9 Gravitational Field

Question 1

Newton’s Law of Gravitation

Answer 1

The force of attraction between any two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation
F = Gm(1)m(2)/r^2

Question 2

Gravitation constant, G

Answer 2

G = 6.67*10^-11 N m^2 kg^-2

Question 3

Kepler’s Third Law

Answer 3

Gravitational force provides for centripetal force
F(g) = F(resultant)
Solving:
T^2 directly proportional to r^3

Question 4

Binary star

Answer 4

m(A) r(A) = m(B) r(B)

Question 5

Geostationary orbit

Answer 5

1. Only one such orbit around Earth (above the equator and a fixed distance 4.2*10^7 m
2. Orbital period is 24h
3. Plane of orbit coincides with the equatorial plane
4. Satellite orbits west to east

Question 6

Gravitational field

Answer 6

A region in space where a mass experiences a gravitational force acting on it

Question 7

Gravitational field strength, g

Answer 7

The gravitational force per unit mass acting on a small mass placed at that point
g = F/m
g = GM/r^2

Question 8

Gravitational potential energy

Answer 8

Work done by an external agent in bringing the mass from infinity to that point without any change in kinetic energy
GPE= -GMm/r

Question 9

Why is gravitational potential energy negative?

Answer 9

1. Work done is taken with infinity as reference, hence gravitational potential energy at infinity is zero
2. Due to attractive nature of gravity, the force by external agent is directed away from the mass producing the gravitational attraction
3. Force by external agent is opposite is direction to the displacement of the mass, m

negative sign does not indicate direction, only means that the potential energy at a point closer to the fixed mass is lesser compared to the potential energy at infinity which is defined as 0

Question 10

Gravitational potential, Φ

Answer 10

Work done per unit mass by an external agent in bringing a mass from infinity to that point
Φ = GPE/m = -GM/r

Question 11

Escape velocity

Answer 11

Minimum kinetic energy required is equal to the gain in gravitational potential energy in reaching infinity
1/2 mv^2 = GMm/r
v = √(2GM/r)