Gravity of the Earth decreases if it stops spinning?

[Buckleymanor]

Here is Fig 3 from http://pages.physics.cornell.edu/~aalemi/random/planet.pdf with some force vectors added :

Point A is ~1.79 times further way than point B, making B's direct attraction 3.2 times stronger. So despite B pulling mosty sidewards, it still creates ~1.43 times more downwards pull than A. Therefore by moving mass from A to B, you increase the surface gravity at the top.

So basically if the Earth stopped spinning the gravitational pull would be much the same over it's entire surface.
The gravity at the poles would decrease whilst at the equator it would increase as the planet became more spherical in shape.
Apart from it being much the same the rest is the opposite as to what I imagined thanks for the clarifications.

 

[BillyT]

I didn't say "nowhere else" but the reduction in gravity would be strongest at the poles. They would move away from the centre, when the stopped planet becomes spherical again.

We agree, I think, that the equatorial diameter would become less and surface gravity there slightly more, IF that were the only change (no relocation of ocean water) but why do you think the distance between the poles would increase, have reduced surface gravity at the poles? The Earth is not an incompressible solid, so the contraction at the equator, does not necessarily mean there must be expansion elsewhere (at the poles). Even if there were, what I discuss in next paragraph very likely lessens the distance between the poles, making surface gravity increase there.

As a great volume of water now near the equator would shift toward the poles; that increased polar weight might even reduce the separation between the poles, and make polar gravity slightly increase. Only thing for sure is the Earth would become on average slightly denser.* That lesser water mass at the equator would partially (or more than?) cancel out some of the "no-spin" contraction effect at the equator.

* Part of this density increase would take a few decades for the colder water, on average, to contract and fill a smaller volume.

 

[Joyousluo]

I think in contrast, gravity will be increased. Because the attraction force applied on us devides into 2 force, one is parallel to the surface and cause the friction between the ground and us. The other is the actual gravity, or weight we perceived. Hence when we launch a rocket, we often go to the equator to save fuel,because the linear velocity is highest and the gravity is smallest. Thus as u say when Earth stop rotating, the gravity will increase.

 

[Joyousluo]

I think in contrast, gravity will be increased. Because the attraction force applied on us devides into 2 force, one is parallel to the surface and cause the friction between the ground and us. The other is the actual gravity, or weight we perceived. Hence when we launch a rocket, we often go to the equator to save fuel,because the linear velocity is highest and the gravity is smallest. Thus as u say when Earth stop rotating, the gravity will increase.

 

[Clark Magnuson]

The rotational energy 1/2 I w^2 is equal to some additional Earth mass.
My seat of the pants guess is that is tiny when pushed through the E= mc^2 formula.

Whereas the centrifugal force closer to the equator is significant and is half of why we launch rockets from our Southern border.

 

[Buckleymanor]

I think in contrast, gravity will be increased. Because the attraction force applied on us devides into 2 force, one is parallel to the surface and cause the friction between the ground and us. The other is the actual gravity, or weight we perceived. Hence when we launch a rocket, we often go to the equator to save fuel,because the linear velocity is highest and the gravity is smallest. Thus as u say when Earth stop rotating, the gravity will increase.

If that were the case then a spinning top or gyro would weigh less when spinning and more when stopped, it does not though.

 

[Triple88a]

If the Earth stopped spinning you'd feel more gravity on the surface. Think about this for a second. Centripetal force negates some of the gravity we have from Earth's mass. If that centripetal force stops the only thing left will be Gravity because of mass.

 

[elenzil]

here's another angle - what about the gravitational effect of the energy of Earth's spin ?
ie, to change Earth from not spinning to spinning, one would have to put energy into the system. where does it go ? into the spin itself.
and e = mC², so from a gravitational point of view, a spinning Earth has more 'mass' than a non-spinning Earth by Δm = Δe/C².

but of course, as many people have mentioned, there are other effects at play which would possibly drown out this change in the force experienced by an observer on the surface of the planet,
but the change in gravity due to the energy of the spin might be measurable from a satellite in orbit.

 

[Triple88a]

The extra energy from the rotation is in direct relation to the centrifugal force.

 

[elenzil]

The extra energy from the rotation is in direct relation to the centripetal force.

right, and a satellite in orbit would not experience the centripetal force but would experience the gravitational force.

 

[looking4sophia]

The FORCE of Gravity we feel on the Surface is 'roughly' defined as 1 G.
It varies slightly from 1 G locally, especially around the Equator and Poles as discussed above by others.

Gravity is a 3D FIELD that varies
from ZERO G at the Center of the Earth
to One G at the Surface

1 G causes Mass to Accelerate at 32 Feet per Second per Second

This Diagram Measures only the GRAVITY in Meters per Second per Second
you would experience on a Journey to the Center of the Earth.
https://commons.wikimedia.org/wiki/File:EarthGravityPREM.jpg

Notice that Gravity Increases
as you dig down to almost half way to the center.

Then tapers off to ZERO G at the Earth's Center.

 

[ProfChuck]

Would the gravity of Earth decrease if the Earth stop spinning? Would the gravity be affected at all? Does the gravity of other orbiting bodies cause the Earth to speed up its rotation and slow down its rotation during the year? thanks.

Actually this is a more interesting question than it first appears. A rotating massive body possesses its intrinsic mass plus the mass of the energy-mass equivalent as derived from e=mc^2. Considering this the gravitational curvature would be less for a non rotating object than for a rotating one. Now this is a general relativity consideration and goes beyond special relativity. Anyway, there is also the Lens-Thirring effect which alters things like the precession rate of a gyroscope in the vicinity of rotating masses among other phenomena. This question deserves some careful consideration.

 

[John Green]

A number of respondents here seem to have centripetal and centrifugal forces confused. First of all centrifugal and centripetal are words that have fundamental meanings outside of physics. Centripetal (Moving or directed toward a center or axis.) e.g. Physiology Transmitting nerve impulses toward the central nervous system ;afferent.
Centrifugal (Moving or directed away from a center or axis.) e.g. Physiology Transmitting nerve impulses away from the central nervous system ;efferent.

Thus when one understands that these words are descriptive one is ready to apply them to physics. So a centripetal force is one that acts toward a center, thus gravity can in this sense be described as a centripetal force while the (apparent) force produced by rotation can be considered a centrifugal force.
So the straightforward answer to the original question (disregarding relatively minor effects like the accommodation of the Earth's shape which would probably take thousands of years(Canada is still rebounding from the weight of the ice sheet 10,000 years ago) ) is that if the planet stopped spinning the force of gravity would not change. The measured weight of any mass however would increase because of the loss of centrifugal force.

 

[looking4sophia]

If the Earth stopped spinning
then the Centrifugal Force FIELD would disappear.

If these Centrifugal Forces were gone, the Volume and Diameter of the Earth would shrink
because Internal Pressures would slightly increase the Density of the Mantel and Cores, imo.

Early Mathematical Models of our Gravity Field had to be adjusted for 'missing mass' which turned out to be underestimating the
extremely DENSE iron and other elements under the HyperPressures near the core.
These Compressive Pressures would Increase as the Centrifugal Forces Decreased if the Earth's spin slowed.

 

[Triple88a]

You bring up a pretty good point. Theres a good chance the surface pressure would increase as well.

 

[BillyT]

Most ignore the huge effect of greater ocean water at the poles. I discussed this in post 37. That increased polar mass probably reduces the separtion of the poles making gravity stronger there. Also the diameter at the equator may increase when this water load is reduced making surface gravity LESS at the equator.

Exactly the opposite of what most are suggesting.

 

[Drakkith]

Several off-topic or nonsensical posts have been removed. I remind all members to please stay on-topic and that only mainstream science is to be discussed here at PF. Posts which do not meet PF Terms and Rules will be removed.

 

[interestedcrl]

interested crl to group: Consider more generally -- suppose the Earth was just a tough steel ball (without significant bulged factor) and was spinning fast. And by gentle means it was slowed to a stop.
The question arises whether the previous fast spinning caused a so-called 'relativistic Mass Increase' and whether, when its spinning was slowed to a halt -- if that Earth would incur less mass, and therefore its gravity would decrease? (Of course, if frictional heat, i.e., energy, was added to the earth, like a brake, that would seem to add mass to the Earth and partially or totally offset the 'relativistic spinning mass gain' that was lost when the Earth stopped spinning.
I don't know for sure what-all would happen -- because maybe molecular and atomic vibration is slowed up a little when the Earth is spinning, i.e., if spinning near the speed of light -- perhaps those hidden vibrations would nearly cease. The question is also complicated by a previous forum proposition that the Hydrogen atom loses a little mass when formed; and that a Compton electron (or proton) may spin at or near the speed of light without gaining infinite mass or very great mass increase.

 

[ToddJS]

An object at rest has less mass than a moving object; a spinning Earth is a (complexly, from the standpoint of general relativity calculations necessary) moving object. Thus, a spinning object would have more mass and exert more distant gravitational pull than a non-spinning object. Local gravitational pull, or the feeling of "weight," will be mitigated by where you are located on the spinning object and the rigidity of the object and many other factors. It's true you weigh less at the equator than you do at the poles but this doesn't have as much to do with spinning forces as it does with you being farther from the center of the Earth (the Earth bulges at the equators as it spins as others have pointed out). It doesn't really have as much to do with the amount of mass between your feet and the center of the Earth either. For example, if you climb Mt. Everest, there is more mass under your feet, but you weigh less (there's less gravitation pull on you) because you're farther from the center of the earth. If the Earth stopped spinning and you were standing on it, it would shrink a little in many parts, which would put you closer to the center of the earth. And you would weigh more. Distant objects in space would perceive less gravitational pull from the Earth however. So, regarding gravity and a spinning earth: it depends.

 

[looking4sophia]

Theres a good chance the surface pressure would increase as well.

If the Radius of the Earth shrank due to loss of rotational Centrifugal forces Pulling outward ( like a Merry Go Round stopping)
we would feel a little bit Heavier on the surface; especially at the Equator .

and All the Mantel and Cores would be subjected to increased Pressure leading to increased Density

which would cause the Earth to shrink slightly
bringing all Earth MASS a little bit closer together in Distance
this Distance Reduction would cause Earth's Gravity to Increase to above 1 G
imo..

Maybe 1.01 G for example
would also Pull more on the Atmosphere increasing Barometric Pressure

 

[bobkolker]

Would the gravity of Earth decrease if the Earth stop spinning? Would the gravity be affected at all? Does the gravity of other orbiting bodies cause the Earth to speed up its rotation and slow down its rotation during the year? thanks.

The gravitational force exerted by Earth (at the surface) is function of its mass which does not change of the planet stops turning. Our weight would increase slightly everywhere but at the poles because the turning of the Earth exerts an outward centrifugal force on bodies which is subtracted from their gravitation force between bodies and the earth.

Bob Kolker

 

[Triple88a]

Our atmosphere would get thicker as well since the centrifugal force is no longer there to push the atmosphere out.

 

[BillyT]

The gravitational force exerted by Earth (at the surface) is function of its mass which does not change of the planet stops turning. Our weight would increase slightly everywhere but at the poles because the turning of the Earth exerts an outward centrifugal force on bodies which is subtracted from their gravitation force between bodies and the earth.

Bob Kolker

You are neglecting that a redistribution of mass (ocean water) towards the poles would occur. Its weight may even reduce the separation between the poles (via greater compressive force) making the solid mass's inverse square law effect cause stronger gravity there as well as having more mass below the surface at each pole increasing local gravity (Two separate important effects are being ignored). More detailed discussion in post 37 and 51.

AS noted in post 57, there is an effect on the atmosphere, but post 57 too ignores the redistribution of air mass towards the poles. The surface air pressure at poles would increase and that at equator decrease especially if the lower weight of water mass at the equator, and its reduced compression effect, more than compenstate for the centrifual force going to zero - making a net increase in Earth's diameter at the equator.

The decreases in centrafugal force, which is all most consider, is small (only 0.234% change in the effect of gravity there). The shift of several meters thick layer of water towards the poles is very much more important than a 0.234% of gravity effect at the equator when spin is zero.

 

[Triple88a]

Yes but one thing to consider is the change of gravity due to increase in sea level. Are we still measuring gravity at the surface if the surface moves?

 

[BillyT]

Yes but one thing to consider is the change of gravity due to increase in sea level. Are we still measuring gravity at the surface if the surface moves?

Why do you think the sea level will rise? As a great mass of sea water, now at the equator will move towards the poles, and become colder, the average temperature of the oceans will DECREASE and they will contract in total volume - lower average surface or lesser average ocean depth.

Several meters less water at the equator, in small part due to thermal contraction but mainly cuased by less ocean water there by the volume that went to the polar regions. This reduces their compressive effect on the ocean floor. Allowing for some expansion of the "solid" earth. That effect will reduce the gravity as "solid Earth" expands. - Perhaps more than the contraction due to zero centrafugal force with spin of zero.

 

[Triple88a]

Because of the centrifugal force the Earth isn't a sphere, If Earth stops it will turn into a sphere again and the oceans will distribute evently.. aka go to the poles. When the planet changes shape from an oval to a sphere the equator will shrink and the poles will expand (aka raise in sea level)

 

[BillyT]

Because of the centrifugal force the Earth isn't a sphere, If Earth stops it will turn into a sphere again and the oceans will distribute evently.. aka go to the poles. When the planet changes shape from an oval to a sphere the equator will shrink and the poles will expand (aka raise in sea level)

Yes, but you did not limit your statement of rise to at the poles in post 59. You said: "... one thing to consider is the change of gravity due to increase in sea level."

I had already told in post 37, 60 and several others about a polar sea level rise AND a lowering of sea level at the equator I noted that the lesser mass of water at the equator would lessen the compression of the solid Earth (ocean floor to center of earth) and that the resulting expansion of solid Earth may be larger than the contraction with removal of Earth's rotation's centrifugal forces.

Consider a thin small surface volume of solid Earth at equator. The centrifugal force goes to zero, but it is small, only 0.234% of gravity force AND, many meters thick layer of water has been take away - to the poles.

I. e. now less weight of water is pressing down; That let's solid Earth expand some. Net effect I think, is Earth expands at equator, not contracts as almost all posting here claim is the result of rotation stopping.

 

[mfb]

The equatorial bulge is 40 km difference in diameter. The ~3 km of ocean water (with the same mass of ~1 km of rock) are irrelevant, the Earth will get more spherical. Compression of rock is an even smaller effect than gravitational forces.
Also, as soon as a roughly spherical shape is reached, water will flow back to the equatorial regions.

 

[bhagya sekhar]

Gravity increases at the equater and no effect at poles

 

[A.T.]

... no effect at poles

Wrong. See post #27 and #35.

 

[BillyT]

The equatorial bulge is 40 km difference in diameter. The ~3 km of ocean water (with the same mass of ~1 km of rock) are irrelevant, the Earth will get more spherical. Compression of rock is an even smaller effect than gravitational forces.
Also, as soon as a roughly spherical shape is reached, water will flow back to the equatorial regions.

Yes and it would still be there, compressing the interior 99+% of the Earth below, but not the water, which has moved to the poles. Why would the water flow back - its bulge up at equator was due to the now absent centrifugal force, Also the average temperature of the water decreases - contraction.

We are considering ONLY what changes.

 

[A.T.]

Yes and it would still be there,

What would be still there?

 

[BillyT]

What would be still there?

All the mobile "solid" but elastic mass of rocks. Only part of the water mass , the centrifugal bulge, moves towards the poles. The total volume of ocean decrease, on a many decades time scale, as its average temperature drops.

Are you aware of fact the Norwegian fiords mountain sides were once below sea level, when the weight of more than a mile thick ice was compressing the "solid" rocks below them? That is another example of expansion when large mass of water above the rocks went else where.

 

[A.T.]

All the mobile "solid" but elastic mass of rocks.

Ok, it sounded like you meant that the 40km bulge would still be there. How elastic is rock, if the 40km equatorial bulge can disappear, without increasing the distance between the poles?

 

[mfb]

The Earth as a whole is quite liquid. It even has tides. Without rotation, the equatorial bulge would vanish over time, leading to some really nasty earthquakes and to a spherical shape of Earth. Once that shape has been reached, the water will be distributed over the whole surface again.

@BillyT: you mention smaller and smaller effects while ignoring the huge one that goes in the opposite direction.