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Apparent weightlessness can also be experienced on earth. Any time you
jump up in the air, you experience the same kind of apparent weightlessness
that the astronauts do. While in the air, you can lift your arms more easily
than normal, because gravity does not make them fall any faster than the
rest of your body, which is falling out from under them. The Russian air
force now takes rich foreign tourists up in a big cargo plane and gives them
the feeling of weightlessness for a short period of time while the plane is
nose-down and dropping like a rock.
10.4Vector Addition of Gravitational Forces
Pick a flower on earth and you move the farthest star.
Paul Dirac
When you stand on the ground, which part of the earth is pulling down
on you with its gravitational force. Most people are tempted to say that the
effect only comes from the part directly under you, since gravity always
pulls straight down. Here are three observations that might help to change
your mind:
•
If you jump up in the air, gravity does not stop affecting you just
because you are not touching the earth: gravity is a noncontact force.
That means you are not immune from the gravity of distant parts of
our planet just because you are not touching them.
•
Gravitational effects are not blocked by intervening matter. For
instance, in an eclipse of the moon, the earth is lined up directly
between the sun and the moon, but only the sun’s light is blocked
from reaching the moon, not its gravitational force — if the sun’s
gravitational force on the moon was blocked in this situation,
astronomers would be able to tell because the moon’s acceleration
would change suddenly. A more subtle but more easily observable
example is that the tides are caused by the moon’s gravity, and tidal
effects can occur on the side of the earth facing away from the moon.
Thus, far-off parts of the earth are not prevented from attracting you
with their gravity just because there is other stuff between you and
them.
•
Prospectors sometimes search for underground deposits of dense
minerals by measuring the direction of the local gravitational forces,
i.e. the direction things fall or the direction a plumb bob hangs. For
instance, the gravitational forces in the region to the west of such a
deposit would point along a line slightly to the east of the earth’s
center. Just because the total gravitational force on you points down,
that doesn’t mean that only the parts of the earth directly below you
are attracting you. It’s just that the sideways components of all the
force vectors acting on you come very close to canceling out.
A cubic centimeter of lava in the earth’s mantle, a grain of silica inside
Mt. Kilimanjaro, and a flea on a cat in Paris are all attracting you with their
gravity. What you feel is the vector sum of all the gravitational forces
exerted by all the atoms of our planet, and for that matter by all the atoms
in the universe.
Gravity only appears to pull straight
down because the near perfect sym-
metry of the earth makes the sideways
components of the total force on an
object cancel almost exactly. If the
symmetry is broken, e.g. by a dense
mineral deposit, the total force is a little
off to the side.
Section 10.4Vector Addition of Gravitational Forces