Gravitation - Satellite with same w as earth

AI Thread Summary
The discussion centers on calculating the distance of a satellite with the same angular velocity as Earth, leading to two different results: 42,300 km and 36,000 km. The first calculation mistakenly used the orbital radius instead of the correct height above Earth's surface. The correct height of a geostationary satellite is approximately 36,000 km, which, when added to Earth's radius of about 6,400 km, gives a total distance of 42,300 km. Additionally, the thread highlights that the Earth's rotational period is slightly less than 24 hours, affecting calculations. The confusion arises from misremembering the orbital radius, underscoring the importance of accurate data in physics problems.
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Homework Statement


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The Attempt at a Solution



as w is same as w of Earth ... so T is 24 hrs

so its like a geostationary satellite
if i use w to find distance ... it comes like 42300 KM
if we used t=24 hrs to find distance ... it comes 36000 KM

what the hell is this? ... 1 question 2 answers?

and answer to (b) is 6hrs
so Time period is 24hrs is confirmed
 

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Show your calculations both ways. At least one of them has an error. :smile:

It might be of interest to know that the rotational period of the Earth on its axis is not quite 24 hours. The sidereal day is 23h 56m 4.091s, or 23.9344696 hours.
 
gneill said:
Show your calculations both ways. At least one of them has an error. :smile:

It might be of interest to know that the rotational period of the Earth on its axis is not quite 24 hours. The sidereal day is 23h 56m 4.091s, or 23.9344696 hours.

Oh I'm really sorry.
i did a question to find height of geostationary satellite above Earth surface and memorized it incorrectly as orbital radius

36000KM + 6400KM ≈ 42300KM
 

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