Time on the moon? Slower?

Quantum Quack

Quantum Quack

Life's a tease...
Valued Senior Member
Hi guys,

Say we take the assumption that gravity and time are interrelated in some definitive fashion.
It has been suggested for instance that time travells slower at the top of mount everest than it does at sea level the reason being gravity ( pressure) ( please correct me if I am wrong)

So if one takes this logic a little further could it be suggested that time travells much slower on the moon than on earth?
Due to it's lighter gravity.

If the moons gravity was the same as sea level earth gravity would the two compare equally?

Maybe this is a silly question....I hope not
 
Not a silly question.

Actually, time goes slower in a stronger gravity field. So, on the moon, your watch will run a little faster than on Earth.
 
ahhh I see.

With all the space shuttle work in low gravity have they been able to record a noticeable difference between very low gravity of orbit and that of sea level?

According to your answer the guys in the shuttle would be travelling in time faster than at sea level, there fore they would be ageing quicker? From a sea level perspective.

I hope I've got the logic right
 
Ugh, hard to comment here.... I'm confused as how lightwaves affect time (If it has something to do with gravity, it must include lightwave too, I guess). Or am I miserably out of line here?
 
Originally posted by Quantum Quack
ahhh I see.

With all the space shuttle work in low gravity have they been able to record a noticeable difference between very low gravity of orbit and that of sea level?

According to your answer the guys in the shuttle would be travelling in time faster than at sea level, there fore they would be ageing quicker? From a sea level perspective.

I hope I've got the logic right
Click to expand...

Two things here.

The time dilation due to gravity is not a consequence of the force of gravity you feel, but is due to how deep you are in the gravity field.

A person standing at sea level is 6378 km from the center of the Earth.

I believe the shuttle orbits at about 300 km altitude. At which point they are still quite deep in the Earth's gravity well. (despite the fact that the astronauts are in freefall and don't feel it. )

The formula for gravitational time dilation(as measured by someone removed far form the source of gravity) is:

T1 = T0/sqrt(1-2GM/Rc²)

Thus for a person sitting at sea level, you get

Te = 1/(sqrt(1- 2*6.672e-11 * 6e24 / (6.378e6 * 3e8²) = 1.0000000006975
for the time difference factor.

For the Shuttle, you get:
Ts = 1/(sqrt(1- 2*6.672e-11 * 6e24 / ((6.378e6+300000) * 3e8²) =
1.000000000666

for the factor.

Comparing these two, you find that the clocks on the shuttle run only 1.000000000031 times faster than one at sea level due to gravity.

The second thing to consider is that the shuttle, in order to maintain orbit must travel at 7743 m/sec relative to someone at sea level.

The time dilation due to relative velocity is

T1 = T0/sqrt(1-v²/c²)

so you get a factor of

Ts = 1/sqrt(1- 7743²/3e8²) =1.0000000003330

Which means that due to velocity, the shuttle clock run this many time slower than one resting at sea level.

Combining these two factors, we find that the shuttle clock ends up running at a rate of 0.9999999997 times that of the sea level clock. IOW, it ends up running just slightly slower.

The upshot is that after 105 years as measured by the sea level clock, the shuttle clock will be slow by one second.

P.S. One thing I did not take into account was the motion of the person at sea level due to the rotation of the Earth, which is about 444 m/s for someone on the Equator. This would reduce the relative velocity between the two clocks slighty and change the final time factor difference; but not enough to prevent the shuttle clock form being the one that runs slower.
 
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To solve for the time difference on the moon:

Time factor for earth sea level(as calculated in last post.):

1.0000000006975

Time factor for the moon. (using the moon's mass and radius).

1.0000000000314

Comparing, we get that a clock runs 1.000000000666 times faster on the moon. as a rough estimate.

This estimate doesn't take into account that the moon is in the Earth's gravity field itself, or the Moon's orbital velocity. Both these factors would reduce this difference slighty.
 
Janus, thanks for all that, fantastic really.

Does the math allow for the sudden shifts in gravitational intensity that occur.

Or does the math consider the gravity well to be a more smooth distribution?
 
In a Black Hole, I mean the Event Horizon, does it take a infinate amount time to reach the entrance. Or is it true that your watch wouldnt work?
 
Guyute
For the person falling into the black hole ie. towards the event horizon, the closer they get to the EH, the slower time runs, so essentially, from their point of view, they never reach the event horizon. Their watch would continue to work, presuming that the gravitational stresses were not too great, etc.
For an observer, stationary relative to the BH, and outside its gravitationl well, the person falls in normally, the only abnormality being the redshifting of the image.
 
Originally posted by geodesic
Guyute
For the person falling into the black hole ie. towards the event horizon, the closer they get to the EH, the slower time runs, so essentially, from their point of view, they never reach the event horizon. Their watch would continue to work, presuming that the gravitational stresses were not too great, etc.
For an observer, stationary relative to the BH, and outside its gravitationl well, the person falls in normally, the only abnormality being the redshifting of the image.
Click to expand...

No I thought it was the opposite. To the guy falling in, everything is normal and the observers on the outside sees things slow down as he gets closer.

This would explain the gravitational 'redshift' u speak of!
 
I once read an article similar to what John said: that the 'falling' person would see strange outside world, while someone from safe spot would see the fallen falling with decceleration (is that a word?).
 
No I thought it was the opposite. To the guy falling in, everything is normal and the observers on the outside sees things slow down as he gets closer.
Click to expand...

I may not have made it clear, but that's pretty much what I meant. Although the guy falling towards the black hole feels that he is falling normally, he never reaches the event horizon from his point of view.

As for the outside observers, why would they see him deccelerating? I'm prepared to believe I was wrong, as I wasn't 100% sure when I wrote the first post.
 
Originally posted by geodesic
As for the outside observers, why would they see him deccelerating? I'm prepared to believe I was wrong, as I wasn't 100% sure when I wrote the first post.
Click to expand...

For the same reason u see the redshift. light is taking longer to reach the eyes of an outside observer until the point comes where light cannot escape at all.
 
For the same reason u see the redshift. light is taking longer to reach the eyes of an outside observer until the point comes where light cannot escape at all.

Granted, as an object moves away, light will take longer to get to the observer, but that is not the cause of redshift or the appearance of deceleration.

The light loses energy as the object moves closer to the black hole and must climb out of the gravity well, shifting the light to the lower end of the spectrum. And, as the gravity field is stronger for the object then the observer, it will appear to slow down to the observer.
 
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