Calculating Work with Kinetic Energy in Orbit

In summary, to calculate the work of the external force on a 62kg satellite orbiting the Earth from a radius of 3.3*10^7 m to 7.7*10^6 m, you must integrate the force (GMm/r^2) and add the kinetic energy (1/2mv^2) for both the initial and final states. This will give you the work done by the external force, which should be a positive value.
  • #1
The_Journey
19
0

Homework Statement


A 62kg satellite orbits the Earth with a radius of 3.3*10^7 m. A net external force acts on the satellite to an orbit of 7.7*10^6 m, what work must the external force do?


Homework Equations


W = integral of F with respect to d


The Attempt at a Solution



Integrate F which in this case is GMm/r^2 which becomes -GMm/r, then plug in the radii. However, the answer that I got was -2.46*10^9, which is incorrect.
 
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  • #2
You need to include the kinetic energy as well, because the velocity of the satellite
in a lower orbit will be bigger
 
  • #3
willem2 said:
You need to include the kinetic energy as well, because the velocity of the satellite
in a lower orbit will be bigger

How would I include the kinetic energy?

Would I approach it as this?

GPE = gravitational potential energy
KE = kinetic energy


GPEfinal + KEfinal = GPEinitial + KEinitial + Workof external force ?
 

What is Energy in Orbit?

Energy in Orbit is the total amount of energy required for an object to maintain a circular orbit around another object, such as a planet or a star. This energy includes both the kinetic energy of the object as well as its gravitational potential energy.

How is Energy in Orbit calculated?

The formula for calculating Energy in Orbit is E = -GmM/2r, where G is the gravitational constant, m is the mass of the orbiting object, M is the mass of the central object, and r is the distance between the two objects.

Why is Energy in Orbit important?

Energy in Orbit is important because it determines the stability and trajectory of an orbiting object. If an object has insufficient energy, it will not be able to maintain its orbit and will eventually crash into the central object. On the other hand, if an object has too much energy, it will escape the orbit and fly off into space.

How does Energy in Orbit affect satellites?

Satellites in orbit around the Earth require a specific amount of energy to maintain their orbit. If they have too much energy, they will drift away from their intended orbit. If they have too little energy, they will fall back towards Earth. Calculating and monitoring the Energy in Orbit of satellites is crucial for their proper functioning.

Can Energy in Orbit be changed?

Yes, Energy in Orbit can be changed by altering the velocity or distance of the orbiting object. This can be done through rocket propulsion or by using the gravitational pull of other objects in the vicinity. However, any changes to the Energy in Orbit will also affect the object's orbit and trajectory.

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