Velocity of the earth's rotation at the equator: 1041 mph or 1070 mph?

Factual Questions
1

Hi,

Which answer is more correct. I look forward to your feedback.
davidmich

1.circumference at the equator (24,902 miles) by the time required for the earth to make one full rotation (23 hours and 56 minutes, or 23.93 hours). The velocity is therefore 24,902 / 23.93 = 1041 (rounded) miles per hour.

Or

2.At the equator, the circumference of the Earth is 40,070 kilometers, and the day is 24 hours long so the speed is 1670 kilometers/hour ( 1070 miles/hr).

2

Velocity is relative to a reference frame. So if you just ask how fast is someone or something standing on the equator moving, either is correct.
Rotation however isn’t relative (or it is, but there’s a preferred non-rotating frame you could/should pick), and 1 is the most correct.

3

That conversion seems off. 1670 km equal 1038 miles, which is well within the rounding error of 1.

4

I agree with naita that there is no “absolute” velocity and with kk_fusion that you need to be more careful with your arithmetic, and with your rounding since the difference between solar and sidereal day is less than 0.3%.

But a key point you might be missing is the difference between a solar day (24 hours) and sidereal (or stellar) day. During the time (1 year) it takes the sun to (apparently) rotate around us 365.24 times, the stars rotate around us 366.24 times! Think about it: the sun is (apparently) moving relative to the stars(*). Of course the distinction between solar and sidereal days has been discussed here before. You can watch Dopers fight their ignorance on this in other threads.

    • If the stars are used as an absolute reference, the Earth rotates 366.24 times per year, but one revolution is canceled by the Earth’s other rotation – the annual orbit! This is similar to the reason Magellan’s crew were a day behind when they got to back to Spain. (Or why I’d be two days ahead if I kept track of my own day/night cycles – I’ve circumnavigated West-to-East twice but never unwound. :cool: )
5

How about this, how long does it take the Earth to rotate 360 degrees? Imagine a vector from the center of the Earth pointing to a theoretical point at infinity that does not change direction as the Earth travels through the universe.

6

That is the sidereal day in septimus’s post. 23 hours 56 minutes 4.0916 seconds on average.