Earth's Frame

[quaternion]

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.

 

[Subduction Zone]

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.

Correct. The Earth is not an inertial frame of reference. In fact an inertial frame of reference is an ideal that does not exist in physics since a body would have to be totally unaffected by gravity. There are situations that are close, at least relative to here. But the concept is used more for thought experiments than for anything else.

Frames of reference are still highly useful. What one runs into most of the time for real world situations are Galilean transformations:

The Galilean Transformation

Those are ones where relativistic effects are small and can be ignored.

 

[quaternion]

OK. I know the effect would be small, but how is it calculated? I remember calculating such things in my physics classes, but it's been a long time.

I'm doing some rounding and approximating to make it easy. Suppose the sun is at rest, and ignore rotation, so we only need to calculate the earth's orbit about the sun. At an average distance of 150,000,000 km at a speed of 107,000 km/h, how much slower is time moving on earth?

 

[Subduction Zone]

OK. I know the effect would be small, but how is it calculated? I remember calculating such things in my physics classes, but it's been a long time.

I'm doing some rounding and approximating to make it easy. Suppose the sun is at rest, and ignore rotation, so we only need to calculate the earth's orbit about the sun. At an average distance of 150,000,000 km at a speed of 107,000 km/h, how much slower is time moving on earth?

For that you need Lorentz transformations if you want to do it yourself:

Lorentz transformation - Wikipedia

Or you could cheat:

Time dilation/length contraction

You can punch in the velocity and the site calculates the answer for you.

 

[quaternion]

I found something similar in my own search, but it seemed too simple, so I thought I must be missing something. Anyway, I got a time dilation of 1.0000174. Interesting.

It's a ridiculous number, but if the speed of the earth's orbit was 0.999999999996c, then a thousand years would seem like a day.

 

[Subduction Zone]

I found something similar in my own search, but it seemed too simple, so I thought I must be missing something. Anyway, I got a time dilation of 1.0000174. Interesting.

It's a ridiculous number, but if the speed of the earth's orbit was 0.999999999996c, then a thousand years would seem like a day.

Why ridiculous? It has been tested and confirmed many different times including with particles moving at a very high rate of speed. Much lower amounts of dilation have been directly measured as well. It still makes my brain hurt at times because we live in a world where the concept of simultaneity appears to be real.

 

[Radagast]

I found something similar in my own search, but it seemed too simple, so I thought I must be missing something. Anyway, I got a time dilation of 1.0000174. Interesting.

The Hafele–Keating experiment (Hafele–Keating experiment - Wikipedia) flew accurate clocks on aircraft, and tested both special-relativistic effects due to speed and general-relativistic effects due to lower gravity at altitude.

Their clocks gained 273 nanoseconds flying west, and lost 59 nanoseconds flying east.

 

[essentialsaltes]

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

That's right. Hence the Coriolis 'force', which is a fictitious force due entirely to our non-inertial frame.