A satellite has a mass of 100 kg and is in an orbit at 2.00*10^6 m above the surface of the Earth (a) what is the potential enegry of the satellite at this location?(b) what is the magnitude of the gavitational forece on the satellite?

a) Since the weight drops somewhat as a result of the inverse square law, you have to use the relation
PE = -GM/r
where G is the universal gravitational constant and M is the mass of the Earth. PE can also be written
PE = -gR^2/r where g is the acceleration of gravity at the earth's surface.
Therefore PE at altitude h, relative to the value at the earth's surface, is
- g R^2 [1/(R+h) - 1/R]

(b) Use the inverse square law and the ratio of the earth's radius to the height of the satellite above the center of the earth.

(a) To calculate the potential energy of the satellite at this location, we can use the formula:

PE = -GM/r

where PE is the potential energy, G is the universal gravitational constant, M is the mass of the Earth, and r is the distance between the center of the Earth and the satellite.

Since we are given the altitude above the surface of the Earth, we need to calculate the total distance by adding the radius of the Earth to the altitude:

Total distance = Radius of the Earth + Altitude = R + h

Now we can substitute this value into the formula:

PE = -GM/(R + h)

(b) To calculate the magnitude of the gravitational force on the satellite, we can use the inverse square law which states that the force between two objects is inversely proportional to the square of the distance between them.

Using this law, we can find the relationship between the gravitational force at the altitude and the force at the Earth's surface. Let's call the force at the Earth's surface F_s and the force at the altitude F_h.

F_s / F_h = (R/(R + h))^2

Since the force at the Earth's surface is equal to the weight of the satellite, we can write:

F_s = mg

where m is the mass of the satellite and g is the acceleration due to gravity at the Earth's surface.

Now we can substitute these values into the equation and solve for F_h:

F_h = F_s * (R/(R + h))^2

F_h = mg * (R/(R + h))^2

Therefore, the magnitude of the gravitational force on the satellite is given by the formula above.