# Quick Question on Kepler & angular momentum conservation

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1. Mar 25, 2016

### RoboNerd

1. The problem statement, all variables and given/known data

2. Relevant equations
I guess kepler's law but most importantly conservation of angular momentum are key here.

3. The attempt at a solution

I put down E as the answer, but the solutions have D as the correct answer. Why is this the case?

Thanks in advance for the help!

2. Mar 25, 2016

### QuantumQuest

I'll first ask why did you choose "E" as the correct answer. Through this you can clear out potential misundenstardings.

3. Mar 25, 2016

### RoboNerd

My rocket exerts a thrust force on it backwards. This pushes it forward and increases its velocity. It must be a greater distance away from earth in order to conserve angular momentum. Thus, E, which has a horizontal bulge, fits this description.

4. Mar 25, 2016

### Staff: Mentor

Does the orbit depicted in E agree with Kepler's First Law?

5. Mar 25, 2016

### RoboNerd

No. the earth has to be at a focus

6. Mar 25, 2016

### QuantumQuest

Exactly.The purpose of my question, was to direct you checking first with Kepler's laws, as gneiil points out, and see why "E" is wrong.

7. Mar 25, 2016

### RoboNerd

OK. so why is D right?

8. Mar 25, 2016

### QuantumQuest

Is "D" OK with Kepler's laws and conservation of energy?

9. Mar 25, 2016

### RoboNerd

yes... it seems so

10. Mar 25, 2016

### Staff: Mentor

See if you can think of an argument that supports it. Consider what qualities of the orbit change when the maneuver is performed. What distinguishes C from D?

11. Mar 27, 2016

### RoboNerd

C has a new orbit that is smaller than the first orbit. This does not work with conservation of angular momentum. It also has the earth at the center, not of the focus.

D has a new orbit that is larger than the first. Earth is at the center. Angular momentum is thus conserved.

Right?

12. Mar 27, 2016

### Staff: Mentor

Because a force was applied when the rocket made its burn neither angular momentum nor energy will be conserved for the satellite. (you would have to include the rocket's exhaust material in the sum to conserve angular momentum, while the KE of the satellite increases because its speed is increased).

The important thing here is the increase in KE. Since the satellite is effectively at the same orbit radius immediately after the burn, the gravitational PE is the same but the KE increased. Thus the total energy of the orbit has increased. What do you know about orbits with larger total energy?

13. Mar 28, 2016

### RoboNerd

I honestly do not know anything about orbits with larger total energy, or rather think I do not.

Sorry.... what do I need to know?

14. Mar 28, 2016

### Staff: Mentor

The total mechanical energy of an orbit comprises its kinetic energy and its gravitational potential energy. Their sum is a constant for a given orbit. For bound orbits (circles, ellipses) the total energy is a negative value. As the energy increases the orbit becomes larger (the semimajor axis increases in size). When the energy value reaches zero the orbit is unbound, and the object will escape (parabolic trajectory for energy = 0, hyperbolic trajectory for energy > 0).

Do a web search on "specific mechanical energy of an orbit". Here's a wikipedia entry that's not too bad.

15. Mar 29, 2016

### RoboNerd

So my energy has increased, and the object is moving away from the center of its orbit, the earth that is pulling it towards itself. Thus orbit should be larger.

16. Mar 29, 2016

### Staff: Mentor

Yes. The location where the KE was added (where the rocket fired) becomes the perigee of the new orbit.

17. Mar 29, 2016

### RoboNerd

Great! Thanks so much for helping me understand this problem

18. Mar 29, 2016

### Staff: Mentor

You're very welcome.