# Does the rotation speed of a planet affect its gravitational pull

• eiyaz
In summary, the conversation discusses the effects of a planet's spin on its gravity and the orbit of objects around it. It is mentioned that the force we identify as gravity on Earth is slightly less due to centrifugal force, but this does not affect objects in orbit. The topic of spinning black holes is also brought up, with the article suggesting that they may not lose their event horizon based on frame dragging. However, conservation of angular momentum is not relevant in this scenario.
eiyaz
For example let's a satellite was orbiting the moon which has no atmosphere. If the moon suddenly started spinning twice as fast would it effect the satellite's orbit even though the satellite is separated by the vacuum of space from the moon?

Easier way to put it, if the Earth suddenly spun 1000 times as fast, would the moon float away? I know that things on the planet may be thrown off due to centrifugal force, but would the Earth's gravitational pull become weaker?

I believe it would, since angular momentum needs to be conserved in such a system.

eiyaz said:
For example let's a satellite was orbiting the moon which has no atmosphere. If the moon suddenly started spinning twice as fast would it effect the satellite's orbit even though the satellite is separated by the vacuum of space from the moon?

Easier way to put it, if the Earth suddenly spun 1000 times as fast, would the moon float away? I know that things on the planet may be thrown off due to centrifugal force, but would the Earth's gravitational pull become weaker?

The force we identify as gravity here in Earth is, in fact, slightly less than it would be if the Earth were not spinning. The full force of gravity is offset to a small amount by the centrifugal force. Or, more precisely, some of the gravity is used as a centripetal force to keep us rotating with the Earth.

This, however, does not affect objects in orbit. The moon's orbit is essentially unaffected by the Earth's spin.

I believe it would, since angular momentum needs to be conserved in such a system.
Why does angular momentum need to be conserved? Centrifugal force is fictitious force when means its not mediated by a particle. If an object is floating a in circular space station in a vacuum and the space station is spinning creating a centrifugal pulling everything down at 9.8 m/s^2, but the floating object will float forever unless it is attached to the station and grabbed by its spin.

The force we identify as gravity here in Earth is, in fact, slightly less than it would be if the Earth were not spinning. The full force of gravity is offset to a small amount by the centrifugal force. Or, more precisely, some of the gravity is used as a centripetal force to keep us rotating with the Earth.

This, however, does not affect objects in orbit. The moon's orbit is essentially unaffected by the Earth's spin.

So a spinning black hole should not lose its event horizon no matter how fast it spins?

eiyaz said:
So a spinning black hole should not lose its event horizon no matter how fast it spins?

Spinning black holes are unique animals. For example, they have two "surfaces", the event horizon and the "ergosurface". Anything that enters the region between these two is forced to orbit with the black hole's rortation due to frame dragging( its impossible for an object to orbit in a direction opposite to the rotation).
The article says nothing about the gravity of the black hole weakening, but instead mentions a theoretical method of "disrupting" the event horizon. (A weakening of the gravity would just lead to the event horizon shrinking.)

The Earth also does some frame dragging, however it is very very weak, and even spinning the Earth up by 1000 times wouldn't cause a significant increase in it.

PeroK
eiyaz said:
So a spinning black hole should not lose its event horizon no matter how fast it spins?
You started this thread asking about the rotational speed of a planet, not a black hole. The gravitational effects of rotation are altogether negligible for a planet, which we can properly analyze using ordinary Newtonian theory.

PeroK
PeroK said:
The force we identify as gravity here in Earth is, in fact, slightly less than it would be if the Earth were not spinning.

eiyaz said:
Why does angular momentum need to be conserved? Centrifugal force is fictitious force when means its not mediated by a particle. If an object is floating a in circular space station in a vacuum and the space station is spinning creating a centrifugal pulling everything down at 9.8 m/s^2, but the floating object will float forever unless it is attached to the station and grabbed by its spin.
Law of Conservation of Angular Momentum

Conservation of angular momentum has nothing to do with the question that the OP is asking.

Khashishi said:
Conservation of angular momentum has nothing to do with the question that the OP is asking.
What, is Conservation of Angular Momentum not a thing anymore? Or has George Gamow been teaching me false information...

With Newtonian gravity, if the planet around which the satellite is orbiting is spherically symmetric then rotation doesn't matter as the satellite "sees" the same gravitational source at all times. If it's not spherically symmetric, then there would be perturbations to the satellite's orbit and those would be different for different rotation speeds.

Comeback City said:
What, is Conservation of Angular Momentum not a thing anymore? Or has George Gamow been teaching me false information...
Conservation of momentum tells us that in order to spin twice as fast, some one or some thing would need to exert an external torque on the moon. So take that as a given. Someone or something has reached in and applied an external torque on the moon, thereby doubling its spin rate. That has little or nothing to do with the orbital velocity of a satellite going around the now faster-spinning moon.

Comeback City said:
What, is Conservation of Angular Momentum not a thing anymore? Or has George Gamow been teaching me false information...
Conservation of angular momentum is a real thing. It just doesn't have anything to do with the question in this thread.

jbriggs444 said:
Conservation of momentum tells us that in order to spin twice as fast, some one or some thing would need to exert an external torque on the moon. So take that as a given. Someone or something has reached in and applied an external torque on the moon, thereby doubling its spin rate. That has little or nothing to do with the orbital velocity of a satellite going around the now faster-spinning moon.
Okay I see now. I guess I misconceived what the OP was proposing. Thanks for clearing that up.

I've never studied relativity but I think the fact that the Earth is rotating increases it's mass very slightly and hence increases gravity very slightly. The effect must be very very small.

CWatters said:
but I think the fact that the Earth is rotating increases

it's actually slowing ... day's used to be somewhat shorter long ago

from wiki ...
Analysis of historical astronomical records shows a slowing trend of 2.3 milliseconds per century since the 8th century BCE

Change in rotational velocity
Tidal interactions
Over millions of years, the Earth's rotation slowed significantly by tidal acceleration through gravitational interactions with the Moon. In this process, angular momentum is slowly transferred to the Moon at a rate proportional to r − 6 {\displaystyle r^{-6}} [PLAIN]https://wikimedia.org/api/rest_v1/media/math/render/svg/5562d12471ec1ca2053ab569f0e5c1451f315d62, where r {\displaystyle r} https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538 is the orbital radius of the Moon. This process gradually increased the length of day to its current value and resulted in the moon's being tidally locked with the Earth.

This gradual rotational deceleration is empirically documented with estimates of day lengths obtained from observations of tidal rhythmites and stromatolites; a compilation of these measurements[41] found the length of day to increase steadily from about 21 hours at 600Myr ago[42] to the current 24 hour value. By counting the microscopic lamina that form at higher tides, tidal frequencies (and thus day lengths) can be estimated, much like counting tree rings, though these estimates can be increasingly unreliable at older ages.[43]
Dave

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Centrifugal force does not only affect the value of gravity on a planet, but the direction of its vector.
If a weight is suspended by a rope, we all assume it points in a vertical line, but that's not right. Let's assume the planet as a sphere ... If the line drawn by the rope were extended downwards, it would not cross through the center of the planet.
Hence ... that vertical line, is not a geometric vertical, but only an apparent one.
This divertion of the vertical line has, for example, very strong effects on atmospheric circulation and winds.

If you add angular momentum to a planet does it not increase its energy and therefor modify its energy-momentum tensor, even if it is negligible for the situation in the OP?

davenn said:
it's actually slowing ... day's used to be somewhat shorter long ago

from wiki ...

Dave

I know the Earth rate of rotation is slowing. I was referring to the fact that Relativity says an object gains mass when its moving. So I think a planet has more mass and gravitational pull when it's rotating than when the same planet is not rotating.

CWatters said:
I was referring to the fact that Relativity says an object gains mass when its moving.

but we are hardly talking about relativistic speeds here, aye

CWatters
CWatters said:
So I think a planet has more mass and gravitational pull when it's rotating than when the same planet is not rotating.

The source of gravity in general relativity is not mass but the stress-energy-tensor. That makes the relation between spin and gravity a bit more complicate.

DrStupid said:
The source of gravity in general relativity is not mass but the stress-energy-tensor. That makes the relation between spin and gravity a bit more complicate.

Maybe I can help the OP to phrase the question better.

Does the

Edit: Does the invariant mass of an object change when it spins?

anorlunda said:
Does the invariant mass of an object change when it spins?

Yes, the invariant mass of a closed system changes when it's rotational energy changes. But I'm not shure that this is what the OP is asking for. The original question is about the orbit of a satellite and that doesn't depend on the invariant mass only but on the complete stress-energy-tensor and of course on the shape of the planet (which also changes with the spin).

Adding speed or momentum does certainly increase energy. But how would that momentum be added ? In fact, there is a substraction, but not an addition.

Rotational speed of the Earth and Earth-Moon system in slowering down, due to energy being continuosly "stolen" by the Tide effect from gravitational forces. Due to this same effect, the distance Moon-Earth increases as well.
Big Earthquakes, other celestial bodies, etc ... can also change orbital parameters.

Nothing measurable to do with Relativity, but with classic dynamics.

Ion Aguirre said:
Rotational speed of the Earth and Earth-Moon system in slowering down, due to energy being continuosly "stolen" by the Tide effect from gravitational forces.

That's another topic.

DrStupid said:
That's another topic.
My apologizes

## 1. How does the rotation speed of a planet affect its gravitational pull?

The rotation speed of a planet does not directly affect its gravitational pull. Gravitational pull is determined by the mass of the planet, while the rotation speed is determined by factors such as the distribution of that mass and the planet's distance from its star. However, the rotation speed can indirectly affect the gravitational pull by impacting the planet's shape and mass distribution.

## 2. Does a faster rotation speed mean a stronger gravitational pull?

No, a faster rotation speed does not necessarily mean a stronger gravitational pull. As mentioned before, the gravitational pull is primarily determined by the mass of the planet, not its rotation speed. However, a faster rotation speed can lead to a more flattened shape of the planet, which can result in a slightly stronger gravitational pull at the equator compared to the poles.

## 3. Is there a correlation between a planet's rotation speed and its gravitational pull?

There is no direct correlation between a planet's rotation speed and its gravitational pull. However, the rotation speed can impact the planet's shape and distribution of mass, which can affect the overall strength of its gravitational pull.

## 4. Can a planet's rotation speed change its gravitational pull over time?

A planet's rotation speed can change over time due to various factors, such as interactions with other objects or internal processes. This can also result in changes in the planet's shape and mass distribution, which can impact the gravitational pull. However, these changes are usually minimal and do not have a significant effect on the overall strength of the gravitational pull.

## 5. How does the rotation speed of a planet affect the orbits of its moons?

The rotation speed of a planet can have an impact on the orbits of its moons. A faster rotation speed can cause the planet to bulge at the equator, which can affect the stability of the moon's orbit. Additionally, the rotation speed can also influence the tidal forces between the planet and its moons, which can affect the orbits over time.

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