- #1

phantomvommand

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- Homework Statement
- I am trying to recall as much of this question as I can. If some of the information I state below is physically false/impossible, do change the question as you see fit.

- Relevant Equations
- Newton's Laws of Gravitation

Effective Potential

Consider only the Earth-Moon system, where both the Earth and Moon are spheres. A horizontal line joins the centres of the Earth and Moon. Consider a point P that lies on the surface of the Earth. The line joining P and the centre of the Earth meets the horizontal line joining the centres of the Earth and Moon at an angle Θ.

(i) Assume the Earth and Moon orbit about the common centre of mass in circular motion. Find the angular frequency w.

I solved this by finding centre of mass, and equating centripetal force required with gravitational force of attraction.

(ii) Find the effective Potential at point P.

I googled and found that effective potential = L^2/2mr^2, but I am not sure how to substitute m and r in the case of 2 planets. m is apparently the reduced mass. Is r the radius of earth, or distance from Earth to centre of mass? I think the latter, but I'm not sure. Furthermore, in circular motion about the centre of mass, there is no radial component of motion. Would the effective potential then just simply be the total energy of the Earth?

(iii) Calculate the difference in tidal height between the point nearest to the moon, and the point farthest from the moon.

I am not sure how to do this at all. However, the answer to part (ii) is relevant.

You are welcome to introduce symbols for radius of earth, distance between Earth and moon, radius of moon, etc.

All help is appreciated. Thank you everyone!

(i) Assume the Earth and Moon orbit about the common centre of mass in circular motion. Find the angular frequency w.

I solved this by finding centre of mass, and equating centripetal force required with gravitational force of attraction.

(ii) Find the effective Potential at point P.

I googled and found that effective potential = L^2/2mr^2, but I am not sure how to substitute m and r in the case of 2 planets. m is apparently the reduced mass. Is r the radius of earth, or distance from Earth to centre of mass? I think the latter, but I'm not sure. Furthermore, in circular motion about the centre of mass, there is no radial component of motion. Would the effective potential then just simply be the total energy of the Earth?

(iii) Calculate the difference in tidal height between the point nearest to the moon, and the point farthest from the moon.

I am not sure how to do this at all. However, the answer to part (ii) is relevant.

You are welcome to introduce symbols for radius of earth, distance between Earth and moon, radius of moon, etc.

All help is appreciated. Thank you everyone!