Gravitational Acceleration

In summary, the Earth's rotation causes the gravitational acceleration to be the least at the equator and the maximum at the poles due to its non-spherical shape and the centrifugal force acting on objects at the equator. This can be quantified by the formula g_{a} = g - r\omega^2\cos^2\theta, where g_{a} is the apparent force of gravity and \theta is latitude.
  • #1
Milind_shyani
42
0
hello
The gravitational acceleration at the equator is the least and at the pole is the maximum due to the rotation of the Earth on its axis.Why?
 
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  • #2
The Earth is not precisely spherical, it is flattened at the poles because of the Earth's rotation. This is simply because of the centrifugal force, objects at the equator have the greatest distance from the axis of rotation so are 'flung outwards' more than at the poles. So at the poles you are closer to the center of the Earth and experience a greater gravitational acceleration.
 
  • #3
It should be borne in mind that "g" is generally meant to mean "effective gravitational acceleration" and includes the effects of a rotating Earth (which predicts a lower g at equator than by the poles), the deviatioric correction due to the non-spherical form of the Earth, as the two main correctional effects.
 
  • #4
Galileo is right - the oblateness of the Earth is the biggest factor in the difference in gravitational attraction.

However, the way the question is worded, I think it's addressing centripetal acceleration. Which point will have a larger linear velocity due to the rotation of the Earth: a point on the equator or a point on one of the poles?

Both the oblateness of the Earth and centripetal force contribute to reducing the net force, and the resulting acceleration, at the equator (with oblateness having nearly twice as much affect).
 
  • #5
I never said that Galileo was wrong..
 
  • #6
arildno said:
I never said that Galileo was wrong..
I did (or at least said that his answer didn't answer the question that was asked).

I didn't comment on your answer because I didn't understand it. :rofl:
 
  • #7
To the OP -- just think about what happens as you spin the Earth faster and faster...what force is acting on the person at the equator that is different from the person at the pole? Quiz question -- how fast to you have to spin the Earth to spit off the person at the equator?
 
  • #8
Think of a girl on a merry-go-round. She will move at a larger speed when she is further away from the center, since the outer regions cover a larger distance in the same time. If the merry-go-round would spin faster and faster the girl would have to hold on for dear life or she would be flung off. She would conclude that some force is pulling her outwards from the center. This force we call the centrifugal force, it is not a real force. It results from her inertia - she wants to keep on moving in a straight line and have to hold on or press up against something in order to keep on the merry-go-round. The same happens with an object on the earth. The further it is away from the rotation axis of the Earth the larger the centrifugal force it experiences. This leads to a decrease in the weight of the object - it wants to fly off the earth. Since the weight is related to the gravitational acceleration and mass (which stays the same under all circumstances) we conclude that gravity was somehow reduced by this effect.
 
  • #9
The effect of 'centrifugal' acceleration can be quanitfied by;
[tex]g_{a} = g - r\omega^2\cos^2\theta[/tex]
where [itex]g_{a}[/itex] is the apparent force of gravity and [itex]\theta[/itex] is latitude. This assumes the Earth is spherical, but is a good approximation for a non-spherical earth.
 

1. What is gravitational acceleration?

Gravitational acceleration is the acceleration experienced by an object due to the force of gravity. It is commonly denoted as "g" and has a value of approximately 9.8 meters per second squared on Earth.

2. How is gravitational acceleration calculated?

Gravitational acceleration can be calculated using the formula g = G * M / r^2, where G is the gravitational constant, M is the mass of the larger object, and r is the distance between the two objects.

3. Does gravitational acceleration vary on different planets?

Yes, gravitational acceleration varies on different planets depending on their mass and radius. For example, the gravitational acceleration on Mars is approximately 3.7 meters per second squared, while on Jupiter it is 24.8 meters per second squared.

4. How does air resistance affect gravitational acceleration?

Air resistance can decrease the acceleration of a falling object due to the upward force it exerts. This is why objects with a larger surface area, such as a feather, experience less gravitational acceleration than objects with a smaller surface area, such as a rock.

5. Can gravitational acceleration be negative?

Yes, gravitational acceleration can be negative if the direction of the force of gravity is opposite to the direction of motion of the object. This is commonly seen in objects that are thrown upwards, as they experience a negative acceleration due to the force of gravity pulling them downwards.

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