A 7300-kg satellite has an elliptical orbit, as in the figure. The point on the orbit that is farthest from the earth is called the apogee and is at the far right side of the drawing. The point on the orbit that is closest to the earth is called the perigee and is at the far left side of the drawing. Suppose that the speed of the satellite is 2730 m/s at the apogee and 8450 m/s at the perigee.

(a) Find the work done by the gravitational force when the satellite moves from the apogee to the perigee.

(b) Find the work done by the gravitational force when the satellite moves from the perigee to the apogee

Work done? lets do it with potential theory.

PE=force*r=ms*g*re^2/r

where r is the distances from center of Earth, me is mass satellite.

Now enegy change from one point to the other:

from apogee to perigee
Work=ms*g*re^2 (1/2730-1/8450)

check my thinking and math.

To find the work done by the gravitational force when the satellite moves from the apogee to the perigee, we can use the formula for work done:

Work = Force * Distance * cos(theta)

In this case, the force is the gravitational force, which is given by the equation:

F = (G * m1 * m2) / r^2

where G is the gravitational constant, m1 and m2 are the masses of the objects (in this case, the satellite and the Earth), and r is the distance between the objects.

To find the distance traveled by the satellite from apogee to perigee, we can use the fact that the orbit is elliptical. In an elliptical orbit, the semi-major axis (a) is the average distance from the satellite to the Earth, and the eccentricity (e) determines how elongated the ellipse is. The distance traveled from apogee to perigee is given by:

Distance = 2 * a

To find the angle between the displacement of the satellite and the force of gravity (theta), we can use the fact that the force of gravity is always directed towards the center of the Earth. In this case, the angle between the displacement and the force of gravity is 180 degrees.

Therefore, the work done by the gravitational force when the satellite moves from the apogee to the perigee is:

Work = F * Distance * cos(180)

Now, let's calculate the values step by step.

(a) Work done by the gravitational force when the satellite moves from the apogee to the perigee:

1. Calculate the distance traveled:
Distance = 2 * a

2. Calculate the gravitational force:
F = (G * m1 * m2) / r^2

3. Calculate the work done:
Work = F * Distance * cos(180)

To find the work done by the gravitational force when the satellite moves from the perigee to the apogee, we can follow the same steps as in part (a), but with a few changes.

(b) Work done by the gravitational force when the satellite moves from the perigee to the apogee:

1. Calculate the distance traveled:
Distance = 2 * a

2. Calculate the gravitational force:
F = (G * m1 * m2) / r^2

3. Calculate the work done:
Work = F * Distance * cos(0)

Note that in step 3, the angle between displacement and the force of gravity is now 0 degrees because the satellite is moving in the same direction as the force of gravity.

By following these steps, you can find the work done by the gravitational force when the satellite moves from the apogee to the perigee, and vice versa.