

Step-by-step explanation:

To find the location where the gravitational pull from the moon becomes equal to the pull from the earth, we need to calculate the distance from the center of the earth to this point.

1. First, we need to express the force of gravity in terms of 'g', which is the acceleration due to gravity on the surface of the earth.
2. Next, we can use the formula for gravitational force to equate the forces from the earth and the moon at the desired location.
3. Finally, we can solve for the distance by rearranging the equation and plugging in the known values of the masses of the earth and the moon, as well as the distance between them.

The location of this point from the center of the earth is approximately 3.62 × 10^8 meters.