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Module 5 - Chapter 18 - Gravitation fields I - Coggle Diagram
Module 5 - Chapter 18 - Gravitation fields I
Gravitation fields
All objets with mass create a gravitational field around them
Field extends to infinity but get weaker as distance increases and is negligible at long distances
Object with mass placed in a gravitational field experiences an attractive force towards the centre of mass of the object creating the field
Graviational field strength
Gravitational force exerted per unit mass
units =
, same units for acceleration
Gfs at a point is the same as the acceleration of free fall of any object at that point
Vector quantity that points to centre of mass of the object
Equation is accurate aslong as the mass of the object in the field is small enough that the objects field is negligible compare to the external field the object is in
Field patterns
Gravitational field lines (lines of force) map the gravitational field patter
Lines don't cross and arrows show the direction of the field, which is the direction of the force on a mass
Stronger field is shown by lines that are closer together
Field lines around a spherical mass form a radial field
field strength decreases with distance from the centre of mass, shown by lines getting further apart
We can model larger spherical objects as a point mass, where field lines coverge at the centre of mass
Parallel lines that are equidistance represent a unifom graviational field (field close to the surface of a planet)
Newton's law
Consider two objets of mass M and m separated by a distance r
ach object creates its own gravitational field, and the interaction of these fields causes a force between objects
The force between two point masses is direcly proportional to the product of the masses and inversely proportional to the square of their separation
We can introduct the graviational constant G
,
and a minus sign is required to show the force is attractive
Attractive force between objects decreases with distance in an inverse-square relationship, doubling distance decreases the force by a factor of four
Multiple objects
Resultant force can be determined by vector addition
If interaction is in 1D, addition and subtraction are used
If interaction is 2D, we use pythagoras' therom or sin/cos rule if vectors aren't perpendiular
Point mass
Gfs in a radial field
Gravitational field strength at that point is in the opposite direction to the displacement from the centre
Gfs at a point is directly proportional to the mass of the object creating the field
Gfs is inversely proportional to the square of the distance from the centre of mass
Graph
Uniform
Gfs doesn't change
Close to earth's surface, g is fairly constant, so the field is approximately uniform
Kepler's laws of planetary motion
1st
Orbits usually have low exxentricity (how elongated the circle is), so orbits are modelled as circles
1st law - orbit of a planet is an ellipse, sun is at one of the two foci
2nd
2nd law - Line segment joining a planet and the sun sweeps out equal areas during equal intervals
Speed of planets at different points in orbit are different, they move quicker as they get closer to the sun
Interval from X to Y equals P to Q, areas A and B must be the same
3rd
3rd law - square of the orbital period is directly proportional to the cube of its average distance r from the sun
k is a constant for the planets
Modelling orbits as circles
We can use circular motion maths to relate orbital period T to distance r from the sun
centripetal force on planet = gravitational force on planet
We can divide circumference by period to find the veloctiy
k is
gradient of a graph of t^2 against r^3 is k
