Gravitational fields Flashcards
Define gravitational force
Two masses experience an attractive force between them. This is the force of gravitation which is F=GMm/r^2.
The fore is directly proportional to the product of the masses, and inversely proportional to the radius squared, and at the centre of the Earth, the gravitational force is 0.
What is Keplers 3rd Law?
Keplers law is that r^3/T^2 is the same for all planets orbiting the sun.
Kepler was interested in the relationship between time period and separation.
Planets are in circular orbits meaning they experience a centripetal force.
He equation mv^2/r = GMm/r^2
We can then substitute v for 2pir/T
We will get T^2 = 4pi^2r^2/GM
4pi^2/GM is a constant so now we know T^2/r^3 is a constant.
What is another way to prove Keplers law?
We can do this my working out the velocity of the object in orbit.
mv^2/r = GMm/r^2
Rearranging for v, we get v=root Gm/r
We can equate this to 2pir/T as this is what velocity is for objects in circular motion
Describe polar orbits
In polar orbits, the satellite orbits over the poles of the Earth . The satellite has a fixed radius and therefore a fixed speed and is able to scan the entire surface of the Earth.
Describe geostationary/geosynchronous orbits
The satellite orbits in the plane of the Earths equator and has a time period of 24 hours. It is useful for transmitting signals to different locations.
Define gravitational field strength
The gravitational field strength is the force per unit mass on a small test mass placed in the field.
It is a vector quantity
g = F/m for a uniform field
g = GM/r^2 for a radial field
The units are Nkg^-1
Free fall in a gravitational field
g = F/m which is acceleration
The force is the weight which equals mg
mg/m = g
g = 9.81
This is the acceleration of an object in free fall
Field patterns
In a radial field. the field lines are always directed towards the centre. Gravitational force is an attractive force so the arrows are towards the mass always, never away from the mass.
The field lines show the strength of the gravitational field, which gets weaker as distance increases.
In a uniform field, the field the field lines are drawn parallel, and they are equally spaced. g is constant so the acceleration is constant.
What happens to field lines when we have 2 bodys
There is a 0 point, where the fields cancel each other out and the gravitational field is 0. We can draw this by drawing a dotted line.
The 0 point will be closer to the object which has the smaller mass.
Is both the bodies have the same mass, the 0 point will be in the middle.
We can see which object has the greater mass by observing the field lines. The greater the density of the field lines around the body, this means the mass is greater.
Gravitational potential energy at close distances near the Earth (uniform)
Work done is force x distance
force is weight so mg
distance = h
W=mgh
We have assumed g is constant and is equal to 9.81 and this is fair as we are near to the surface of the Earth where the field is uniform.
We can find the gravitational potential energy from the area under a force - distance graph
Gravitational potential energy on a global scale (radial) where the field strength is not constant (U)
In a radial field, gravitational potential energy is negative because the gravitational force is an attractive force and we take 0 potential energy to be at infinity, and work needs to be done to move from inifnity to the point we are interested in.
W=-GMm/r
How can we work out escape velocity?
Total energy is the sum of potential energy and kinetic energy
= 1/2mv^2 - Gmm/r
so 1/mv^2 = Gmm/r when we rearrange
Now we can rearrange to find v and we get v = root 2GM/r
This is the minimum speed of an object must have to escape the gravitational force and escape to infinity.
Changes in gravitational potential energy
The change in gravitational potential energy is the difference in the potential energy of an object as it moves between two points in a gravitational field.
Remember, in physics, changes are final - initial.
-GMm/r - - GMm/r
= -GMm/r + GMm/r
Define Gravitational potential (V)
The work done per unit mass in bringing a test mass from infinity to a defined point.
It is U/m = gravitational potential energy / mass
It has negative values because we define 0 potential at infinity and negative work is done to move the test mass away from infinity.
Units are Jkg^-1
Gravitational potential difference
This is final - initial
Vf - Vi
