# Do tidal forces slowly make orbits more circular?

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## Main Question or Discussion Point

Feynman's lectures said:
The actual motion of the planets, in general, should be ellipses, but during the ages, because of tidal forces, and so on, they have been made almost symmetrical.
I don't understand, how can tidal forces make the orbits more circular?
Perhaps it has something to do with the fact that in elliptical orbits (unlike in circular orbits) the velocity is not always perpendicular to the acceleration?
Or maybe it does not have to do with the tidal forces from the sun but instead with the tidal forces from the moon? But then we would also need an explanation of why more energy is lost when the Earth is moving faster (which must be the case in order to become more circular, right?).

I know nothing about astronomy. Perhaps I'm misunderstanding what "tidal forces" are so I will explain what I think it means. In my understanding, "tidal forces" refers to the effect that the force of gravity tends to stretch large bodies along one direction (parallel to the net force) and compress large bodies in the other (perpendicular) direction. But I can't figure out how this could cause orbits to become more circular over time.

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ehild
Homework Helper
How does Feynman explain it?

What I think is that the shape of the planet changes along its orbit, so the angular momentum changes. Look at the figure, and assume that the planet does not rotate with respect the Sun. The angular momentum L=Iω is conserved, but then the angular velocity changes if the moment of inertia changes. It gets increased at perihelion, so ω gets slower than that of a rigid planet. The centripetal force needs to be less, the perihelion distance of the planet increases.

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How does Feynman explain it?
He doesn't explain it. It wasn't really relevant to the chapter so he didn't go into it, it was like a side-note. (He was talking about symmetries and near-symmetries.) That quote was all he said about it.

What I think is that the shape of the planet changes along its orbit, so the angular momentum changes. Look at the figure, and assume that the planet does not rotate with respect the Sun. The angular momentum L=Iω is conserved, but then the angular velocity changes if the moment of inertia changes. It gets increased at perihelion, so ω gets slower than that of a rigid planet. The centripetal force needs to be less, the perihelion distance of the planet increases.
Nice idea :)

But... it seems to me the perihelion distance would only increase relative to that of a perfectly rigid body (in an otherwise identical situation).
In other words, I think this effect would not cause the perihelion distance to increase over time.

What do you think?

ehild
Homework Helper
But... it seems to me the perihelion distance would only increase relative to that of a perfectly rigid body (in an otherwise identical situation).
In other words, I think this effect would not cause the perihelion distance to increase over time.

What do you think?
Well, it was just an idea. And thinking of the centripetal force at perihelion, mrω2 (r is the radius of the curvature of the orbit), it is equal to GmM/R12 , r should increase as ω decreases even when the perihelion distance stays the same. Increasing the radius of curvature means the "peak" of orbit getting flatter .

You should solve the equation of planetary motion for a non-rigid planet to see, how its orbit evolves in time... :)

Nugatory
Mentor
I don't understand, how can tidal forces make the orbits more circular?
Google for "tidal lock". That's a different phenomenon than the one that Feynman is talking about, but it has a similar explanation.

Wes Tausend
Gold Member
Google for "tidal lock". That's a different phenomenon than the one that Feynman is talking about, but it has a similar explanation.
I think I agree with Nugatory's path to understanding here.

My simple way of looking at it is to realize that if our moon were to rotate it's face with respect to earth (probably once did), the "moving bulges" of planetary stretching demands some frictional work be done. The moon bulges occur at both the closest and furtherest points from the mother planet (earth) because of the gradiant of gravity caused by the difference in earth-proximity distances of the moon face-to-backside. The energy for this friction is subtracted from the rotation of the moon (a satellite), which eventually slows it's momentum to rotate relative to earth.

When a planet follows an elliptical path, it periodically is elongated (stretched) differently because the varied gradiant of gravity, caused by the proximity of it's mother planet, which also changes from the minor axis to major axis. This varied force creates a "work" friction within the planetary body that must take it's energy to do work from some other source rather than just possible satellite rotation which may already be nil. The source is the unequal orbit radii. The stolen work energy is dissipated into colder space as heat.

In both tidal locking and ellipsoidal movement (and other things), the path of least resistance seems to rule.

One thing does bother me. Since the end of classical Newtonian gravity, it is technically incorrect to speak of gravity as an "attraction". I believe gravity is more properly defined as an acceleration within curved spacetime, "equivalent" to inertia. I find it difficult to intuitively explain tidal forces this way (sans attraction) and I'm probably not alone.

Wes
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