Consider the motion of a point mass under the influence of an attractive central force. The potential for the force is proportional to the inverse distance from the central point O to the point mass. For every value of the angular momentum L of the object around O we have an equilibrium point in the radial direction, which corresponds to a circular orbit. We now consider a small perturbation of a circular orbit into a low eccentricity ellipse with the same angular momentum. If we look at the radial distance from O to the object on the elliptical orbit, we see that the distance changes from some rmin to rmax with some frequency f. If at L1=1 kg⋅m2/s we get f1=f(L1)=1 Hz, find the frequency f2 for L2=10 kg⋅m2/s in Hz.

Bonus thought: The value of the frequency at L3=0 (without angular momentum) is defined as the bare frequency. Is this a finite value?

I found this question on someone's profile,I have done the question,and i would like to know how the solution was approached,can anyone send me the link to the solution page.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

There are no comments in this discussion.