Energy required to move an object in orbit?

In summary, the International Space Station, with a mass of 370,000 kg, needs to be boosted from its current orbit of 335 km to a new orbit of 352 km. To calculate the energy needed, the formula Ep = GMm/r was used, taking into account the Earth's mass (M), gravitational constant (G), and initial and final distances from the Earth's center. The total energy required was found by adding the gravitational potential energy (Ep) with the kinetic energy (Ek), which is also dependent on the fixed speed for each orbital height (v = sqrt(MG/r)). The difference in total energy between the two orbits was calculated to be 6.2x10^7 J, which represents the minimum
  • #1
Peto
9
0
The International Space Station, with a mass of 370,000 kg, is orbiting the Earth at a height 335 km and needs to be boosted to an orbit of 352 km. Calculate the energy needed to boost the ISS to its new height.

m = 370,000 kg
M = 5.98 x 10^24 kg
G = 6.67 x 10^-11 Nm^2/kg^2
Initial distance from Earth's center = (6.38 x 10^6m) + 335000m
Final distance form eath's center = (6.38 x 10^6m) + 352000m


Using Ep = GMm/r

I calculated
Epi = (6.67x10^-11)(5.98x10^24)(370000)/((6.38x10^6)+(335000)) = 2.316682247E13

and

Epf = (6.67x10^-11)(5.98x10^24)(370000)/((6.38x10^6)+(352000)) =2.316676064E13

I found the difference of the two, and took it as my answer, 6.2x10^7 J

I feel I'm doing something wrong, Thanks in advance for any help!
 
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  • #2
Have you considered the difference in speed (and so Kinetic energy) for the two orbits?
 
  • #3
mgb_phys said:
Have you considered the difference in speed (and so Kinetic energy) for the two orbits?

Hmmm, so I would have to find the total energy,

Et = Ep + Ek = G Mm/r + .5mv^2

ok I think I got it now.
 
  • #4
Remember that V is also a function of r and M (there is a fixed speed for each orbital height)
 
  • #5
mgb_phys said:
Remember that V is also a function of r and M (there is a fixed speed for each orbital height)

yes, v = sqrt(MG/r)

so figuring out the difference in total energy, would that give me the amount of energy needed to boost the space station to its new height?
what I mean is, does difference in total energy = amount of energy required to boost to new height?
 
  • #6
Yes actualy that's the minimum energy, assuming you want it to orbit in the same direction
 

1. How is the energy required to move an object in orbit determined?

The energy required to move an object in orbit is determined by its mass, the radius of its orbit, and the gravitational force between the object and the body it is orbiting.

2. Does the energy required to move an object in orbit vary depending on the shape of the orbit?

Yes, the energy required to move an object in orbit will vary depending on the shape of the orbit. For example, a circular orbit will require less energy than an elliptical orbit of the same radius.

3. How does the energy required to move an object in orbit change if the mass of the object increases?

If the mass of the object increases, the energy required to move it in orbit will also increase. This is because a larger mass will require a greater gravitational force to maintain its orbit.

4. Can the energy required to move an object in orbit be calculated using only the mass of the object?

No, the energy required to move an object in orbit cannot be calculated using only the mass of the object. The radius of the orbit and the gravitational force between the object and the body it is orbiting are also necessary to determine the energy required.

5. How does the energy required to move an object in orbit change if the radius of the orbit increases?

If the radius of the orbit increases, the energy required to move the object will also increase. This is because a larger orbit means a greater distance to travel, which requires more energy to maintain the object's speed and trajectory.

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