Gravitational Field

Question 1

State Newton’s Law of Gravitation

Answer 1

Newton’s Law of gravitation states that two point masses attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
F = GMm/r^2

Question 2

Define gravitational field

Answer 2

A gravitational field is a region of space in which a mass experiences a force due to the presence of another mass.

Question 3

Define gravitational field strength

Answer 3

Gravitational field strength at a point in a gravitational field is defined as the gravitational force per unit mass acting on a test mass placed on that point.
g = F/m = GM/r^2

Question 4

Define gravitational potential energy

Answer 4

The gravitational potential energy of a mass at a point in a gravitational field is defined as the work done by an external agent in bringing the mass from infinity to that point
U = -GMm/r
F = -dU/dr

Question 5

Define gravitational potential

Answer 5

The gravitational potential at a point in a gravitational field is defined as the work done per unit mass by an external agent in bringing a test mass from infinity to that point
φ = -GM/r = U/m
g = -dφ/dr

Question 6

How to calcuate escape velocity?

Answer 6

-GMm/r + 1/2mv^2 = 0
v = √ 2GM/r

Question 7

Why gravitational potential is negative?

Answer 7

Gravitational potential at infinity is zero
Since gravitational force is atttractive in nature, to bring a mass from infinity to a point in the gravitational field, the direction of the external force is opposite to the direction of displacement of the mass.
This results in negative work done by the external force.
Hence, based on its definition, gravitational potential has a negative value.

Question 8

Why does an astronaut experience weightlessness?

Answer 8

The only force acting on the system is the gravitational force of Earth on the astronaut, F.
Since the system is in a circular orbit around the Earth, F provides for the centripetal force required for the system to move in a circular orbit.
Hence, the astronaut, space vehicle, and weighing machine all experience the same acceleration of g.

Question 9

Geostationary orbit

Answer 9

-directly above earth’s equator
-orbital period equal to earth rotational period (24 hrs)
-orbit from West to East