Chapter 18 - Gravitational Fields Flashcards
Gravitational Attraction
The force caused by objects that have mass. It can be shown as a radial field around a point mass.
When is a gravitational field uniform?
When the field lines are parallel and equidistant
Force equation
F = -GMm/r^2
Where G is the gravitational constant, M and m the two masses and r the distance between the objects
Multiple objects
Add and subtract the gravitational forces between each pair of objects on each object based on direction
G
6.67 x 10^-11 Nm^2kg^-2
Non-parallel forces
Find the force in each direction and use pythag/trig to find the resultant force
Gravitational field strength a distance from the centre of an object
g = -GM/r^2
g = -GM/r^2 derivation
Substitute F = mg into F = -GMm/r^2
Kepler’s First Law
The orbit of a planet is an ellipse with a star at one of the two foci
Kepler’s Second Law
Two line segments joining a planet and a star sweep out an equal area in equal time
Kepler’s Third Law
The square of the orbital period, T, of a planet is directly proportional to the cube of its average orbital radius, r, about the Sun
Kepler’s Third Law Formula
T^2 = (4π^2/GM)r^3
1AU
The distance from the Earth to the Sun
Speed of a satellite
v = root(GM/r)
Uses of satellites
Communication, weather and climate monitoring, GPS
Geostationary satellites
- in an orbit above the earths equator
- rotate in the same direction as the Earth’s rotation
- have an orbital period of 24 hours
Gravitational potential definition
The work done per unit mass to move an object from infinity to a point in space
Gravitational potential (V )
g-GM/r
Gravitational potential energy from gravitational potential
E = m V
g
GPE = mass x gravitational potential
GPE in a radial field
E = -GMm/r
Work done from a force-distance graph
Area under
Escape velocity
The minimum velocity for an object to “escape” an object’s gravitational field, based on it having enough energy to overcome the gravitational potential energy
Escape velocity formula
v = sqrt(2GM/r)
Speed of a geostationary orbit
v = root(GM/r)
