Gravitational Field

Question 1

Newton’s Law of Gravitation

Answer 1

only applicable to sizes that are small compared to their separation

Newton’s law of gravitation states that two point masses attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the separation between them.
( F = GMm / r² )
- uniform density

Question 2

Define gravitational field

Answer 2

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

Question 2

Define gravitational field strength

Answer 2

The gravitational field strength at a point in a gravitational field is defined as the gravitational force per unit mass acting on a small test mass placed at that point.
#the per unit can be replace with the kg or g depending on qn.

g = F / m , g = GM / r²

Question 3

Similarities between solid and hollow sphere

Answer 3

The gravitational field strength outside a uniform solid sphere and hollow sphere varies inversely with r².

The direction of gravitational field strength acts towards the centre of mass M.

Question 3

Difference between solid and hollow sphere

Answer 3

The gravitational field strength inside a uniform solid sphere varies linearly with distance r from its centre while the gravitational field strength inside a hollow sphere is zero.

Question 3

Define gravitational potential energy

Answer 3

Gravitational potential energy in the work done by an external agent in bring the mass from infinity to that point.
( U = -GMm/r )

Question 4

What is the GPE at infinity

Answer 4

Zero. At infinity, the gravitational force due to mass M is zero.

Question 4

Define escape velocity

Answer 4

The minimum value of the initial speed such that the object will escape the Earth’s Gravitational field and reach infinity.

Question 5

Escape velocity equation

Answer 5

E at earth surface = E t infinity
-GMm/R + 0.5mv² = 0 + 0
0.5v² = GM/R
v = √(2GM/R)

Question 6

Define gravitational potential

Answer 6

Gravitational potential is the work done per unit mass by an external agent in bringing a small test mass from infinity to that point.
φ = U/m
φ = -GM/r

Question 7

Kepler’s third law

Answer 7

The square of the period of revolution of the planets is directly proportional to the cubes of their mean distances from the sun.
( T² = r³ )

Question 8

List advantage of geostationary satellite

Answer 8

There is continuous surveillance of the region under it
It is easy for the ground station to communicate with it as it is permanently within view.
Due to high altitude, the satellite can transmit and receive signals over a large area.

Question 9

List disadvantage of geostationary satellite

Answer 9

The distance from earth’s surface is large compared to Low-Earth Orbit satellites, thus leading to:
- a significant loss of signal strengths
- poorer resolution in imaging satellites
- time-lag in telecommunication