variations in gravitational field (1 Viewer)

[nfreidman]

A textbook I'm reading says this:
Because the Earth has a slightly larger radius near the equator than at the poles (the ‘equatorial bulge’), g is slightly lower at the equator. Except at the poles, there is an additional (fictitious) decrease in g measurements that gets more severe as one approaches the equator. Because of the earth’s rotation, the (downward) centripetal acceleration of the ground appears to be subtracted from the true value of g. In fact this centripetal effect is responsible for the formation of the equatorial bulge.


- Why do they say ‘except at the poles’?
- what do they mean the centripetal acceleration of the ground “appears” to be subtracted from the true value of g? if a centripetal acceleration vector is downward, and so is a gravitational acceleration vector, wouldn’t they add together to make the gravitational field seem stronger rather than one being subtracted?
- why would the centripetal effect be responsible for an equatorial bulge?

I basically don't understand any of it
thank you!

 

[karnbmx]

okay. First of all, acceleration due to gravity on earth varies slightly as a result of several factors.

One of the factors is the distance of the body from the centre of the Mass. The earth isn't perfectly spherical, so therefore, the distance from the centre isn't a constant value. The further away you are from the centre, the smaller the g-value becomes. At the equator, the distance is the largest, whereas at both the poles, this distance is the shortest. As a result:

- g on the surface of the earth is least along the equator BUT the value of g is the greatest at the poles

The reason for the earth's "oval like" distortion is because the Earth is spinning on its axis. This spinning also has another effect. It creates a centrifugal force (which is equal but opposite in direction to the centripetal force) that acts against gravity to give a smaller effective value for g. The book is wrong in saying it is centripetal force. It is more a cause of centrifugal force.

I'm not exactly sure why the bulging occurs, but my best guess would be because the spin of the Earth causes it to throw its mass outward due to inertia. This causes the equator to "bulge out" (cause it is the most dense/matter heavy part of the earth).

Hope this helps.

 

[nfreidman]

wow! thank you so much!
so would the centrifugal force be greatest at the equator (thereby decreasing the effective value for g) because the earth's linear orbital speed is greatest at the equator?

 

[deswa1]

wow! thank you so much!
so would the centrifugal force be greatest at the equator (thereby decreasing the effective value for g) because the earth's linear orbital speed is greatest at the equator?

Yep. At the poles, the Earth isn't rotating at all (try and visualise this if you can). The closer to the equator you get, the faster the Earth at that part rotates. I think there's a formula, something like 464cosx m/s where x is the latitude but I read that formula ages ago so the numbers are probably wrong.

 

[barbernator]

okay. First of all, acceleration due to gravity on earth varies slightly as a result of several factors.

One of the factors is the distance of the body from the centre of the Mass. The earth isn't perfectly spherical, so therefore, the distance from the centre isn't a constant value. The further away you are from the centre, the smaller the g-value becomes. At the equator, the distance is the largest, whereas at both the poles, this distance is the shortest. As a result:

- g on the surface of the earth is least along the equator BUT the value of g is the greatest at the poles

The reason for the earth's "oval like" distortion is because the Earth is spinning on its axis. This spinning also has another effect. It creates a centrifugal force (which is equal but opposite in direction to the centripetal force) that acts against gravity to give a smaller effective value for g. The book is wrong in saying it is centripetal force. It is more a cause of centrifugal force.

I'm not exactly sure why the bulging occurs, but my best guess would be because the spin of the Earth causes it to throw its mass outward due to inertia. This causes the equator to "bulge out" (cause it is the most dense/matter heavy part of the earth).

Hope this helps.

Centrifugal force does not exist

 

[Kimyia]

Centrifugal force does not exist

Yes, I was wondering about that. I thought it was only centripetal foce.

 

[karnbmx]

Centrifugal force does not exist

True that. I forgot. People mistake "centrifugal force" as inertia. That's what I did in my definition. Sorry.

EDIT: I guess you COULD say that the inertia of the person/object as it spins on the Earth's surface is to blame for this net g-value. It's a guess, but that could substitute for the misinterpretation of "centrifugal force".

 

[barbernator]

True that. I forgot. People mistake "centrifugal force" as inertia. That's what I did in my definition. Sorry.

EDIT: I guess you COULD say that the inertia of the person/object as it spins on the Earth's surface is to blame for this net g-value. It's a guess, but that could substitute for the misinterpretation of "centrifugal force".

So yes, at the poles, g is the greatest. At the equator, g is the smallest, and this is due to the earths rotation. The earth is a fraction larger at the equator due to the tangential inertia of the mass at the equator forcing the earth "outwards" (why people get confused with centrifugal force). In effect, this is not an "outward" force, rather the tangential inertia of the earth being curbed by gravitational centripetal force pulling the mass towards the centre. This circular velocity results in the effect of the acceleration due to gravity being slightly less, as the mass is continually moving at right angles to the direction of centripetal force, allowing it to get minutely further away throughout the entirety of the circumference rather than at the poles where there is no circular velocity.

 

[karnbmx]

So yes, at the poles, g is the greatest. At the equator, g is the smallest, and this is due to the earths rotation. The earth is a fraction larger at the equator due to the tangential inertia of the mass at the equator forcing the earth "outwards" (why people get confused with centrifugal force). In effect, this is not an "outward" force, rather the tangential inertia of the earth being curbed by gravitational centripetal force pulling the mass towards the centre. This circular velocity results in the effect of the acceleration due to gravity being slightly less, as the mass is continually moving at right angles to the direction of centripetal force, allowing it to get minutely further away throughout the entirety of the circumference rather than at the poles where there is no circular velocity.

Yep, that makes sense.

I doubt the syllabus wants us to go into THAT much detail, but meh. Better to understand it the right way.

 

[Fizzy_Cyst]

Centrifugal force does not exist

For the sakes of HSC physics, yes, It does not exist.

In reality, it depends on the frame of reference .. In rotating frames, it definitely does exist and is termed an 'inertial force', just like gravity is in the context of general relativity! So, in different frames, gravity can be viewed equally "ficticious" to centrifugal force!

 

[karnbmx]

For the sakes of HSC physics, yes, It does not exist.

In reality, it depends on the frame of reference .. In rotating frames, it definitely does exist and is termed an 'inertial force', just like gravity is in the context of general relativity! So, in different frames, gravity can be viewed equally "ficticious" to centrifugal force!

hah, lovely brainbend we have there.