Gravitational potential energy, orbital speed, binding energy.

In summary, we discussed the gravitational potential energy, orbital speed, and binding energy of a satellite orbiting the Earth at a distance of 6.3 x 10^5 m above the surface. By using the equivalence of gravitational force and centripetal force, we calculated the gravitational potential energy to be -1.03 x 10^11 J and the orbital speed to be 7548.57 m/s. We also considered the binding energy, which is the energy required for the satellite to escape its orbit, and found it to be 1/2 GMm/Ro, or 5.128277145 x 10^10 J.
  • #1
Lolagoeslala
217
0

Homework Statement


a satellite having a mass of 1800 kg orbits the Earth at a distance of 6.3 x 10^5 m above the surface find the gravitational potential energy of the satellite while in orbit, the orbital speed and the binding satellite.

The Attempt at a Solution



gravitational potential energy
Eg = -GMm/Ro
Eg = -(6.67x10^-11 Nm^2/kg^2)(5.98x10^24kg)(1800kg)/(6.37x10^6m)+(6.3x10^5m)
Eg = -1.03 x 10^11 J

the orbital speed

Ek = 1/2(GMm/Ro)
Ek = 0.5 x -1.03 x 10^11 J
Ek = 5.128277145 x 10^10 J

Ek = 1/2mv^2
V = 7548.57 m/s

binding satellite
Eb = 1/2(GMm/Ro)
Eb = 0.5 x -1.03 x 10^11 J
Eb = 5.128277145 x 10^10 J
 
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  • #2
Lolagoeslala said:
the orbital speed
Ek = 1/2(GMm/Ro)
Whilst that is true, I would prefer to use the equivalence of the gravitational force and the centripetal force required to maintain the orbit. That seems to me to be a more fundamental principle.
binding satellite
Eb = 1/2(GMm/Ro)
I'm not sure about that. Does binding energy take into account the KE? Maybe it does.
 
  • #3
haruspex said:
Whilst that is true, I would prefer to use the equivalence of the gravitational force and the centripetal force required to maintain the orbit. That seems to me to be a more fundamental principle.

I'm not sure about that. Does binding energy take into account the KE? Maybe it does.
You mean like this

m(v^2/Ro) = GMm/Ro^2 ?

Well binding energy is the energy required for the orbiting satellite to escape. So the total energy should be zero...

Well yes Ek is included...

Eg + Ek = Et1
- GMm/Ro + 1/2GMm/Ro = - 1/2 GMm/Ro

Et1 + Eb = Et2
- 1/2 GMm/Ro + Eb = 0 J
Eb = 1/2 GMm/Ro
 
  • #4
Lolagoeslala said:
You mean like this

m(v^2/Ro) = GMm/Ro^2 ?
Yes.
Well binding energy is the energy required for the orbiting satellite to escape. So the total energy should be zero...

Well yes Ek is included...
OK.
 
  • #5


The binding energy of the satellite is the same as its kinetic energy, as they both represent the amount of energy needed to keep the satellite in orbit. This means that the satellite's binding energy is 5.128277145 x 10^10 J. This also tells us that the satellite's orbital speed is 7548.57 m/s, which is the speed at which it orbits the Earth. Finally, the gravitational potential energy of the satellite while in orbit is -1.03 x 10^11 J, which represents the potential energy stored in the satellite due to its position in Earth's gravitational field.
 

1. What is gravitational potential energy?

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It is equal to the product of the object's mass, the acceleration due to gravity, and its height above a reference point.

2. How is orbital speed related to gravitational potential energy?

Orbital speed is directly related to gravitational potential energy. As an object's orbital speed increases, its gravitational potential energy also increases. This is because the object has to overcome a larger gravitational force to maintain its speed.

3. What factors affect an object's binding energy?

An object's binding energy is affected by its mass, the distance between the object and the center of the gravitational field, and the strength of the gravitational force. Additionally, the object's shape and composition can also play a role in its binding energy.

4. How is gravitational potential energy calculated?

The formula for calculating gravitational potential energy is PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height above the reference point. This formula assumes a constant gravitational field and neglects any other potential energy sources.

5. Can gravitational potential energy be converted into other forms of energy?

Yes, gravitational potential energy can be converted into other forms of energy, such as kinetic energy, as an object falls towards a gravitational source. This conversion is described by the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted.

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