Understanding Kinetic Energy, Angular Momentum & Torque

[Riemannenthusiast]

Homework Statement

So in this scenario, a spaceship is in an elliptical orbit. It then fires its rockets straight upward. The question asks me what happens to the kinetic energy and angular momentum.

Relevant Equations

mvrsintheta=mvrsintheta

Well I am pretty sure that the kinetic energy stays the same because in this case the velocity vector and energy make a ninety degree angle so no work is done, but I am lost about angular momentum. It could decrease maybe if the torque is clockwise while the ship is going in a counterclockwise direction so they could cancel out, the same because the rockets torque is perpendicular to angular momentum, or increase because the radius increases. Can someone set me on the right path?

 

[jbriggs444]

When does the craft fire its rockets? At the high point in the orbit? At the low point in the orbit? Somewhere in between?

What does it mean to say that the rockets are fired vertically upward. Does that mean that the craft points the thrusters vertically outward and then fires them? Or does it mean that it carefully aims so that the exhaust stream moves vertically upward from the point of view of an inertial observer on the object being orbitted?

Are we to consider the mass of the expelled propellant? Or are we expected to think of an infinitely fast exhaust stream with negligible mass?

When you talk about energy, are you including or excluding the energy in the exhaust stream?

When you talk about angular momentum, are you including or excluding the angular momentum in the exhaust stream?

What axis of rotation are you assuming for the angular momentum?

With the answers to these questions in mind, is there a relevant torque and, if so, how might you go about calculating it?

 

[etotheipi]

I wonder whether it's worth introducing a slight simplification of the situation in order to get a handle on what's going on. Suppose we replace the mechanism of propulsion (i.e. the exhaust stream) with a short taut string exerting a force which is orthogonal to the plane of the initial elliptical orbit, so we can ignore issues pertaining to the relative velocities of the exhaust stream in different frames of reference. This "rocket" is then a constant mass system, and we can also skip over this detail for now.

Let's also say the force only acts for a very short time, so we can also ignore how the plane of the ellipse changes over time. In this setup, what torque acts on the rocket (wrt a suitable choice of coordinate system), and also is any work done in the ensuing motion?

As @jbriggs444 alluded to, what's actually going on can only be meaningfully analysed when the parameters of the problem are fully specified! I hope I've understood the problem correctly, please do let me know if this is too much abstraction!

 

[jbriggs444]

how the plane of the ellipse changes over time

Interesting. When I read the problem statement, I was assuming a radial thrust in the orbital plane but outward from the planet being orbited. While you seem to have assumed a thrust perpendicular to the plane of the orbit. I wonder which of us matched the problem setter's expectations.

 

[etotheipi]

Interesting. When I read the problem statement, I was assuming a radial thrust in the orbital plane but outward from the planet being orbited. While you seem to have assumed a thrust perpendicular to the plane of the orbit. I wonder which of us matched the problem setter's expectations.

I think you're right, yours would indeed make more sense in the context of the problem. Apologies!