A gravitational field is the force field that exists in the space around every mass or group of masses. This field extends out in all directions, but the magnitude of the gravitational force decreases as the distance from the other object increases.
The units are N/kg
i.e force per mass
Law of universal gravitation
The law of universal gravitation says
that every object exerts a gravitational pull on every other object. The force
is proportional to the masses of both objects and is inversely proportional to
the square of the distance between them (or the distance between their centers
of mass if they are spherical objects).
Or in another way,
The law of universal
gravitation states that every particle of matter in the universe attracts every
other particle with a force which is directly proportional to the product of
the masses of the particles and inversely proportional to the square of the
distance between them.
Mathematically,
The magnitude of the force is given by
Where m1 and m2
are the masses of the particles, r is their distance apart and G, the constant
of proportionality is the universal constant of gravitation.
G= 6.67 x 10-11
newton metre2/kilogramme2 (Nm2 kg-2)
WEIGHT
A
body on the surface of the earth is attracted towards the Centre of the earth.
It is also attracted by other bodies in the
universe such as the sun, the moon and the planets but these bodies are far
away so their effects are negligible. So it is the attraction of the earth that
dominates.
It means that there is force that tends
to pull a body towards the earth and a force that tends to pull the body away
from the earth.
The force which tends to pull
the body towards the centre of the earth is known as weight.
Let Re be the
radius of the earth, Me the mass of the earth and m is the mass of
the body on the earth’s surface, then
The weight of a body on
the surface of the moon is
Where Mo and Ro
are the mass and the radius of the moon respectively. Although the moon’s
radius is less than that of the earth,
the mass of the
moon is only 1/81.3 of the mass of the earth
while its radius is about
0.274Re.
Because the mass of the
earth greatly exceeds that of the moon, the ‘weight’ of
a man or a spacecraft landing on the moon is much less than the weight on the
surface of the earth.
The force per unit mass of the moon is
only about one-sixth that on the earth,
and a freely falling body on the moon would have an acceleration of about 1.63
ms-2.
Variations of Acceleration
due to gravity
The acceleration of free fall due to gravity
is the acceleration imparted to a body due to its own weight.
If R is the distance of the body from the
centre of the earth, then
The earth is not a perfect sphere and points on the earth’s surface near
the equator are further from the centre than points in the vicinity of the
poles.
The result is that the value of g is least at the equator and
becomes greater with increase in latitude.
Since the earth rotates about its axis, the effect of this also causes g
to increase with latitude.
The value of g also varies with altitude.
Suppose a body is at height h above the sea level
R= Re + h
The value of acceleration of free fall due to gravity is
where go is the value of g at the earth’s surface.
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