Gravitational Fields !

Question 1

Prove T^2 = ( 4Pi^2 / GM ) r^3

Answer 1

F = mW^2 r, W 2Pi / T , F = GMm / r^2

Equate, cancel out ‘m’ and one ‘r’

Question 2

Prove equation used for velocity of orbital bodies.

Answer 2

F = mv^2 / r , F = GMm / r^2
Rearrange for v^2,

v^2 = GM / r

Question 3

Name geostationary orbit factors and uses.

Answer 3

• 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.

Question 4

Define Newton’s Law of gravitation, state the equation and also the word equation.

Answer 4

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

Question 5

State Kepler’s three laws of gravitation

Answer 5

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

Question 6

Define gravitational field strength, g

Answer 6

Force per unit mass at a point in a gravitational field.

- g = F / m