Why do orbits become more eccentric when changing speed?

[nothingbetter]

From what I understand (and also assuming that the mass of one body is much greater than the other), if we had a body performing a circular orbit, and we put more (or less?) energy into the orbit by changing the speed of the body, the orbit will become more eccentric, i.e. elliptical.

My question is: If this is the case, then why is it so, instead of the orbit remaining circular but with a different radius?

I have a feeling that I sort of have the answer, but I'm not entire sure about it: That would be the case if the acceleration was at a certain angle, with a radial component. Is this right?

I also have another question relating to elliptical orbits: since the speed of bodies in elliptical orbits isn't constant, it implies that the body is always being accelerated. With Earth itself being in an elliptical orbit, shouldn't we be able to measure this acceleration? Is it because its magnitude is too small (since the Earth's orbit is huge and rather circular anyway), or is there some other reason?

Thanks!

 

[gneill]

From what I understand (and also assuming that the mass of one body is much greater than the other), if we had a body performing a circular orbit, and we put more (or less?) energy into the orbit by changing the speed of the body, the orbit will become more eccentric, i.e. elliptical.

My question is: If this is the case, then why is it so, instead of the orbit remaining circular but with a different radius?

I have a feeling that I sort of have the answer, but I'm not entire sure about it: That would be the case if the acceleration was at a certain angle, with a radial component. Is this right?

If you think about it, two different circles have two different radii, so that a body cannot be on two different concentric circles at the same time. That means there must be a path with a radial component (change in radius) to get from one circle to the another. The resulting trajectory cannot be circular.

However... nothing prevents you from making the radial change gradually and uniformly. This would be a spiral path. With the right direction of applied thrust such a spiral path can be achieved. This is the kind of path favored for constant low-thrust spacecraft with ion propulsion (See for example the Dawn mission spacecraft ).

I also have another question relating to elliptical orbits: since the speed of bodies in elliptical orbits isn't constant, it implies that the body is always being accelerated. With Earth itself being in an elliptical orbit, shouldn't we be able to measure this acceleration? Is it because its magnitude is too small (since the Earth's orbit is huge and rather circular anyway), or is there some other reason?

You can measure the acceleration by referencing an external "stationary" frame of reference such as one provided by the distant background of stars. You might also infer the acceleration by noting the rate of change of the apparent size of the Sun throughout the orbit. Again, this is using an external reference. But if you are restricted to a closed laboratory on Earth you won't be able to detect it. This is because the Earth and its contents are in free-fall around its orbit, following a geodesic path through spacetime. This is the spacetime equivalent of uniform motion with no detectable external forces!