Gravitational Fields Flashcards
define gravitational field
region of space where a mass experiences a force due to the gravitational attraction of another mass
direction of a gravitational field
towards the centre of mass
define gravitational field strength
the gravitational field strength at a point is the force per unit mass of an object at that point
differences between a gravitational field and electric field
- G is only between masses, E is between charges
- E can be both attractive and repulsive; G is only attractive
what is a uniform sphere and why can it be considered a point mass
- evenly distributed mass
- its mass seems to act from the centre: a point
when is an object regarded as a point mass
its gravitational field covers a very large distance as compared to its size, so, to study its size, motion or dimension can be neglected
what are radial fields
- non uniform fields (not parallel, equally spaced lines)
- go circular around an object
- so the gravitational field strength varies with distance from the centre
state newtons law of universal gravitation
the gravitational force between 2 point masses is proportional to the product of the masses and inversely proportional to the square of thier separation
state the conditions required to use Fg=Gm1.m2/r^2
- objects must be point masses
- separation must be large
what provides planets with the centripetal force to stay in their circular orbits.
gravitational force between sun and planet, which is perpendicular to the direction of travel
therefore there is centripetal acceleration as the direction is constantly changing but with a constant speed in its fixed orbit
state Keplers 3rd law of planetary motion
for planets/satellites in circular orbit about the same central body, the square of the time period T is proportional to the cube of the radius of the orbit
Formula for strength of gravitational field
g=Fg/m
Formula of newton’s law of universal gravitation
FG= Gm1•m2 / r^2 hence G is the constant of proportionality
What equation do you get after equating newton’s gravitation equation to centripetal force of a planet
v^2 = GM /r
What is keplers 3rd law equation
T^2 = 4pi^2×r^3 /GM
What does the gravitational field strengrh at a point describe
How strong or weak a gravitational field is at that point
2nd formula for gravitational field strength
g= GM / r^2 where M is the one causing the field
Is gravitational field strength vector or scalar
Vector
What is the direction of g
Towards centre of the body creating the gravitational field
Outside the earth’s surface g is not constant. How does it vary then?
As r increases g decreases by a factor or 1/r^2
Inverse Square law relationship
Describe graph of g against r
-when rR, g is inversely proportional to r^2 ie a reciprocal graph: as x increases y rapidly decreases
why is g approximately constant for small changes in height above earth’s surface
because compared to earths radius any heigh addition, according to the inverse sqaure law relationship g ~1/r^2, the value doesnt change by much
define GPE on the earths surface
energy object has when lifted off ground because work is done to do this
ie change in GPE= mg*change in h
define GPE outside the earths surface
energy object possesses due to its position in a gravitational field
define gravitational potential
work done per unit mass in bringing a test mass from infinity to a defined point (aka gpe/unit mass)
explain your understanding regarding gravitational potential
whe bringing an object from infinity back to earth energy is lost because work is done by gravity to attract the object back (positive work)
whereas in the opp case as an object moves away from earth, GPE is gained with increasing distance to infinity because work is done against gravity. and this GPE increases because with more distance more work must be done against gravity to move from there to infinity. At infinity GPE=0 so even though we say GPE is increasing with distance, it is denoted in the negative because this is the only correct mathematical way to reach infinity by obeying the thoery ie values becomes less negative and therefore both approach 0 and also increase
what is the equation for gravitional potenial, fye
= -GM/r
what is the significance of the - on the formula for gravitional potenial
since the gravitional potenial at infinity is 0, and the gravitional potenial of all points that are below infinity is less than 0, these all must be negative
is kinetic energy related to gravitational force and centripetal force? (planets)
yes.
equate GF to CF then make v^2 subject and substitute in 0.5mv^2
state what is meant by gravitational force
force exterted by an object in a gravitional field on another mass in that field
