Gravitational Field

Question 1

State Newton’s Law of Gravitation and the formula from this law.

Answer 1

Newton’s Law of Gravitation states that the gravitational force between two point masses is proportional to product of their masses and inversely proportional to square of separation/distance between them.
F = GMm/r^2

Question 2

Define gravitational field.

Answer 2

A gravitational field is a region of space where a mass experiences a gravitational force.

Question 3

Define gravitational field strength and its formula.

Answer 3

Gravitational field strength at a point is the gravitational force exerted per unit mass placed at that point.
g = GM/r^2

Question 4

Define gravitational potential Φ and its formula.

Answer 4

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 small test mass from infinity to the point without any change in kinetic energy.
Φ = -GM/r

Question 5

Why is gravitational potential and gravitational potential energy negative?

Answer 5

Direction is taken from the direction of gravitational force exerted. Thus, work done to bring a small test mass to infinity is in the opposite direction to the gravitational force, and thus it is negative.

Question 6

Define gravitational potential energy and its formula.

Answer 6

Gravitational potential at a point in a gravitational field is defined as the work done by an external agent in bringing a small test mass from infinity to the point without any change in kinetic energy.
U = -GMm/r

Question 7

Using Newton’s Law of gravitation and the definition of gravitational field strength, derive the equation g = GM/r^2

Answer 7

g = Gravitational Force/Mass
= F/M
= GMm/r^2 ÷ m
= GM/r^2

Question 8

Define an object’s escape velocity, and using the Principle of Conservation of Energy, derive its formula as v = √2gr.

Answer 8

The escape velocity of a body is the minimum velocity required such that said body is able to travel to infinity away from a planetary mass.
Ki + Ui = Kf + Uf
½mv^2 + (-GMm/r) = 0 (taking final point as infinity)
v = √2GM/r = √2gr (g = GM/r^2)

Question 9

What are the features of a geostationary satellite?

Answer 9

A geostationary satellite is in geostationary orbit and maintains the same position relative to a point on a planet’s surface.

• Orbital period is same as the planet’s rotation period
(24 hours for Earth)
• Plane of orbit is the same as the planet’s equator
• Direction of orbit is same as the planet’s direction
of rotation (eastward for Earth)