Thrust needed for Orbit of a satellite

In summary: The energy required to circularize an orbit with a radius of 1.5*r is greater than the energy required to circularize an orbit with a radius of r.
  • #1
Kalus
37
0

Homework Statement



A satellite is fitted with a station keeping rocket capable of producing thrust of 500N. Its speed is 500Km/hr. Mission control wishes to increase the radius of orbit by a factor of 0.5. For how long should the rocket be fired to achieve this? (The weight of the satellite and rocket is 200kg, neglect the weight of fuel used during the burn)


Homework Equations



F= Gm1m2/r^2 (although m2 is not known)

F/m1 = Gm2/r^2

a= Gm2/r^2

a= V^2/r

so,

V^2/r = Gm2/r^2

V= root(Gm2/r)

also

m1v1 + F*t = m1v2


The Attempt at a Solution



My idea was to try and find the velocity of orbit at 1.5r, but I am not sure how i can do that without using the mass of the body that the rocket is orbiting about. After that my idea was to use the above momentum formula and rearrange for t? Its really the calculation of the new velocity that I am stuck on.
 
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  • #2
The question, as written, is a bit ill-posed. Increase the radius of an orbit (implying circular orbits) requires two burns. The first burn places the vehicle in an elliptical orbit that brings the vehicle to the desired altitude. At some later time the vehicle will be at the desired altitude. The second burn takes place then and circularizes the orbit. The most efficient way of transferring from one circular orbit to another is the Hohmann transfer.

You don't need to know the mass of the planet.
 
  • #3
Thanks for your input. We haven't been taught about the Hohmann transfer, so it is unlikely i need theory from it. The question assumes just one burn.

I've realized that from the equations I've listed below i can form:

V1^2 * r = V2^2 * 1.5r = G*m2

However, this suggests that the speed in the second case with a bigger radius will be higher? I thought it was the opposite of this?
 
  • #4
That suggests the speed in the second case is lower. Whenever you have a relationship of the form xa*yb=constant, with a and b > 0, then increasing x means you have to decrease y.

Simply decreasing the vehicle's speed from the initial v1 to v2 will not achieve the desired goal. It will do just the opposite: It will send the vehicle into a lower orbit (more specifically, an elliptical orbit with a lower semi-major axis). A single burn of any sort will not achieve the desired goal.

Could you write the problem as stated in your text?
 
  • #5
The way i have stated the problem is exactally how it is written in the text. The only other information given is 5 possible answers (its from a multiple choice past exam paper). It may assume a simplified situation (e.g. no elliptical orbits and one firing).

If we were to assume it could be done, using the parameters i listed in my first post how could you solve to find a V2 with the new radius 1.5r?

Many thanks, Andy
 
  • #6
What is the difference in mechanical energy (kinetic plus potential) for an object in a circular orbit with radius r versus that for an object in a circular orbit with radius 1.5*r? Whatever that difference is, you will have to supply at least this much energy in terms of delta-V.
 

1. How is thrust needed for orbit of a satellite calculated?

The thrust needed for orbit of a satellite can be calculated using Newton's second law of motion, which states that force (thrust) equals mass times acceleration. In this case, the mass is the satellite's mass and the acceleration is the centripetal acceleration required for orbit. The formula for centripetal acceleration is v^2/r, where v is the satellite's orbital velocity and r is the radius of its orbit.

2. What factors determine the amount of thrust needed for orbit?

The amount of thrust needed for orbit depends on the mass of the satellite, the desired orbital altitude and velocity, and the gravitational pull of the body the satellite is orbiting around. Other factors such as atmospheric drag and solar radiation pressure can also affect the required thrust.

3. Is the amount of thrust needed for orbit constant?

No, the amount of thrust needed for orbit is not constant. As the satellite moves along its orbit, the gravitational pull and other external forces acting on it change, requiring adjustments to the thrust in order to maintain a stable orbit.

4. How is thrust provided for a satellite to achieve orbit?

Thrust for a satellite can be provided by a variety of propulsion systems, such as chemical rockets, ion thrusters, or solar sails. The specific type of propulsion system used depends on the mission requirements and the capabilities of the satellite.

5. Can a satellite achieve orbit without any thrust?

No, a satellite cannot achieve orbit without any thrust. In order to enter and maintain a stable orbit, a satellite must continuously counteract the pull of gravity with a certain amount of thrust. Once in orbit, some satellites may use minimal thrust to make small adjustments to their trajectory, but they still require some amount of thrust to remain in orbit.

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