Equivalence Principle and Gravity

In summary, the conversation discusses the effects of the Earth's slowing rotation on gravitational acceleration and centripetal acceleration. There would be a slight increase in the falling speed of objects due to the reduction of centrifugal acceleration, and the Earth's shape would also change, affecting gravitational acceleration at the poles and equator. It is also mentioned that the acceleration towards the bottom would increase due to the rotation of the Earth.
  • #1
schaefera
208
0
I'm reading a book wherein the Earth's rotation is supposedly slowing down. The author claims that a ball thrown in the air would fall faster and harder... But if the rotation slows, wouldn't the equivalence principle say that the smaller acceleration could also be interpreted as a smaller force of gravity?
 
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  • #2
hi schaefera! :smile:
schaefera said:
… if the rotation slows, wouldn't the equivalence principle say that the smaller acceleration could also be interpreted as a smaller force of gravity?

what acceleration? :confused:

the force of gravity doesn't depend on whether either body is moving

(ok, technically, there will be an undetectably slight difference, caused by the undetectably slightly slower mass of a slower-rotating Earth :wink:)
 
  • #3
Centrifugal acceleration (or the requirement of centripetal acceleration if you like inertial frames) would be reduced. As a result and if we neglect other effects, objects would fall a bit quicker (about 0.3% at the equator) and not perfectly vertical.
One of those other effects: Earth would change its shape a bit, too, and become more spherical. This changes the distance between its surface and the center, reducing gravitational acceleration at the poles and increasing it at the equator even more.
 
  • #4
I was thinking that there would be a smaller centripetal acceleration from us being pulled along with the rotations. And while this would increase apparent weight (normal forces on us would slightly increase due to the lower centripetal acceleration), it wouldn't make gravity stronger for anything else...
 
  • #5
but the author was talking about a falling ball, so there's no normal forces :confused:
 
  • #6
Gravity (as fundamental force) does not get stronger, but the acceleration towards the bottom does.

@tiny-tim: Earth is not a perfect sphere.
 
  • #7
Why does the acceleration toward the bottom get bigger-- what equations could I consider?
 
  • #8
In a frame relative to the surface of earth, and neglecting coriolis force and the non-spherical shape of earth: $$\vec{a}= -\frac{MG}{r^3} \vec{r} - \omega \times (\omega \times \vec{r})$$
where r is the vector between surface and center of earth. I hope I got the sign right.
The second part always points away from the surface (perpendicular on the equator, in other directions elsewhere), if you remove it (by setting ω=0), the acceleration towards the ground gets reduced.
 

1. What is the Equivalence Principle?

The Equivalence Principle is a fundamental concept in physics that states that the effects of gravity and acceleration appear identical to an observer. This means that the laws of physics should be the same for an observer in a uniform gravitational field and an observer in an accelerating frame of reference.

2. How does the Equivalence Principle relate to gravity?

The Equivalence Principle is closely related to the concept of gravity. It suggests that gravity is not a force, but rather a curvature of spacetime caused by the presence of mass or energy. This curvature affects the motion of objects and is what we experience as the force of gravity.

3. What is the difference between the Strong and Weak Equivalence Principles?

The Strong Equivalence Principle states that the effects of gravity are indistinguishable from the effects of any other force, while the Weak Equivalence Principle states that the effects of gravity are indistinguishable from uniform acceleration. The Strong Equivalence Principle is more general and applies to all forms of matter, while the Weak Equivalence Principle is limited to point particles in a vacuum.

4. How was the Equivalence Principle first tested?

The Equivalence Principle was first tested by Galileo in the 16th century, who dropped objects of different masses from the Leaning Tower of Pisa and observed that they fell at the same rate. Later, in the 20th century, Einstein's theory of General Relativity provided a more precise explanation and predictions for the effects of the Equivalence Principle, which have been subsequently verified by numerous experiments.

5. Can the Equivalence Principle be violated?

At present, there is no evidence to suggest that the Equivalence Principle can be violated. However, some theories, such as string theory, suggest that there may be small violations at the quantum level. These violations have not yet been experimentally observed and are still a subject of ongoing research.

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