0

If the earth is rotating at some $465~\text{m}/\text{s}$ at the equator and that's really fast.

  1. Shouldn't we in that case be in orbit with the earth just not fast enough?
  2. How fast do we need to move?
  3. If the earth stopped rotating (gradually), shouldn't gravity increase significantly?
  4. Do satellites need extra speed when they are released or does it just depend on their inertia from the earth's rotation?
  5. If the satellite decelerated against the earth direction of rotation will it fall?
  6. If the earth rotated extremely fast, shouldn't the earth's crust along with everything else get ejected away by the centrifugal force?

I'm sorry if the questions cover many matters but I preferred to ask them all at once instead of asking each separately.

Bernhard
  • 5,085
Force
  • 558

1 Answers1

2

The acceleration of uniform circular motion is a very basic computation that we do for first year students. $$ a = \frac{v^2}{r} $$ which for someone standing on the Earth's equator comes to $$ a_\text{equator} \approx \frac{\left(465\text{ m/s}\right)^2}{6400\text{ km}} = 0.03\text{ m/s}^2$$ or less than 1% of g.

That is a measurable quantity, but not very significant. Indeed fluxuations of local $g$ at that level can (and do) occur simple due to local deposits of heavy ore. Mining and oil companies use precise gravitation maps in surveys for exactly this kind of reason.