Chapter 18 - Gravitational Fields

Question 1

What is the weight of an object

Answer 1

Any object placed in a gravitational field will experience an attractive force towards the centre of mass that’s creating the field.

Question 2

What is the gravitational field strength

Answer 2

At a point within a gravitational field is defined as the gravitational force exerted per unit mass on a test mass placed at that point.

Question 3

How to calculate g?

Answer 3

g= F/m

Question 4

What are gravitational field lines?

Answer 4

They are directed towards the centre of the mass, around a spherical mass forming a radial field.
The stronger the field, the closer together the lines will be.

Question 5

What type of quantity is g?

Answer 5

It’s a vector quantity and it always points to the centre of mass.

Question 6

What is Newton’s Law of Gravitation

Answer 6

It states the attractive force between 2 point masses is:
directly proportional to the product of their masses
And inversely proportional to the square of their separation.

Question 7

What is the Gravitational Constant

Answer 7

6.67 x 10-11 Nm2kg2

Question 8

How can you derive the expression for Gravitational field strength in a radial field.

Answer 8

Use the F= -GMm/r2. Take the f and put it into the g=F/m.

Question 9

What is a electrostatic field?

Answer 9

A region of space within which a positive test mass experiences a force per unit charge.

Question 10

What is a positive test mass

Answer 10

It has no fields; so its fields can’t interact with the field that your trying to measure in the first place. This way you can get an accurate measure of the field that you are trying to measure.

Question 11

What is a magnetic field?

Answer 11

An region around bodies that are magnetic and exert a force on other magnetic bodies.

Question 12

What is Keplar’s 1st Law of Motion

Answer 12

All planets move about the Sun in an elliptical orbit, having the Sun as one of the foci.

Question 13

What are the implications of a point body

Answer 13

By treating bodies as point bodies, for any given displacement w.r.t, the displacement will stay the same.

Question 14

What is the eccentricity

Answer 14

The ellipticity of an ellipse.

Question 15

Keplar’s 2 Law of Motion

Answer 15

A radius vector joining any planet to the Sun sweeps out equal areas in equal lengths in time.

It implies the the speed of a planet about its orbit IS NOT CONSTANT. So, closer to the Sun, the Earth will move faster and cover more distance in 1 month, than it will when it if further away and travels slower, and covers less distance.

Question 16

Keplar’s 3 Law of Motion

Answer 16

The square of the orbital period, T of a planet is directly proportional to the cube of its average distance form the Sun.

Question 17

Derivation of Keplar’s 3rd Law

Answer 17

You say that GMm/r2 = mv2/r.
Rearrange to find v.
V= 2πr/T. Rearrange to get:
r3/T2 = GM/4π2 = k.

Question 18

Geostationary satellites

Answer 18

They have the same time period as the Earth (24 hours)

They can only orbit above the equator.

Question 19

Polar orbits

Answer 19

Goes from North to South.

Has a lattitude of 90 degrees.

Question 20

What are Geostationary satellites used for

Answer 20

GPS.

Question 21

What are polar satellites used for

Answer 21

Spys, cameras , weather.

Question 22

Determining the r for Geostationary satellites

Answer 22

Since T is the same as the Earth, and for them all, then the radius that they travel at is also equal.

Question 23

Uses of satellites

Answer 23

Communications 
Military uses 
Scientific research 
Weather and climte 
GPS

Question 24

GPS

Answer 24

There are 32 satellites, in the lower orbit. Each satellite gives info about the time of transmission and current position etc.
1 position needs at least 4 satellites.

Question 25

Equation for Gravitation potential - Vg

Answer 25

-GM/r.

Question 26

How can you calculate Vg

Answer 26

Integrate the (-GMm/r2) from limits infinity to r.

Question 27

What is the Vg- definition

Answer 27

Work done per unit mass in moving a body from infinity to the a point in a gravitational field.

Question 28

What do you lose energy in Vg

Answer 28

Because at infinity, you will have 0J. So anywhere away from it, will be negative.

Question 29

Graph for Vg

Answer 29

X axis: r/Mm.
Y axis: Vg
You would get a graph thats an upside down curve. It would have a limit at the line x=r, which it would touch at the correct Vg. The gradient would be -GM/r.

Question 30

If there are 2 equipotential lines of 2 planets intersecting at -40MJ/kg, what would the Vg at this point

Answer 30

-40+-40 = 80 MJ/kg.

Question 31

What is the GPE

Answer 31

m Δ Vg.

Question 32

Derivation for Vg

Answer 32

Integrate the (GMm/r2) over the limits of rb and ra.
This gives you:
-GMm/ra – GMm/rb.

-m (GM/ra + GM/rb)

= b (Va - Vb)

Question 33

What is the escape velocity

Answer 33

The minimum velocity required in order for a non-propelled body to escape the gravitational pull of a planet.

Question 34

Assumptions in escape velocity

Answer 34

It is the least minimum velocity.
all KE is transferred to GPE.

The object is non-propelled. Only impart energy, so one big boost, and a lot of force in a small amount of time.

Escape
You need to just no longer feel the gravitational pull of the planet.

Question 35

How to calculate the escape velocity

Answer 35

V= √2GM/r

Question 36

Derivation for escape velocity

Answer 36

m Vg = mv2 / r

GMm/ r = mv2/r

V= √2GM/r

Question 37

Graph for escape velocity

Answer 37

Plot Vg against1/r.

Gradient = -GM.

Question 38

How can you calculate the total energy in moving an object from the surface of a planet to a point?

Answer 38

Kinetic energy + (- GMm/r)

Question 39

Why will lg-lg graphs stay a straight line?

Answer 39

Because GM is constant, and so the gradient will always be -2.

Question 40

Why is the gradient always -2 on a lg-lg graph

Answer 40

Because g = k/r^2. This means that for every planet, the gradient will always be -2.