Earth's Frame

[noithatgooccho]

I feel somewhat stupid that it never occurred to me before, and I'll feel even stupider if I'm wrong. But, assuming I'm correct, here on earth I am not in an inertial reference frame, am I?

Since we are rotating on an axis along with orbiting the sun (and orbiting whatever else), we are experiencing a centripetal acceleration are we not? That would mean time appears to pass a tiny bit slower on earth than it would for something in space that is at rest.

 

[Hans Blaster]

I feel somewhat stupid that it never occurred to me before, and I'll feel even stupider if I'm wrong. But, assuming I'm correct, here on earth I am not in an inertial reference frame, am I?

Since we are rotating on an axis along with orbiting the sun (and orbiting whatever else), we are experiencing a centripetal acceleration are we not? That would mean time appears to pass a tiny bit slower on earth than it would for something in space that is at rest.

A rotating reference frame (for example, the Earth) has pseudo (or fictitious) forces when you view things from the rotating frame itself. The Coriolis force is one of these fictitious forces. It is noticeable only on large scales. The launching of rockets and long-range artillery shells need to account for the Coriolis force. The other place this is seen in the bending of the winds in large scale weather systems. Large storms spin the opposite directions in the two hemispehrs. (Contrary to popular myth, the swirling of water down a drain is not affected noticeably by the Coriolis effect. The spin direction is driven by the (small) angular momentum in the basin.)

The orbit of the Earth around the Sun and the Sun around the Galactic center also mean that these aren't technically inertial frames either, but the effects are very small.

 

[essentialsaltes]

here on earth I am not in an inertial reference frame, am I?

That's correct. As Hans has mentioned, hurricanes and ballistics/rockets show these effects in the real world. As does the Foucault pendulum you may have seen at some science museum or observatory.

That would mean time appears to pass a tiny bit slower on earth than it would for something in space that is at rest.

It is a very very very tiny amount.

 

[Subduction Zone]

It is a very very very tiny amount.

But at times significant. GPS has to be corrected using both Special and General Relativity.

 

[Shemjaza]

But at times significant. GPS has to be corrected using both Special and General Relativity.

I had assumed that it was from the gravity well, not the spin velocity.

 

[Subduction Zone]

I had assumed that it was from the gravity well, not the spin velocity.

Both are needed, though the effect of General Relativity is greater. An orbiting clock loses about 7 micro seconds a day compared to a stationary point on Earth due to General Relativity. And it gains about 45 micro seconds a day due to Special Relativity:

GPS and Relativity

 

[sjastro]

I had assumed that it was from the gravity well, not the spin velocity.

Even if the object is stationary in a gravitational field with acceleration -g, it is the same as being accelerated a in the opposite direction when a = g.

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This is Einstein's equivalence principle.
An atomic clock "doesn't know" if time dilation is due to being stationary in a gravitational field or being accelerated in a gravity free field.

 

[Astrophile]

Both are needed, though the effect of General Relativity is greater. An orbiting clock loses about 7 micro seconds a day compared to a stationary point on Earth due to General Relativity. And it gains about 45 micro seconds a day due to Special Relativity:

GPS and Relativity

If I understand this correctly, the orbiting clock gains a total of about 38 microseconds a day due to the combined effects of Special and General Relativity. Over the age of the Earth (4540±20 million years) this amounts to an error of about 729 days, or almost exactly two years.

 

[haruko176]

I had assumed that it was from the gravity well, not the spin velocity.