
Hello, A couple of my students were wondering
about the following questions, and rather than
give a partially correct answer I was hoping you
could give me the complete answer. Thank you so
much. 1. Why is there only some gravity on
earth. Yes, I know that 1/6 of the earth's
gravity is found on the moon, but why? 2. If
there was no gravity on earth would there be
hurricanes and tornadoes?

Question Date: 20040910   Answer 1:
The value of the gravitational acceleration on
the surface of a planet of radius R and mass M is
g = GM/R^{2}. So the gravity on the
moon is 1/6th that of Earth because the moon is
far less massive than the Earth and has a
different radius(R) as well. The mass of the
moon is 1/82nd of the earth's and the
radius of the earth is 6300 km whereas for the
moon its only 1738 km.
There are motions in the atmosphere and
oceans because of the rotation of the earth and
because of the gravity. If there was "no
Gravity" the earth would not be here! The
earth accreted from a bunch
(trillions upon trillions) of rocks. What
forced these rocks to accrete?
GRAVITY!!!!!!!!!!
So with no gravity the earth's atmosphere
would drift off to space within a few years!!! no
atmosphere, no terrible IVAN's !!!!!!!
  Answer 2:
Every object in the Universe, planets, stars
etc., and also smaller objects such as moons
exert a gravitational pull. This means that
other objects will be drawn towards them. The
strength of the attraction is directly related to
the size of the planet or moon. Therefore as the
moon is a fraction of the size of the earth it's
gravitational pull is 1/6th as strong as that of
the earth. Gravity is a basic property of every
object in the universe and cannot be 'shared'
between objects as your question suggests. We
expect the moon to have less gravity because it is
smaller, the force felt by people walking on the
moon is independent to any force felt by people
walking on the earth.
If there was no gravity on earth there would
be no atmosphere (i.e. no air to breath) so there
would not be wind at all. There would also be no
life on earth!!
Weather patterns such as hurricanes and
tornadoes are caused by complex interactions
between rising and sinking air (convection) as a
result of the sun's heat. You could look into this
in more detail on the web probably. They are not
affected by gravity however, gravity is a
constant force.
  Answer 3:
The gravitational acceleration that we feel on
the surface of the earth is (approximately)
governed by the following equation:
a = GM/R^{2}
where: G = the Gravitational constant (which
presumably is the same everywhere in the
universe) M = mass of the Earth (in kilograms,
for example) R = radius of the Earth (in
meters, for example).
For the Earth, if you plug in the appropriate
numbers, you get acceleration equals 9.8 meters
per second squared. Since the
moon or another planet or the sun have different
values for mass and radius, you would get a
different answer for the gravitational
acceleration on the surface of that object.
For example, the Moon's radius is 0.27 of the
earth's and the moon's mass is 0.012 of the
earth's mass. So if you take
0.012/(0.27)^{2} you get 0.16 which is
about 1/6.
If there was no gravity on earth there
wouldn't be hurricanes or tornadoes because
there wouldn't be an atmosphere! Gravity is
necessary to keep the atmosphere from literally
floating away.
  Answer 4:
The acceleration of gravity on the surface of
the earth (or any spherical planet) depends
both on the planet's total mass and its
density.
To a good approximation the acceleration
a = G*M/(R*R) where G is the gravitation
constant, M is the mass and R is the radius.
So, on the moon, the mass is much less, but
the radius is also much lower, giving the moon
a surface acceleration of about 1/6 that of the
earth.
Since the two bodies are so close (238,000
miles)lunar gravity does affect the earth,
mainly this is visible in the tides. (Earth's
gravity keeps the moon in orbit around the Earth).
Without gravity, there could not be hurricanes
and tornadoes since both rely on energy gained
from falling air masses.
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