Equivalence Principle and Gravity


by schaefera
Tags: equivalence, gravity, principle
schaefera
schaefera is offline
#1
Dec28-12, 04:04 PM
P: 208
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?
Phys.Org News Partner Physics news on Phys.org
Physicists design quantum switches which can be activated by single photons
'Dressed' laser aimed at clouds may be key to inducing rain, lightning
Higher-order nonlinear optical processes observed using the SACLA X-ray free-electron laser
tiny-tim
tiny-tim is offline
#2
Dec28-12, 04:22 PM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,167
hi schaefera!
Quote Quote by schaefera View Post
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?

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 )
mfb
mfb is offline
#3
Dec28-12, 04:28 PM
Mentor
P: 10,813
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.

schaefera
schaefera is offline
#4
Dec28-12, 04:30 PM
P: 208

Equivalence Principle and Gravity


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...
tiny-tim
tiny-tim is offline
#5
Dec28-12, 04:36 PM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,167
but the author was talking about a falling ball, so there's no normal forces
mfb
mfb is offline
#6
Dec28-12, 04:58 PM
Mentor
P: 10,813
Gravity (as fundamental force) does not get stronger, but the acceleration towards the bottom does.

@tiny-tim: Earth is not a perfect sphere.
schaefera
schaefera is offline
#7
Dec28-12, 06:10 PM
P: 208
Why does the acceleration toward the bottom get bigger-- what equations could I consider?
mfb
mfb is offline
#8
Dec29-12, 08:49 AM
Mentor
P: 10,813
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.


Register to reply

Related Discussions
Equivalence principle - are all accelerations actually equivalent to gravity? Special & General Relativity 14
Principle of Equivalence Special & General Relativity 5
The Equivalence Principle Special & General Relativity 0
Equivalence of DAlembert's principle and Action Principle Classical Physics 4
gravity / equivalence principle Special & General Relativity 10