Prove T^2 = ( 4Pi^2 / GM ) r^3
F = mW^2 r, W 2Pi / T , F = GMm / r^2
Equate, cancel out ‘m’ and one ‘r’
Prove equation used for velocity of orbital bodies.
F = mv^2 / r , F = GMm / r^2
Rearrange for v^2,
v^2 = GM / r
Name geostationary orbit factors and uses.
- Have a period of 24 hours (on Earth),
- Always directly above the equator
- So they are always in the same place in the sky. Good so that TV dish can be fixed to one point in sky, Dish doesn’t have to track satellite.
Uses: GPS, weather, spy, mapping and surveying.
Define Newton’s Law of gravitation, state the equation and also the word equation.
Force is proportional to the product of the masses and inversely proportional to the square of their separation.
F = - GMm / r^2
Gravitational force (prop. sign) Mass 1 x Mass 2 / (separation of masses)^2
State Kepler’s three laws of gravitation
1) Planets travel around the sun in elliptical orbits.
2) A line joining the sun to a point will sweep out equal areas in equal times.
3) The time period of the orbit squared is proportional to the mean radius cubed.
- T^2 proportional r^3
- T^2 = ( 4Pi^2 / GM ) r^3
- T^2 / r^3 = Constant
Define gravitational field strength, g
Force per unit mass at a point in a gravitational field.
- g = F / m
