Gravitational Fields

Question 1

What are some properties of the gravitational force between 2 masses?

Answer 1

Always attractive, prop to product of masses, follows an inverse square law

Question 2

What is a force field?

Answer 2

A region in space where objects experience non-contact forces

Question 3

How do you find acceleration in a grav field?

Answer 3

Combine g = F/m and F = ma to get a = g

Question 4

How do you find the field strength for a radial grav field?

Answer 4

Combine g = F/m and F = Gm1m2 / r^2 to get g = GM/r^2.

Question 5

What is the grav field strength at the surface for a planet of radius R?

Answer 5

g = GM / R^2

Question 6

What is the grav potential energy at a point in a grav field?

Answer 6

E(p) = Vm = -GMm / r, for a mass m in a field caused by a mass M

Question 7

What are the units of grav potential?

Answer 7

Jkg^-1

Question 8

Where is grav. potential zero?

Answer 8

At an infinite distance away from a mass.

Question 9

Why is grav. potential always negative?

Answer 9

As work must be done to move objects apart, but Ep can only have a max of zero, so grav. potential must always be negative.

Question 10

How do you find change in grav potential?

Answer 10

Area under the graph of g against r

Question 11

Where is g (field strength) largest?

Answer 11

At the surface of a planet.

Question 12

What is the work done moving along an equipotential?

Answer 12

0J

Question 13

What is the potential gradient in a field?

Answer 13

Change in potential per metre, potential grad = change in V / change in r

Question 14

How is grav field strength related to potential gradient?

Answer 14

g = -delta V / delta r. So g can be found from a gradient of a V against r graph.

Question 15

What is the escape velocity?

Answer 15

The minimum energy an object must be given to escape a body’s grav field. So must be energy used to move from infinity to the surface.

Question 16

What is the equation for escape velocity?

Answer 16

1/2 mv^2 = GMm / R; v(esc) = root (2GM/R)

Question 17

Is escape velocity the same for all masses in a given grav field?

Answer 17

YES

Question 18

What are some equations linking time period and radius of orbits?

Answer 18

T^2 / r^3 = c; T1^2 / r1^3 = T2^2 / r2^3

Question 19

What is the derivation for T^2 / r^3 = c?

Answer 19

GMm / r^2 = mv^2 / r
GM/r = v^2
v = 2pi r / T,
GM / r = (2 pi r)^2 / T^2
so T^2 = 4 pi^2 r^3 / GM,
pi ^2 / GM is a constant so
T^2 directly prop to r^3

Question 20

What is the total energy of a satellite?

Answer 20

Etotal = Ek + Ep = -Gmm / 2r

Question 21

What are some features of geostationary orbits?

Answer 21

Remain at the same point above the equator
Orbits in the equatorial plane
Has a time period of 24 hours (!)
Moves in the same direction that the earth rotates
Orbits around 36,000km above earth, so orbital radius of about 42000km
Useful as communication satellites, receivers can point in a fixed direction

Question 22

What are some features of low orbits?

Answer 22

Orbit less than 2000km above the Earth. Move at a right angle to the equatorial plane.
Will pass over every point on the Earth as it rotates beneath them
Useful for scanning the Earth for imaging, mapping, weather prediction.