Topic 12: Gravitational Fields

Question 1

What is a gravitational field?

Answer 1

Gravitational field is a force field in which objects with a mass experience a non-contact force.

Question 2

What are the two types of gravitational fields?

Answer 2

Uniform field: Exerts identical gravitational force on a mass everywhere in the field .
Radial field: Force exerted depends on position of object in the field. As object moves away from center, magnitude of force would decrease as distance between field lines increase.

Question 3

What is the definition and formula of gravitational field strength?

Answer 3

Gravitational field strength is the force per unit mass exerted by a gravitational field on an object.
g= F/m

Question 4

What does newton’s Law of Gravitation show and what is the formula?

Answer 4

Newton’s Law of Gravitation shows that magnitude of gravitational force between 2 objects is directly proportional to product of the 2 masses and inversely proportional to the square distance between them.
F=Gm₁m₂ / r²

Question 5

Derive the formula for a radial field’s gravitational field strength.

Answer 5

F=Gm₁m₂ / r² g= F/m₂; F = m₂g
m₂g = Gm₁m₂ / r²
g = Gm₁ / r²

Question 6

What is gravitational potential?

Answer 6

Gravitational potential at a point is work done per unit mass when moving an object from infinity to that point. As an object moves from infinity to a point, energy is released as GPE decreases.

Question 7

What is the formula for gravitational potential for an object in a radial field?

Answer 7

V = -GM/r

Question 8

What is gravitational potential difference?

Answer 8

Gravitational potential difference is the energy required to move a unit mass between 2 points.

Question 9

What does Kelper’s 3rd law state?

Answer 9

Kelper’s 3rd Law states the the square of orbital period is directly proportional to the radius cubed
T² ∝ r³

Question 10

How is Kelper’s 3rd Law proven?

Answer 10

When an object orbits a mass, it experiences a gravitational force towards the centre. This force acts as a centripetal force so equate mv²/r and GMm / r².
1. Rearrange for v²
2. Change v² to (2π/T)²
3. Rearrange for T²

Question 11

What are the similarities/differences between grav/elec fields?

Answer 11

Similarities
- Follow inverse square law
- Field lines; can be uniform/radial

Differences
- In G fields, force exerted only attractive
- E fields act on charge, G fields act on mass