Can someone Check this (Energy Question)

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In summary, the total energy of a geosynchronous satellite with a mass of 1500 kg, orbiting Earth at a height of 325 km and an orbital speed of 5000 m/s, is approximately 2.353x10^10 J or 2.353x10^7 kJ. The calculation involves adding the potential energy due to the satellite's height and the kinetic energy due to its orbital velocity. However, using the equation for gravitational potential energy, Ep = -Gm1m2/r, is more accurate for objects at these heights rather than using mgh.
  • #1
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Q: Calculate the total engery of a geosynchonous satellite (one that orbits over a fixed spot) with amass of 1500 kg, orbiting Earth at height 325 km (325 000m) with an orbital speed of 5000 m/s or 5.0x10^3

My Solution: Et = Ep + Ek
Ep = Mg delta H
Ek = 1/2 (m) V^2
thus Et = Mg(H) + 1/2 (m) v^2
(1500)(9.8)(325000) + 1/2(1500) (5000)^2
= 4.78x10^9 + 1.875x10^10
=2.353x10^10 j or 2.353x10^7 Kj

Is there a mistake in my calculations or has this question been done correctly?
 
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  • #2
quickslant said:
Q: Calculate the total engery of a geosynchonous satellite (one that orbits over a fixed spot) with amass of 1500 kg, orbiting Earth at height 325 km (325 000m) with an orbital speed of 5000 m/s or 5.0x10^3

My Solution: Et = Ep + Ek
Ep = Mg delta H
Ek = 1/2 (m) V^2
thus Et = Mg(H) + 1/2 (m) v^2
(1500)(9.8)(325000) + 1/2(1500) (5000)^2
= 4.78x10^9 + 1.875x10^10
=2.353x10^10 j or 2.353x10^7 Kj

Is there a mistake in my calculations or has this question been done correctly?
using g = 9.8m/s/s is valid only near earth. What can you say about GPE at those heights?
 
  • #3
i have no idea? is it 0? or is it very small? i have no idea
 
  • #4
Look up the general expression for the gravitational PE between two masses (such as the Earth and a satellite).

As PhanthomJay pointed out, mgh is only useful for finding changes in PE for objects close to the surface of the earth.
 
  • #5
ok.. Ep = Gm1m2/r
 
  • #6
quickslant said:
ok.. Ep = Gm1m2/r
Don't forget the minus sign: Ep = -Gm1m2/r
 
  • #7
ok thank you
 

What is energy?

Energy is the ability to do work. It is the force that makes things happen and allows objects to move or change.

Why is energy important?

Energy is important because it is essential for all living organisms to survive. It is also necessary for technology and machines to function, and it is a crucial part of the global economy.

What are the different forms of energy?

There are several forms of energy, including kinetic energy (energy of motion), potential energy (stored energy), thermal energy (heat), chemical energy (stored in bonds between atoms), and electromagnetic energy (energy from light).

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Energy is typically measured in joules (J) or calories (cal). Other units of measurement include kilowatt-hours (kWh) and British thermal units (BTU).

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