# Do tidal forces slowly make orbits more circular?

• Nathanael
In summary, the motion of planets is generally elliptical but tidal forces have caused them to become almost symmetrical over time. This may be due to changes in the shape and angular momentum of the planet along its orbit, as well as frictional work caused by the varied gradient of gravity. Tidal locking and ellipsoidal movement both follow the path of least resistance, and explaining tidal forces in terms of curved spacetime rather than attraction can be difficult.

#### Nathanael

Homework Helper
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.

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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ehild said:
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.

ehild said:
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?

Nathanael said:
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... :)

Nathanael said:
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.

Nathanael
Nugatory said:
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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## 1) How do tidal forces affect the shape of orbits?

Tidal forces can cause the shape of an orbit to become more circular over time. This is because tidal forces create friction and drag on the orbiting object, which causes it to lose energy and gradually spiral closer to the central body. As the orbit becomes more circular, tidal forces become less significant and the orbit stabilizes.

## 2) Do all objects in orbit experience the same level of tidal force?

No, the strength of tidal forces depends on the mass and distance of the orbiting object from the central body. Objects closer to the central body will experience stronger tidal forces compared to those further away.

## 3) Can tidal forces eventually cause an object to fall into the central body?

Yes, if an object orbits close enough to a central body, tidal forces can cause it to spiral closer and eventually collide with the central body. This is known as tidal disruption and is often seen in the case of comets or other small bodies orbiting close to a massive planet or star.

## 4) How long does it take for tidal forces to significantly affect the shape of an orbit?

This depends on the specific characteristics of the orbit and the central body. In general, it can take thousands to millions of years for tidal forces to significantly alter the shape of an orbit. However, this time frame can vary greatly depending on the size and distance of the orbiting object.

## 5) Can objects in highly elliptical orbits be affected by tidal forces?

Yes, even objects in highly elliptical orbits can experience tidal forces. However, the effect may not be as significant compared to objects in more circular orbits. This is because the strength of tidal forces is strongest at the point where the orbiting object is closest to the central body.