Calculating energy of a geosynchronous satellite

In summary, the conversation is about calculating the total energy of a geosynchronous satellite with a mass of 1500kg orbiting Earth at a height of 325km and an orbital speed of 5000 m/s. The student uses the equations for kinetic energy and potential energy and takes into account the change in gravity at this height. However, there is a discrepancy with the question as geosynchronous satellites do not orbit at 325km height.
  • #1
mikee
30
0

Homework Statement



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hey i was just wondering if i was on the right track here, the question is calculate the total energy(E) of a geosynchronous satelite (that orbits around a fixed spot) with a mass of 1500kg orbiting Earth at a height of 325km with an orbital speed of 5000 m/s,

Homework Equations



ok i was taught that Total E = Kinetic E + Potential E, and also that Kinetic E= 1/2mV^2 and Potential E= mgH

The Attempt at a Solution


ok i took into account that gravity would not be 9.8 so
i calculated what it would be Using Fg=Gm1m2/d^2 and i came up with 1.32x10^4,also note that to calculate distace i added 325km to the radius of the earth, then i plugged
in 1/2(1500)(5000)^2 + 1.32x10^4(1500)325000 = Total E, does this seem correct? thanks
 
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  • #2
Remember energy is force * distance and so gravitatonal potential energy = GMm/r
 
  • #3
There is a problem with the question. Geosynchronous satellites do not orbit at 325 Km height. And a satellite at 325km with an orbital speed of 5000m/s will fall back to earth.
 

Related to Calculating energy of a geosynchronous satellite

1. How do you calculate the energy of a geosynchronous satellite?

The energy of a geosynchronous satellite can be calculated using the formula E = mgh, where E is the energy in joules, m is the mass of the satellite in kilograms, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the satellite's orbit in meters.

2. What factors affect the energy of a geosynchronous satellite?

The energy of a geosynchronous satellite is affected by its mass, the height of its orbit, and the acceleration due to gravity at that height. Other factors that may also have an impact include atmospheric drag, solar radiation, and gravitational forces from other celestial bodies.

3. Can you explain the concept of potential energy in relation to a geosynchronous satellite?

Potential energy is the energy that an object possesses due to its position or state. In the case of a geosynchronous satellite, it has potential energy due to its position in a high orbit above the Earth's surface. This potential energy is converted into kinetic energy as the satellite moves in its orbit.

4. How does the energy of a geosynchronous satellite compare to that of a low Earth orbit satellite?

The energy of a geosynchronous satellite is significantly higher than that of a low Earth orbit satellite. This is because the geosynchronous satellite is at a much higher orbit and therefore has a greater potential energy due to its position above the Earth's surface.

5. Is the energy of a geosynchronous satellite constant?

No, the energy of a geosynchronous satellite is not constant. It changes over time due to various factors such as atmospheric drag and gravitational forces from other celestial bodies. However, these changes are relatively small and can be accounted for in calculations.

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