Grav Fields Chapter 18 Flashcards
Remember how do fields work
An object with any mass or any property will create a RADIAL field around it.
If another kbkect with same property, and thus itsown field, enters the presence of the first field, then they will itnersctuslting in a force acting in BOTH objects by Newton’s law which is same type but on OPPSITE BODIES
Remember that normala nd weight aren’t Newtonian pairs, becsude they aren’t of same type ( gravity vs electorstattic) although they do act on separate bodies,
How do we map the fields
Map them with grab field lines
X closer they are together the stronger the field ( hence near surface)
- if straight then it’s uniform field strength and parallel lines
We model close to surface as uniform as not much change
How dow e model planets and bigger masses?
By modelling them as POINT MASSES ( which they are if observed from very far away), we can model them using these ideas
Rememebr fields are ( additon subtraction resuktsnt)
Fields are VECTORS, so must do vector additon
Resolving it also using Pythagorean with arries
Cancel arrows out if ipositr direction and same field strength
Explain g against r graph as it goes to moon? Where would the rwofus of the earth/ vs the radius fi thr moon be? Why does graoh tend like it does
If you plot actual g against rm the. Potential is most negative closest to earth, so comes up from negative infinith
- now rememebr fields are vectors. If one field earth point this way and other that way then somewhere there must be 0 field strenght!
ALWAYS DRAW ARROW TO HELP
So as it gets away from earth field strength becomes less nagtive and so cloerr to 0 , hits 0 and now gets closer to moon itsgonna go higher
- now remember there will be a certain r at which you hit core of the moon which si technically infinite field strength, that’s why the graoh goes up again
Rwofus of earth and moon will be in different parts way through to the ash tiled
Don’t lack for this!
Kepler first law
Second law
Explain this one
Is that orbit of a planet is an ELLIPSE with the sun being one of its two foci
That in EQUAL TIME PERIODS a, line segment joining the planet and the sun will sweep out EQUAL AREAS
- here, the closer it is to the sun, the faster it is due to having higher grab FIRCE and so higher velocity , but the radii is less due to closer to the sun. However forever her away, as it’s far the velocity is less, but the radii is much bigger, overall the same area is swept
How do we derrive Keplers third law, using what assumption
We assume we’ll it’s true, that most olajets have LOW ECCENTRICITY, which is a measure of how sqaushed the elipseis. Low eccentricity means we can approximate it to a cirucle, and thus use circular motion ideas of the planet orbiting a sun
Therefor the centripetal force is given by the gravational force
Darangeht to show that the time periods 2 is prieotinal to the radius cubed or something
- and drawing a graph of radius vs time becomes x to 1.5 so like quadratic
Now explain using 2nd law why close to sun is fadtersttime
Kepler 2nd law states that a line segment joining the sun and the asteroid will sweep out the same area in the same time interval
As the disgance from sun to asteroid at point x is the least, in any tiem period, this will have the fastest speed in order to make up for same area swept . As distance si further , in the same time period, it will be trwblkitm wt lower speed to sweep out same arww
Rememebr the only way to derirve Kepler third law is if you assume low eccentricity
So that circular emotion physics can take place
Remmeber how to do these time period questions
Which mass are you taking to be big m. In the derivation itd the olane tobeitijgthe sun so sun is big m, but if you want the orbit of the sun then do little planet as big m
Doing this shoudlngiveyou 1 year
How can we use equations to model orbits of satellites
, we can use keplers laws for ANYTHIGN. Therefore, at certain height above the earth, by equation, the satellite must have a specific velocity. If it goes lower then higher velocity is given, so two thinks could link up like this
Also the time period can be set of orbit based on where it is.
In krder to acihieved a GEOSTATIOANRY IBRIT, this is where the 1) orbit is the same as the earth so 24 hours) 2) trabels in same direction as earth. as a result , it’s peprnsmelyy above a position in earth as relative velocity to observer is 0
For this to happen it MUST GO AT THE EQUATOR, as it spins around axis at this point, and in same direction of spin
- anywhere else on earth, it would spin around, but not fixed above a certain point
What cna satelities be used for
In General, reconnaissance, gps, weather, dearth , etc
Gravitational potentials
As grab potentials or any for attractive forces ( brva always attractive) are NEGATIVE, going towards it gives a negative change in potential, and times by max ss megative energy, which means ENERGY IS RELEASED
Going away gives a positive change, and so energy MUST BE PUT IN TO TWKE IT HERE
Negative potential represnets the energy needed to be put in to twke it to infinity
Explain poet William graph earth vs moon
Potential is negative and highest closes to the object. Going away from earth reduced the potential and its on its way to 0 closer to infinity
However meets moon, and so now closer to moon potential rises again
Thus there will be a MAX / min potential (depending on how you graoh it )
Rememebr how to find energy
Change in gpe times mass
