Magnetic Fields - Gravitational Potential Energy

satellite

obj or body that revolves around another body due to the grav attraction to the greater mass

ex. planets are NATURAL SATELLITES

artificial satellite

man-made obj’s orbiting earth or other solar bodies

GPS

a network of 24 satellites

• stands for global posi sys

GPS cont’d

finds obj’s based on the intersections of the range of two or three or four satellites

orbital radius

dist from satellite to the center of the larger mass

motion of a satellite depends on

the centripetal force (the force of grav) and the orbital velocity

orbital velocity

the velocity a satellite needs to maintain its orbit

orbits are acc _______________

elliptical and deviates slightly from a circualr path

the orbital speed is the

same for all orbiting objects of the same large mass with the same orbital radius

orbital eccentricity

extent to which an obj is elliptical/deviates from a perf circ

four fundamental forces in nature

1. weak nuclear force

2. strong nuclear force

3. electromagnetic force

4. force of gravity

weak nuc force

responsible for radioactive decay; changes type of elementary particle (neutron → proton); vv short range

strong nuc force

strongest force but vv short range; holds nucleus together (repulsive forces of protons’ attraction, attraction between e- and p+)

electromagnetic force

responsible for everyday forces like friction (therefore contact forces); infinite range; opposites attract and like-like repels

force of gravity

weakest of all forces but infinite range; matter attracts matter; least understood of all forces

newton’s law of universal grav

there’s a grav attraction btwn any two objects

• grav attraction is directly proportional to the masses individually and inversely proportional to the sqr of the radius dist between the centers)

newton’s law of gravitation related to his third law

magnitude of the Fg of mass one on mass two = mag of Fg of mass two on mass one → action rxn pair (therefore oppo directions)

newton’s law of gravitation related to inverse sqr law

Fg is inversely proportional to the sqr of the radius (therefore Fg decreases rapidly as radius increases and vice versa)

when is the grav force noticeable (newton’s law)

when at least one of the obj’s have a mass that is large compared to the dist bwteen the obj centers

[insert pic of earth w arrows that get smaller as it’s drawn further away from earth] what do the arrows represent

grav field vectors

(Fg are force vectors) → g is weaker as the radius increases

field

• property of space

• an obj influences the sapce around it

• the obj producing the the change aka the field is the SOURCE

grav field

grav field is rep by the force/field vectors surrounding obj

• a grav field exerts forces on any obj w mass

grav field strength

force of attraction per unit mass of an obj that is placed in a grav field

• Fg/m, therefore N/kg (also the “acceleration” bc of newton’s 2nd law)

as dist increases, grav field strength ___

rapidly decreases

derivation of the grav field strength using newton’s uni law of grav

mg = Gm1m2/r² (see first worksheet)

explain how grav field strength can be measured from the center of one obj to another

center of mass can be considered at earth’s center that exerts Fg on a person or obj at dist r (the earth’s radius)

what is the g value dependent on

• mass of central planet

• dist to centre of mass

• G constant

what does g not depend on?

the obj’s own mass

orbital speed formula derivation

see notes

Fc = Fg and isolate for v (Fg = newt formula NOT mg)

geosynchronous

describes an orbit that has an orbital speed that exactly matches Earth’s period of rotation

• takes one day to travel around the earth and will appear to pass thru every 24 hours

geostationary

describes an orbit that is geosynchronous but orbits directly over the equator

• would appear to remain fixed inthe same pt in the sky at all times

kepler’s three laws of planetary motion

1. law of ellipses

2. law of equal areas

3. law of harmonies

kepler’s laws: law of elipses

each planet moves around the Sun in an elliptical orbit with the Sun at one focus of the ellipse.

• BUT its a vv small deviation from circ path

kepler’s laws: law of eq areas

a straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time

• planet speeds up as it approaches sun and slows as it moves away

kepler’s laws: law of harmonies

the cube of the average radius r of a planet’s orbit is directly proportional to the square of the period T of the planet’s orbit

proportionality constant would be Cs (kepler’s constant)

Cs (proportionality constant)

• tells us that the planet belongs to the solar system

• the kepler’s constant

• Cs for our sun is 3.35 × 10^18 m³ / s²

everything spins ________ bc of _____

counter clockwise; the big bang

finding velocity from period and vice versa

v = d/t therefore v = 2(pie)r/T

derivation of sun’s kepler’s constant

see notes

singularity

1D pt where the mass and density are infinite

schwarzschild radius

radius of black hole measured from the center to the event horizon

event horizon

the boundary b/w the edge of the black hole and the universe; the pt of no return

escape speed of a black hole

c (speed of light)

3 × 10^8 m/s

the area under a force distance graph

work done

as radius approaches infinity, Fg approaches

0

value for Eg is always negative since

at at infinity, the obj has no potential en since no work needs to be done to separate the bodies as Fg = 0

as r increase, Eg ___________

increases and becomes less negative as more work is done to separate the objects so more potential

as r appraoches infinity, Eg approaches

0 but from the negative direction so the Eg gets bigger

new Eg formula compared to old formula

past Eg formula did not account for the differing g value from higher elevations

at r infinity, Eg2 would be

0

as object ascends, you assume Eg2 is

0 bc it is propelling away from planet and makes change in Eg only equal to Eg1 which becomes positive

derive a formula for the escape speed

see notes

what changes of a rocket as it ascends into space

• mass (as it uses up its propellent)

• air resistance

for escape speed,

Ek and Eg2 are 0, bc obj will continue to drift off into infinity radius and v = 0 due to no further propulsion

proving that an object’s speed was not enough to escape the bounds of the grav field

if the mag of Eg is greater than the mag of Ek and Et is negative (Eg is neg)

proving that an object had the speed that would escape the bounds of the grav field w some speed left

mag of Ek is greater than mag of Eg and Et is pos

Et = ___ when you have the escape speed w no further propulsion

0

escape speed for balck holes

speed of light (c = 3.00 × 10^something)

bc grav pot en is neg, it is a

potential well and work must be done to get it out

why does Eg increase as the dist increases (unlike force)

bc MORE WORK WAS DONE TO SEPARATE THE MASSES. less work is done when the obj’s are closer toegther

GPE always increases with height either

by increasing positively or decreasing negatively (less and less negative) whether its measured from the perceived lowest pt or infinoity

if the velocity surpasses the escape speed, then

it would follow a curved path and then veer off

principle of equivalence

there’s no way to test whether acceleration occurs bc of a grav force or because their reference frame is accelerating

differences between theory of relativity and newtonian gravity

1. speed limit in general relativity (the speed of light) while newton says that a change in position of mass in one part of universe instantly changes its grav field in all other parts of universe

2. general relavity predicts that gravity affects light while newton says that light has no mass therefore exerts no force but light has been observed to bend and distort when passing super large masses

black hole

regions in space where the grav field is so strong that nothing including light can escape and form as one possible product of the end of a stars life

black holes are hard to study because

they are not visible as no light escapes however scientists can still detect them by observing how the surroundings behave

• when material gets pulled into black hole, it emits xray and other particles that we can detect on earth

derive for the mass of the sun

use the orbital speed formulas