21 Gravitational Fields

Question 1

what is the strength of a gravitational field, g?

Answer 1

the force per unit mass on a small test mass placed in the field

Question 2

what is the formula for g?

Answer 2

g = F/m

Question 3

what else is g?

Answer 3

the acceleration of a freely falling object

Question 4

what is a radial field?

Answer 4

a field in which the field lines are straight and converge or diverge as if from a single point

Question 5

what is a uniform field?

Answer 5

a region where the field strength is the same in magnitude and direction at every point in the field

Question 6

what is the gravitational potential energy?

Answer 6

the energy of an object due to its position

Question 7

what is gravitational potential, V?

Answer 7

the work done per unit mass to move a small object from infinity to that point

Question 8

what is the formula for V?

Answer 8

V = W/m

Question 9

what is an equipotential?

Answer 9

a surface with a constant gravitational potential

Question 10

what is a potential gradient?

Answer 10

the change in the potential per metre at a point

Question 11

what is the formula for change of potential?

Answer 11

potential gradient = ΔV/Δr (Δr = small distance

Question 12

what is gravitational field strength equal to?

Answer 12

negative of the potential gradient
g = -ΔV/Δr

Question 13

what is Kepler’s 3rd law?

Answer 13

r³ ∝ T³
r = average radius of orbit
T = time period for orbit

Question 14

what is Newton’s law of gravitation?

Answer 14

the gravitational force F between two point masses m₁ and m₂ at a distance r apart is given by:
F = Gm₁m₂ / r²

Question 15

what is G?

Answer 15

the universal constant of gravitation

Question 16

what is a formula for g using Newton’s law of gravitation?

Answer 16

g = GM / r²

Question 17

how does g vary with distance from the centre of a spherical planet?

Answer 17

follows the inverse square law

Question 18

what is escape velocity?

Answer 18

the minimum velocity an object must be given to escape from the planet when projected vertically from the surface

Question 19

how do you derive the escape velocity formula?

Answer 19

• substitute V = -GM/r into W = mV
• equate Eₖ = 1/2(mv²) to W = mV
• Rearrange to make v the subject

Question 20

what is a formula for gravitational potential?

Answer 20

V = - GM/r

Question 21

How can you prove Kepler’s third law by using Newton’s law of gravitation?

Answer 21

• g = GM/r² and g = v²/r (centripetal acceleration)
• equate these and v² = GM/r
• v = 2𝜋r / T
• so, (2𝜋r)² / T² = GM / r
• rearrange, r³/T² = GM/4𝜋²

Question 22

what are geostationary satellites?

Answer 22

orbits the earth directly above the equator and has a time period of exactly 24 hours.
This means it remains in a fixed position above the equator

Question 23

what is the total energy of a satellite?

Answer 23

E = gravitational potential energy + kinetic energy