Answer 1:
A planet's gravity extends far out into space.
Despite what you have heard about
"weightlessness" in space, the space
station and its crew experience gravity about 80%
as strong as gravity on Earth's surface. The
weightlessness effect is due to both station and
astronauts "falling" along the same path, so the
astronauts don't seem to move inside the station.
If you were in a falling elevator, you would
also float like the astronauts until the elevator
hit the basement floor. The space station doesn't
hit the ground because it orbits at 5 miles per
second, which is so fast that the earth's surface
curves out from under the station as it falls.
The station falls in a circle, along with its
astronauts inside.
Isaac Newton discovered that the force of
gravity between any two objects is
F =
G*m_{1}*m_{2}/r^{2} ,
where the m's are the masses of the objects, r is
the distance between their centers, and G is a
constant number. For your question, the important
thing is that the force falls off with the square
of the distance between the objects.
One additional Earth radius (~4000 miles) above
our heads, Earth's gravity is 1/4 as strong as it
is down here. 8000 miles above our heads (3 Earth
radii from Earth's center), gravity is 1/9 as
strong, etc.
Most planets have moons, and from studying
their orbits, it is easy to determine the strength
of gravity required to keep the moons in their
orbits. You get the planet's gravity at the
distance of the moon's orbit, but knowing this,
just multiply by (Moon's orbit radius /
planet's radius)^{2}, and you get the
gravity on the planet's surface.
For moonless planets, surface gravity can still
be determined by measuring how their gravity
causes slight changes in the orbits of neighboring
planets. Scientists determine the strength of
the gravity which made the perturbation, and
then they multiply by (distance between planets
/ planet's radius)^{2} , as before, to
get the surface gravity. This method was
actually used to discover Neptune they
noticed a slight wobble in Uranus's orbit, and
calculated that it could only have been caused by
a planet in Neptune's position.
The only way to remotely determine the gravity
of lone asteroids is to send a probe flying
past and measure its deflection based on the
timing of its radio signals.
