Chapter 3- Universal Gravitation Flashcards
Gravitational field def
Is a region in which a mass feels a force
Is a uniform field
Lines of force are parallel, equally spaced and the arrows are downwards
Size of the force is the same at all points
Grav field strength eq
g= Fg (size of gravitational force) / m (body of mass)
All objects fall with the same acceleration in…
The same gravitational field
Gravitational field strength def
The grav field strength at a point in a grav field is defined as the grav force per unit mass acting on a mass at that point
The field is a radial field so the strength…
Decreases with height
What is a surface called when it is taken as a place where objects have zero gravitational potential energy?
Equipotential surface
Within an equipotential surface…
There is no change in GPE
No work is needed to move an object along such a surface
To change between equipotential surfaces…
A change in GPE occurs to move upwards between two adjacent surfaces
(Change is negative)
What is newtons law?
States that the force between two objects is proportional to the masses of these objects and inversely proportional to the square of the distance between the objects
What is newtons law known as
The inverse squared law
Newtons law applies to :
Spherical objects such as planets
And to
Particles
Newtons law in an equation
F= Gm1m2/ r^2
A body on which the only force acting is the pull of the earth on it (its weight) is said to be in the…
State of free fall
What state are satellites in as they circle the earth
They are in the state of free fall all the time
There is only one force acting on the satellite which is…
The gravitational attraction of the earth towards the earth’s centre
Applying Newton’s second law and his law of gravitation to the satellite gives….
mv^2/r = GmMearth/r^2
As v = 2pie(r)/T
Then…
r^3 = GMearthT^2/4pie^2
r^3 is proportional to T^2
(Kepler’s third law)
The further the satellite is the longer it will take to orbit the earth
Free fall is often called
Weightlessness (although weight is acting on it at all times-is just the only force that is)
What are radial gravitational fields
Gravitational fields that act around the radius of an object that is spherical
The lines of force become wider as they spread out
Since gravitational potential increases by equal amounts between the equipotential lines then they too become further apart as the distance from the earth increases
Gravitational force per unit mass eq
g= Fg/m
g= GmmE/r^2 / m
So…
g= GmE/r^2
mE= the mass of the earth
What does the graph of g between r for the Earth look like
Values of g are negative because…
Values of r are positive because….
Is an inversely square relationship
Looks like an exponential
Values of g are neg because r is measured away from the earth but g is measured towards the earth
(Can’t know in detail how g varies below the earths surface)
In uniform field what is the gravitational potential difference eq
Vg= g🔺h (g is constant)
In a radial field the relationship between gravitational potential and the distance from the centre of the earth is….eq
Vg= -GmE/r
g= GmE/r^2
What is the gravitational potential difference between two distances from the centre of the earth….
Vg= -GmE( 1/r1 - 1/r2 )
If one value is close to infinity then it just goes back to
Vg= -Gm/r
