Chapter 18 Grav Fuelds Flashcards
Grav fields
Field strength same equation for elec
Force per unit charge , so here the force is F and charge is M
So g = F/M
Close to earth is uniform field, thus what happens?
Field strength constsnt at 9.81
Newton fav law
F by two masses felt by both is attractive and thus negative
F = - GMm/r2
G is a constsnt
Equation for grav field stentgh caused by a point mass
G = - GM/ r2
Remember r is to centre of the thing
Remmeber how to add fields etc
Vector addition of field and forces
Scalar addition of potential
Thus why is there 0 grav field between earth and moon somewhere
Because it’s vector addition, some in between there will be 0 , and past it increases again
Kepler 1st law
The orbit of a player is an ellipse with the sun at one of the two foci
Why can we mostly model planets orbits as circular
Because they have low eccentricity , meaning BASICSLLY a bit flat circle but basicallt a circle
Kepler second law
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
Kepler third law
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
How to explain Kepler third law
How to derive
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
What does third law mean
The closer you are to the centre, the less the time periods is
S
Keplers laws apply to anything in orbit . How does it show that only mass of the objec it is orbiting around is needed
V2 = GM/r, this shows
How to make a geostationary orbit and what is this
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
How to ensure geostationary irbil
Using mass, set time period ton24 hours and work out the radius it needs to be at from the earth
Grav potential
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
What is potentials
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
Graph fo potential against r?
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
What about agsin the moon?
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
To find total energy change from one height to other, how can we do using graph
We know work done = force x distance
So integrate the area between limits
How to derive equation fir escape velocity?
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
What special about escape velocity
Seen as tho we can not achieve this how do we still escape
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
Why does tension = weight and centripetal force normally
Even when flung out has to sustain the weight as weight is thrown away too
Remember for frequency as revolutions, it had ti be per second!
Not per minute
To solve CHANGE IN ENERGY questions what should you do
Work out change in potential
Then muktilky by mass
DO THIS SELRATLEY
Remember to use MINUS SIGNS
