Find the energy necessary to put 5kg , initially at rest on Earth's surface, into geosynchronous orbit.

do i use the formula U=-GMm/r

I get 290 MJ?

You also need to consider the kinetic energy, unless you are thinking of using a giant space elevator (in that case you get the kinetic energy free of charge from the Earth's rotational energy).

What do you mean by the kinetic energy it hasn't given me anything

First you need to look up or compute the radial distance of the satellite from the center of the earth. It is about 41,000 km.

Then you need to provide not only the larger potential energy to get the satellite that high up, but also provide enough kinetic energy in the circular orbit to let the satellite maintain that orbital altitude.

To find the energy necessary to put an object into geosynchronous orbit, you can indeed use the formula for gravitational potential energy:

U = -GMm/r

Where:
U is the gravitational potential energy
G is the gravitational constant (approximately 6.674 × 10^-11 m^3 kg^-1 s^-2)
M is the mass of the Earth (approximately 5.972 × 10^24 kg)
m is the mass of the object (5 kg in this case)
r is the distance between the center of the Earth and the object (radius of Earth plus the orbit altitude in meters)

However, to calculate the energy required to put 5 kg into geosynchronous orbit, we need to consider a few additional factors:

1. Geosynchronous Orbit: A geosynchronous orbit is an orbit around Earth where the satellite completes one orbit in exactly 24 hours, matching the rotation period of the Earth. The altitude at which this orbit is achieved is approximately 35,786 kilometers (22,236 miles) above the Earth's surface.

2. Initial Rest: The energy required to put an object into orbit from Earth's surface depends on both the change in potential energy and the change in kinetic energy. Since the object is initially at rest, the initial kinetic energy is zero.

To calculate the gravitational potential energy, we first need to calculate the altitude. The distance from the Earth's center to the geosynchronous orbit altitude is the sum of the Earth's radius (approximately 6,371 kilometers) and the altitude (35,786 kilometers).

r = 6,371,000 meters + 35,786,000 meters

Now, substitute the values into the formula for gravitational potential energy:

U = -GMm/r

U = -((6.674 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) * (5 kg)) / (6,371,000 meters + 35,786,000 meters)

Calculating this equation will give you the gravitational potential energy required to put the object of 5 kg into geosynchronous orbit from rest on Earth's surface.