Chapter 18 Grav Fuelds

Question 1

Grav fields

Answer 1

Field strength same equation for elec

Force per unit charge , so here the force is F and charge is M

So g = F/M

Question 2

Close to earth is uniform field, thus what happens?

Answer 2

Field strength constsnt at 9.81

Question 3

Newton fav law

Answer 3

F by two masses felt by both is attractive and thus negative

F = - GMm/r2
G is a constsnt

Question 4

Equation for grav field stentgh caused by a point mass

Answer 4

G = - GM/ r2

Remember r is to centre of the thing

Question 5

Remmeber how to add fields etc

Answer 5

Vector addition of field and forces

Scalar addition of potential

Question 6

Thus why is there 0 grav field between earth and moon somewhere

Answer 6

Because it’s vector addition, some in between there will be 0 , and past it increases again

Question 7

Kepler 1st law

Answer 7

The orbit of a player is an ellipse with the sun at one of the two foci

Question 8

Why can we mostly model planets orbits as circular

Answer 8

Because they have low eccentricity , meaning BASICSLLY a bit flat circle but basicallt a circle

Question 9

Kepler second law

Answer 9

A line segment joining a planet and the sun sweeps out equal areas in equal time periods

• this is because closer to the sun , the greater the faster it is as grav force stringer and orbit faster. Therefore can still in same time sweep out same area

Question 10

Kepler third law

Answer 10

The square of the orbital time period of a planet is propritnsk to the cube if the average distance it is away from the sun

Question 11

How to explain Kepler third law

How to derive

Answer 11

Assume low eccentricity to model as a circle

Equate the centripetal force causing th Siri it to the grav force

Replace velocity with omega r and omega with 2pi / t
Rearrange ti show t3 is prorotinsl to r2

Question 12

What does third law mean

Answer 12

The closer you are to the centre, the less the time periods is

S

Question 13

Keplers laws apply to anything in orbit . How does it show that only mass of the objec it is orbiting around is needed

Answer 13

V2 = GM/r, this shows

Question 14

How to make a geostationary orbit and what is this

Answer 14

An orbit above the equator
With orbital period of 24 hours
And rotates in same direction as earth spins

Such that it appears relative velocity wise as 0

Question 15

How to ensure geostationary irbil

Answer 15

Using mass, set time period ton24 hours and work out the radius it needs to be at from the earth

Question 16

Grav potential

Answer 16

Is integral from infinity to a point r of the firce with respect to dr

Should get - GM/r

Remmeber sd going other way, always integrate negative f

Question 17

What is potentials

Answer 17

At infinity potential is 0, 1/ infinty is 0, so anywhere coming back, as an attractive force, actually releases energy (converted to kinetic ) if brought back as it is attractive force

Thus all potential negative but change of potential is positive when you go up still

Question 18

Graph fo potential against r?

Answer 18

As lrotnetiak is epe optional to 1/r, it is a 1/r graph, and as negative in the 3rd quadrant only

If went to 0 it would be infinity so it goes down, and if went to infinty goes to 0 so tends to that

Question 19

What about agsin the moon?

Answer 19

We know that the closer you get it amiss grav potential decreases and further away increases

So away from earth increase until max and then decrease (becomes more negative) the closer to moon

Remember potential I’d a scaler addition don’t lack

Question 20

To find total energy change from one height to other, how can we do using graph

Answer 20

We know work done = force x distance

So integrate the area between limits

Question 21

How to derive equation fir escape velocity?

Answer 21

For an object to escape the gavitsltion al field it must be given the energy needed = to the gain in grav potential energy as it escapes atmospheric

Equate kinetic energy sssuming it thrown into air

Rearrange for velocity

Question 22

What special about escape velocity
Seen as tho we can not achieve this how do we still escape

Answer 22

Escape velocity is the same for any thing no matter the mass

This is because a constsnt firce is applied , otherwise in a single firce not possible

Question 23

Why does tension = weight and centripetal force normally

Answer 23

Even when flung out has to sustain the weight as weight is thrown away too

Question 24

Remember for frequency as revolutions, it had ti be per second!

Answer 24

Not per minute

Question 25

To solve CHANGE IN ENERGY questions what should you do

Answer 25

Work out change in potential

Then muktilky by mass

DO THIS SELRATLEY

Remember to use MINUS SIGNS