Calculating the Energy Required to Launch a Satellite into Orbit

In summary, to find the energy required to launch a satellite from Earth into circular orbit at radius 5Re in units of joules, you can use the conservation of forces to calculate the change in potential and kinetic energy. The potential energy formula for points near the Earth's surface is U=mgh, but for a general formula, you can use U=-GMEms/r2. To find the change in potential energy, you can subtract the potential energy at the orbit's radius from the potential energy at the Earth's surface. Finally, you can calculate the change in kinetic energy by using the equation for centripetal force and rearranging it to solve for velocity.
  • #1
dkgojackets
38
0

Homework Statement



Find the energy required to launch a satellite from Earth into circular orbit at radius 5Re in units of joules.

Msat = 1000 kg
Me = 5.98e24 kg
Re = 6.37e6
G = 6.67259e-11

Homework Equations



F = GMm/(r^2)

The Attempt at a Solution



I'm thinking somehow using conservation of forces, ending up with (mv^2)/r, and that v can be used to find final kinetic energy, which can be added to potential energy found using mgh, where g = GM/(r^2). I don't know how to get there though.
 
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  • #2
The energy required to launch that satellite should be the change in the mechanical energy of the satellite when put in orbit. You will increase potential energy and kinetic energy. The potential energy formula you have, U=mgh, is just right for points near the Earth surface, you need the general formula, which is:

U=-GMEms/r2

I hope I could help you.
 
  • #3
The idea about adding up changes in potential and kinetic energies seems correct to me. Getting the change in potential energy is quite easy (using the equation mentioned by gyroscope) and finding the change in kinetic energy isn't that difficult. Just realize that the centripetal force of the circular motion around the Earth is equal to the gravitational force. Then rearrange this equation to get the velocity.
 
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  • #4
Gyroscope said:
The energy required to launch that satellite should be the change in the mechanical energy of the satellite when put in orbit. You will increase potential energy and kinetic energy. The potential energy formula you have, U=mgh, is just right for points near the Earth surface, you need the general formula, which is:

U=-GMEms/r2

I hope I could help you.

For U as potential energy, wouldn't I multiply it by the 4R above the Earth's surface?
 
  • #5
Assuming the satellite was initially situated on the surface of the Earth, you've got to calculate the difference in potential energy between the surface and its orbit, i.e. the energy needed to move the satellite on its orbit:

change in PE = U(5Re) - U(Re)
 
  • #6
The energy also depends on whether you launch the satellite against or in the direction of the rotation of the Earth. But that's probably beyond the scope of your assignment.
 

What is the energy required to launch a satellite?

The energy required to launch a satellite varies depending on several factors such as the satellite's mass, desired orbit, and type of launch vehicle. On average, it can range from 50,000 to 300,000 kilojoules (kJ) for a small satellite and up to 1.5 million kJ for a larger one.

How is energy converted into thrust to launch a satellite?

Energy is converted into thrust through the use of rocket engines. These engines burn fuel, usually liquid hydrogen or kerosene, and oxidizer, usually liquid oxygen, to produce hot gas that is expelled out of the back of the rocket, propelling it forward.

What is the role of potential energy in launching a satellite?

Potential energy is the stored energy of an object due to its position or configuration. In the context of launching a satellite, potential energy is used to overcome the Earth's gravitational pull and propel the satellite into orbit. This is achieved by gradually increasing the potential energy of the rocket as it ascends through the atmosphere.

What are the different types of energy used in launching a satellite?

The main types of energy used in launching a satellite are chemical energy, thermal energy, and kinetic energy. Chemical energy is used to power the rocket engines, thermal energy is produced from the burning of fuel, and kinetic energy is used to propel the rocket forward.

How does the location of the launch site affect the energy required to launch a satellite?

The location of the launch site can significantly impact the energy required to launch a satellite. Launching closer to the equator requires less energy due to the Earth's rotation. Launching from higher altitudes also reduces the energy needed due to the thinner atmosphere. Launching from a site with a strong magnetic field can also help protect the satellite from harmful radiation, reducing the energy required for shielding.

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