Solving the Shuttle's Orbital Recovery: Angular Momentum

In summary, a space shuttle and satellite are in circular orbits. The shuttle increases its speed by 280 ft/s at point B to enter an elliptical orbit, and then increases by 260 ft/s at point C to enter a second elliptical orbit. With the distance from O to C known, the problem involves determining the amount by which the shuttle's speed should increase at point D to insert it into the satellite's circular orbit. The use of conservation of angular momentum and Newton's law of gravity may be helpful in solving this problem.
  • #1
negatifzeo
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Homework Statement


A space shuttle S and a satellite A are in the circular orbits shown. In order for the shuttle to recover the satellite, the shuttle is first placed in an elliptical path BC by increasing it's speed by deltaVb=280 ft/s as it passes through B. As the shuttle approaches C, it's speed increases by DeltaVc=260 ft/s to insert it into a second elliptical orbit CD. Knowing that the distance from O to C is 4289 mi, determine the amount by which the speed of the shuttle should increase as it approaches D to insert it into the circular orbit of the satellite.

Homework Equations


I know this uses conservation of angular momentum for elliptical orbits, but I can't get a workable equation.

The Attempt at a Solution



The equations for angular momentum involve mass(which cancels here), velocity and radius. The radius is known in one position, the velocity isn't known in any position, only the change in velocity. As a result, I'm confused.
 

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  • #2
You might try to mix in Newton't law of gravity and mass of Earth to get the speeds.
 

FAQ: Solving the Shuttle's Orbital Recovery: Angular Momentum

What is angular momentum and why is it important in solving the shuttle's orbital recovery?

Angular momentum is a physical quantity that measures the rotational motion of an object. In the case of the shuttle's orbital recovery, it is important because it determines the amount of force and torque needed to change the shuttle's orbit.

How does angular momentum affect the shuttle's orbit?

Angular momentum affects the shuttle's orbit by determining the shape, size, and orientation of the orbit. A change in angular momentum can cause the shuttle to move closer or further away from its original orbit.

Can angular momentum be conserved during the shuttle's orbital recovery?

Yes, angular momentum is a conserved quantity, meaning it cannot be created or destroyed. It can only be transferred from one object to another. This is why it is crucial to consider angular momentum when solving the shuttle's orbital recovery.

How can we change the shuttle's angular momentum during orbital recovery?

The shuttle's angular momentum can be changed by applying a force or torque on the shuttle. This can be done through the use of thrusters or other propulsion systems, which can alter the shuttle's velocity and direction of motion.

Are there any challenges in solving the shuttle's orbital recovery using angular momentum?

Yes, there are several challenges in solving the shuttle's orbital recovery using angular momentum. One of the main challenges is accurately calculating and predicting the effects of angular momentum on the shuttle's orbit, as it is influenced by various factors such as gravity, air resistance, and external forces.

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