the speed of a satellite while bringing it into orbit

Maniac wrote:

Hi!

the shuttle starts on earth, it has a speed of 72360km/h according to
the rotation of the earth.

Erm, well, the Earth actually rotates at about 1,609km/h at the
equator. Slower the farther away you get from the equator.

So if this is true, what happens if the
shuttle gets out of the athmosphere? Is the speed reduced
automatically, or has the shuttle now the task to de-/accellerate to
the correct speed for an orbit position?

Not the speed, but the *acceleration* (ie. the burning fuel) is stopped
completely. The shuttle will keep travelling at the speed it had before
engine cut-off since there is no atmosphere to slow it down. From
launch, the shuttle accelerates until it reaches the speed it needs for
the orbit they want and then turn the engines off. Once in space,
changing orbits significantly actually takes a lot of fuel to
accomplish, so they launch into the orbit they want to start with.

So, is any shuttle leaving
the athmosphere "flying" with the speed of the earth rotation?

They are *all* flying faster than the speed of the Earth's rotation. As
seen by an observer NOT on Earth, that is. Since we ARE on Earth, we
don't count the Earth's spinning speed when talking about how fast
something is going (ie. you'd say walk about 8km/h an hour, not 1617km/h
or 1601km/h - depending on direction of travel)

The shuttle starts out with the speed of the Earth at it's latitude and
heads off in a generally Easterly direction to take advantage of that
speed. If it were launched from, say, Calgary and headed West, it would
require much more fuel to get into orbit since it has less 'Earth speed'
to take advantage of, and is heading against the rotation of the Earth.
Which is, of course, why it launches from the southern part of Florida:
lots of Earth speed to take advantage of.

As for acceleration/deceleration in orbit: if the shuttle slowed down a
bit, gravity would pull it closer to the Earth and the shuttle would
then be going faster than it was. Likewise, if the shuttle sped up a
bit, it would fly farther from the Earth and therefore be going slower.
Welcome to the fun and crazy world of orbital mechanics

Cheers,
Kent