A2 - Gravitational Fields

Question 1

What is the relationship between kinetic energy and gravitational potential energy for an object moving away from Earth’s surface?

Answer 1

Its potential energy increases from a negative value to zero, and its kinetic energy decreases.

Question 2

Define gravitational field strength

Answer 2

The force per unit mass that acts on a small test mass placed at a point in the field.

Question 3

Define gravitational potential energy

Answer 3

The energy per unit mass moving a small test mass from infinity to a given point in the field.

Question 4

What is the shape of a gravitational potential vs distance graph moving away from Earth’s surface towards the moon?

Answer 4

Gentle curve upwards as it escapes the gravity well of Earth, moving towards zero, then dipping down as it goes through the gravity well of the moon. Make sure the line is not too steep.

Question 5

Give the equation for gravitational field strength in a radial and uniform field

Answer 5

Radial field: g=Gm/r^2

Uniform: g=f/m

Question 6

Is the work done by a field moving an object from infinity to that point positive or negative?

Answer 6

Negative, because the field is attractive, so potential energy decreases and is converted into kinetic. Like falling into a gravity well, no work is done

Question 7

What is the potential gradient?

Answer 7

The change in potential per meter. The gradient decreases as you get further away from the object because the equipotentials are further apart. It is the negative of the field strength.

Question 8

What is the equation for gravitational potential in a radial field? What is the unit for gravitational potential?

Answer 8

V=-GM/r = W/m

Measured in j/kg

Question 9

Derive an equation for the gravitational field strength starting with W=F*R for an object moving away from a sphere in a radial field.

Answer 9

F=GMm/r^2
Fgrav = -F
V=W/m => F*r/m => F=mV/r
g=Fgrav/m = (mV/r)/m = V/r

Question 10

What is the relationship stated in Keplar’s third law?

Answer 10

r^3/T^2 is constant for all planets

Question 11

What is the equation for the force between 2 objects?

Answer 11

F=GMm/r^2

Question 12

What assumption can we make about spheres?

Answer 12

The mass is concentrated in the centre

Question 13

What is the relationship between potential and radius from a planet?

Answer 13

Inversely proportional v=-Gm/r

Question 14

What can we say about the time period of all satellites?

Answer 14

They follow Keplar’s relationship.

Question 15

Prove Keplar’s third law applies to satellite motion. Start with g=GM/r^2

Answer 15

g=GM/r^2= centripetal acceleration
a=v^2/r=GM/r^2
v^2=GM/r
v^2 = (2*pi*r)^2/T^2
(2*pi*r)^2/T^2=GM/r
r^3/T^2 = GM/4*pi^2

Question 16

Use Keplar’s third law to find the radius of a geostationary satellite.

Answer 16

r^3/T^2=GM/4pi
r^3 = GMT^2/4pi^2
Radius is r-6400km
Subtract radius or Earth, since we consider the mass of the planet to be concentrated in the centre.

Question 17

What is a polar orbit, and what is it used for?

Answer 17

An orbit that moves above the poles and orbits vertically. It is used for weather and spying, as it covers a large area of land quickly.

Question 18

What is an equatorial orbit? What is it used for?

Answer 18

An orbit that moves around the equator of Earth. Used for communications.

Question 19

What is the energy for escape? what two parts does it contain?

Answer 19

E(t)=0.5mv^2-(GMm)/r

Kinetic energy plus the work done due to the gravitational potential.

Question 20

In a radial field, what happens to field line further from the central object producing the gravitational field?

Answer 20

The separation between the field lines increases, showing the potential gradient and field strength are reducing.

Question 21

Which way do field lines go in a gravitational field?

Answer 21

Towards the mass causing the gravitational field

Question 22

What does Keplar’s third law state?

Answer 22

r^3/T^2 constant for all orbiting bodies

Question 23

What assumption can we make about planets to make it easier to model their gravitational fields?

Answer 23

Their mass is concentrated in the centre

Question 24

What is the gravitational potential/radius graph moving away from planet earth?

Answer 24

Inverted exponential increase from -60 mj/kg tending to zero. Smaller negative dip for the moon.

Question 25

How does gravitational field strength vary with distance in a radial field?

Answer 25

it decreases exponentially from 9.8Nkg-1 at Earth’s surface tending towards zero as distance increases to infinity.

Question 26

What general shape does gravitational potential/distance follow?

Answer 26

1/r

Question 27

What general shapes does gravitational field strength/distance follow?

Answer 27

linear from zero to Earth’s radius, then 1/r^2 decrease tending towards zero

Question 28

What is the link between gravitational field strength and gravitational potential?

Answer 28

Negative potential gradient(-v/r) = gravitational field strength at that point.

Question 29

What link can we make between centripetal acceleration and gravitational potential?

Answer 29

GM/r^2 = v^2/r

Gravitational potential = centripetal acceleration.

Question 30

When calculating the force acting on a satellite, what is the radius?

Answer 30

Radius above earth + radius of earth

Question 31

How do you calculate the radius of an orbit given only the angular speed?

Answer 31

GMm/r^2 = mw^2r

GM/w^2 = r^3

Question 32

State Newton’s law of gravitation

Answer 32

force is proportional to the product of the two masses divided by the centre separation squared