Calculating Work to Place Satellite in Synchronous Orbit

• six789
In summary, the calculation for the amount of work needed to raise a 650kg satellite into synchronous orbit around Earth is 3.75x10^10 J. The mistake in the initial calculation was due to the confusion between potential and kinetic energy.
six789
here is another problem...
a 650kg satellite is to be placed into synchronus orbit around Earth.
What amount of work must be done onthe satellite to raise it into synchronous orbit?

i did..
W=GMm(1/r of Earth - 1/r of synchronous satellite)
= 6.673x10^-11N m^2/kg^2 (5.98x10^6kg)(650kg)(1/6.38x10^6m - 1/4.22x10^7m)
W = 3.442998737X10^10 J

the right answer is 3.7x10^10 J... is ther something wrong with the significant digits?? can anyone tell me the mistake that i did?

six789,

What kind of energy did you calculate for the satellite? Does it have any other kind when it's in orbit?

a) the gravitational potential energy is -4.1x10^10 J
b) the total enrgy is -3.1x10^9 J

d) the kinetic enrgy is 3.1x10^9 J

The kinetic energy in this case is not the same as the potential energy. The only time kinetic energy = Potential energy is when the change in kinetic energy is caused by a change in potential energy. In this case, the potential energy is always cosntant as in a circular orbit, the satelite is always the same distance from the earth.

i get the right answer from doc al... he said that...
change of energy = Work-Energ(total)

change=work
therefore.. Work = Work-E
=3.442998737X10^10 J - (-3.1x10^9 J)
=3.75x10^10J..

thanks again for the help...

1. How do you calculate the work required to place a satellite in synchronous orbit?

The work required to place a satellite in synchronous orbit can be calculated using the formula W = Fd, where W is the work, F is the force applied, and d is the distance traveled. In this case, the force would be the gravitational force between the satellite and the Earth, and the distance traveled would be the distance from the satellite's initial position to its final position in synchronous orbit.

2. What is synchronous orbit and why is it important?

Synchronous orbit is an orbit where the satellite's orbital period is equal to the rotational period of the planet it is orbiting. In the case of Earth, this means that the satellite will complete one orbit in the same amount of time that it takes for Earth to rotate once on its axis. This is important because it allows the satellite to remain in a fixed position above a specific location on Earth, making it ideal for communication and observation purposes.

3. What factors affect the work required to place a satellite in synchronous orbit?

The work required to place a satellite in synchronous orbit is affected by several factors, including the mass of the satellite, the distance from the planet, and the strength of the gravitational force between the satellite and the planet. Other factors, such as atmospheric drag and the rotation of the planet, may also have an impact on the work required.

4. Can the work required to place a satellite in synchronous orbit be reduced?

Yes, the work required to place a satellite in synchronous orbit can be reduced by utilizing the planet's rotation to assist in the satellite's orbit. This is known as a geostationary transfer orbit, where the satellite is initially placed in an elliptical orbit and then raised to synchronous orbit using the planet's rotation. This method reduces the amount of work required from the satellite's propulsion system.

5. How is the work calculated for placing multiple satellites in synchronous orbit?

The work required to place multiple satellites in synchronous orbit can be calculated by adding together the individual work calculations for each satellite. This would involve considering the mass and distance of each satellite from the planet, as well as any additional factors that may affect the work required. Additionally, the work required to place the first satellite in synchronous orbit can be used as a reference for calculating the work required for subsequent satellites, as the initial orbit will have been affected by the presence of the first satellite.

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