Energy transfer from x altitude to geosynchrous altitlude

In summary, to make a Hohmann transfer from a circular to elliptical orbit, the satellite needs to have initial potential and kinetic energy in the lower orbit, and add energy to reach the higher orbit.
  • #1
tnutty
326
1

Homework Statement



INTRO TO THE PROBLEM :For a circular orbit around a massive gravitating body, the speed depends on the radius according to the equation V = sqrt (GM/r) ; for elliptical orbits, the speed varies according to the equation v^2 = 2GM([ 1/r - 1/(2a), where r is the distance from the massive body and a is the semimajor axis of the ellipse (i.e., half the sum of the closest and farthest distances). A satellite can be transferred from one circular orbit (at radius r1) to a higher orbit (at radius r1) by boosting the circular speed v1 at v2 to the appropriate speed for an elliptical orbit whose distance varies between r1 and r2 , and then boosting the speed in the elliptical orbit at r2 to the circular speed v2. This is called a Hohmann transfer.

THE PROBLEM STATEMENT :
How much energy is required for the first boost in such a transfer to take a 280kg satellite from a circular orbit at a 400 km altitude to the altitude of a geosynchronous orbit?

change in K_1 = _________J

Homework Equations




stated above in the intro

The Attempt at a Solution



clueless?
 
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  • #2
The conservation of energy still works doesn't it?

(Potential + Kinetic) before + Energy = (Potential + Kinetic) after?
 
  • #3
so,

1/2mv^2 - GMm/r = 1/2mv^2 - GMm/r

?
 
  • #4
tnutty said:
so,

1/2mv^2 - GMm/r = 1/2mv^2 - GMm/r

?

The Δ anyway. Mustn't that be the additional energy?
 
  • #5
I'm sorry i am confused
 
  • #6
tnutty said:
I'm sorry i am confused

You have initial potential energy and kinetic energy in lower orbit.

You add energy.

You get a higher orbit with kinetic energy and potential energy.
 
  • #7
how about saying it mathematically. can you start me off?
 
  • #8
tnutty said:
how about saying it mathematically. can you start me off?

You have the equation below. I'm sure you can do it.

Besides if it comes up on a quiz, I won't be there to start you off. It's good practice.
 
  • #9
So what's the formula to delta k ?
 
  • #10
tnutty said:
So what's the formula to delta k ?

Don't they give you the formulas for how to calculate the v2's
 
  • #11
ok. r is the radius of the Earth + 400km and a is ? And that formula above v^2 =...
is delta K ?
 
  • #12
tnutty said:
ok. r is the radius of the Earth + 400km and a is ? And that formula above v^2 =...
is delta K ?

Well that's a good part of it, but strictly speaking you want to be working with ½mv² for KE. so use the v² 's that you find to determine your ½mv² 's.
 
  • #13
How would I represent (a) as? in the equation above?
 
  • #14
Don't look now, but they tell you how to determine a in the problem. If your ellipse is to vary between r1 and r2, what is the semi-major axis?
 
  • #15
(r1+r2) / 2
 
  • #16
tnutty said:
(r1+r2) / 2

That would seem so.

So plug 'em in and get'er done.
 

1. How does the energy transfer from low altitude to geosynchronous altitude work?

The energy transfer from low altitude to geosynchronous altitude involves the use of rockets or other propulsion methods to accelerate a spacecraft to a high enough speed to reach geosynchronous orbit. This speed allows the spacecraft to counteract the Earth's gravitational pull and remain in a circular orbit at a fixed altitude.

2. What type of energy is involved in the transfer process?

The energy involved in the transfer process is primarily kinetic energy. This is the energy that is associated with the motion of an object. In this case, it is the energy required to accelerate the spacecraft to the necessary speed to reach geosynchronous altitude.

3. What factors affect the efficiency of the energy transfer from low altitude to geosynchronous altitude?

The efficiency of the energy transfer is affected by factors such as the mass and design of the spacecraft, the type and amount of propellant used, the distance and speed required to reach geosynchronous altitude, and the gravitational pull of the Earth. Other factors, such as atmospheric conditions and external forces, may also play a role.

4. Are there any potential energy losses during the transfer process?

Yes, there can be potential energy losses during the transfer process. These losses can occur due to factors such as atmospheric drag, inefficiencies in the propulsion system, and gravitational interactions with other bodies in space. However, these losses are often minimized through careful planning and design of the spacecraft and its trajectory.

5. How is the energy transfer from low altitude to geosynchronous altitude monitored and controlled?

The energy transfer process is closely monitored and controlled by engineers and scientists on the ground using various tracking and communication systems. These systems allow for adjustments to be made during the transfer to ensure the spacecraft reaches its desired altitude and maintains its intended orbit. Additionally, onboard sensors and propulsion systems can also aid in monitoring and controlling the energy transfer process.

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