A satellite moves in a circular orbit of radius 35.793 km. The Earth's radius and mass are Re = 6.37e6 m, and Me = 5.97e24 kg.

For the satellite, calculate the work done to put the satellite in orbit (mass of satellite is 1000 kg).

use the gravitation formula to find the attractive force

... this is also the centripetal force ... m v^2 / r

the work done on the satellite is its kinetic energy ... 1/2 m v^2

Work done= change in PE + change in KE.

change in PE= GMm (1/re^2 -1/(re+1000)^2)

To calculate the work done to put a satellite in orbit, we can use the equation for gravitational potential energy. The work done is equal to the change in potential energy, which in this case is the difference between the potential energy of the satellite on the Earth's surface and the potential energy of the satellite in orbit.

First, let's calculate the potential energy of the satellite on the Earth's surface. The potential energy of an object near the surface of the Earth is given by the equation:

PE = m * g * h

where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the reference level. In this case, the reference level is the Earth's surface, so h is equal to the sum of the radius of the Earth and the altitude of the satellite.

Given:
Mass of satellite, m = 1000 kg
Radius of the Earth, Re = 6.37e6 m
Altitude of the satellite, h = 35.793 km = 35,793 m

Acceleration due to gravity, g, can be calculated using the equation:

g = G * Me / Re^2

where G is the gravitational constant, Me is the mass of the Earth, and Re is the radius of the Earth. Given:
Gravitational constant, G = 6.67e-11 N m^2 / kg^2
Mass of the Earth, Me = 5.97e24 kg

Now, let's calculate the potential energy on the Earth's surface:

PE_surface = m * g * (Re + h)

PE_surface = 1000 kg * (6.67e-11 N m^2 / kg^2 * 5.97e24 kg / (6.37e6 m)^2) * (6.37e6 m + 35,793 m)

Next, let's calculate the potential energy of the satellite in orbit. The potential energy is given by the equation:

PE_orbit = - G * Me * m / Ro

where Ro is the radius of the orbit. In this case, the radius of the orbit is already given:

Ro = 35.793 km = 35,793 m

Now, let's calculate the potential energy in orbit:

PE_orbit = - (6.67e-11 N m^2 / kg^2 * 5.97e24 kg) * 1000 kg / (35,793 m)

Finally, the work done to put the satellite in orbit is the difference between the potential energy in orbit and the potential energy on the Earth's surface:

Work_done = PE_orbit - PE_surface

Substituting the values calculated above and calculating the difference will give you the work done to put the satellite in orbit.