Find Speed Changes for Spacecraft Orbit Transfer: Mplanet/MEarth = 0.75

In summary, the spacecraft starts in elliptical orbit JK and transfers to elliptical orbit MN by changing its speed at K and then inserting into the circular orbit KL. At L, it changes speed again to insert into elliptical orbit LM, and finally at M, it changes speed to insert into the final orbit MN. The changes in speed are necessary due to the mass of the planet being 0.75 times that of Earth, with a radius of 3000 miles. The values for a, b, c, and d are 400, 1200, 300, and 1000 miles respectively. However, the calculations need to be revised as they have produced incorrect results due to mixing miles and the metric system. It
  • #1
Faraz
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Question
A spacecraft starts in elliptical orbit JK (red solid curve) around some planet and transfers to elliptical orbit MN (blue solid curve). To do so, it changes its speed at Kand inserts into the circular orbit KL (dashed green curve). At L, it changes speed again to insert into elliptical orbit LM (dashed magenta curve). Finally, at M, it changes speed to insert into the final orbit MN. Find all the changes in speed. Mass of planet compared to mass of Earth: Mplanet /MEarth = 0.75 Radius of planet: Rplanet = 3000 mi a = 400 mi b = 1200 mi c = 300 mi d = 1000 mi

Homework Equations


I just want to make sure I did it correctly before submitting my answer (ATTACHED)

The Attempt at a Solution

 

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  • #2
Faraz said:
Question
A spacecraft starts in elliptical orbit JK (red solid curve) around some planet and transfers to elliptical orbit MN (blue solid curve). To do so, it changes its speed at Kand inserts into the circular orbit KL (dashed green curve). At L, it changes speed again to insert into elliptical orbit LM (dashed magenta curve). Finally, at M, it changes speed to insert into the final orbit MN. Find all the changes in speed. Mass of planet compared to mass of Earth: Mplanet /MEarth = 0.75 Radius of planet: Rplanet = 3000 mi a = 400 mi b = 1200 mi c = 300 mi d = 1000 mi

Homework Equations


I just want to make sure I did it correctly before submitting my answer (ATTACHED)

The Attempt at a Solution

Your calculations need total revision.

You've mixed miles and the metric system in you calculations and produced some really strange results.
 
  • #3
...Also note that in your formula for velocity, the r variable is the value of the orbit radius at the point of interest, not the radius of the planet.
 

What is the purpose of finding speed changes for spacecraft orbit transfer?

The purpose of finding speed changes for spacecraft orbit transfer is to efficiently and accurately transfer a spacecraft from one orbit to another, such as from one planet to another. This ensures that the spacecraft reaches its intended destination with the correct speed and trajectory.

Why is Mplanet/MEarth set to 0.75?

Mplanet/MEarth is set to 0.75 because it represents the ratio of the mass of the planet the spacecraft is leaving from (Mplanet) to the mass of the planet it is traveling towards (MEarth). This value is used in the calculations to determine the necessary speed changes for the spacecraft.

How are the speed changes for spacecraft orbit transfer calculated?

The speed changes for spacecraft orbit transfer are calculated using the vis-viva equation, which takes into account the gravitational force between the spacecraft and the two planets, as well as the distance between them. This equation is then solved for the necessary velocity change.

Are there any other factors that need to be considered when calculating speed changes for spacecraft orbit transfer?

Yes, there are other factors that need to be considered, such as the spacecraft's current velocity and trajectory, the gravitational forces of any other celestial bodies, and the desired destination orbit. These factors can impact the necessary speed changes and must be taken into account in the calculations.

How accurate are the calculations for speed changes in spacecraft orbit transfer?

The accuracy of the calculations depends on the accuracy of the input data and the assumptions made in the equations. With precise data and careful consideration of all factors, the calculations can be very accurate. However, there may be some margin of error due to uncertainties in the data or unforeseen external influences.

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