Module 5 - Gravitational Fields Flashcards
A gravitational field
a force field generated by any object with mass which causes any other object with mass to experience an attractive force
Newton’s law of gravitation
the force acting between two point masses is proportional to the product of their masses and inversely proportional to the square of the distance between their centres of mass
F = (-GMm)/r^2
Gravitational field strength
the force per unit mass
g=F/m
Gravitational potential
(at a point) the work done in moving a unit mass from infinity to that point
Gravitational potential energy
gravitational potential multiplied by its mass
E = mVg = (-GMm)/r
Escape velocity
the velocity needed so an object has just enough kinetic energy to escape a gravitational field
Use KE = 0.5mv^2 and energy = (-GMm)/r
v=squroot (2GM/r)
Satellite
any smaller mass which orbits a much larger mass
How do you calculate orbital speed?
Use F = (GMm)/r^2 and F = mv^2/r
mv^2/r = (GMm)/r^2
v^2 = (GM)/r
v = squroot(GM/r)
How do you calculate orbital period?
w = 2Pi/T and a = w^2r => a = (2Pi)^2r/T^2 => a = 4Pi^2r/T^2 F=ma and F=(-GMm)/r^2 4Pi^2rm/T^2 = (-GMm)/r^2 4Pi^2r^3/T^2 = -GM T^2 = -4Pi^2r^3/GM
Geostationary satellites
- Travel directly over the equator
- Always above the same point on Earth
- Travel at same angular speed as the Earth
- Travels west to east
- Orbit time = 24hrs
Kepler’s first law
Each planet moves in an ellipse around the Sun, with the Sun at one focus
Kepler’s second law
A line joining the Sun to a planet will seep out equal areas at equal times
e.g. Travelling the same amount of time (same arc length) will give the same area when traced back to the Sun
Kepler’s third law
Time period squared is directly proportional to radius cubed
