Physics OCR Chapter 18 (Gravitational Fields)

All objects with mass create gravitational fields, that extend to infinity

Gravitational field strength at a point 'g' is the gravitational force exerted per unit mass on a small object placed at that point.

g = F/m

Field is radial, and force is attractive arrows point in.

The force between two point masses are directly proportional to the masses F ∝ Mm, and inversely proportional to the square of the distance between them F ∝ 1/r²

F = - (G M m / r²)   swhere, G=gravitational constant (6.67x10−11)

Using the equation for newtons law of gravitation and the definition of gravitational field strength we can derive an equation for the gravitational field strength in a radial field

F = - GMm / r²

g = F / m     F = gm

gm = -GMm / r²

g = - GM / r²

Kepler's First Law: The orbit of a planet is an ellipse with the san at one of the two foci

Kepler's Second Law: A line segment joining a planet and the sun sweeps out equal areas during the same time interval

Kepler's Third Law: The square of the orbital period, T, of a planet is directly proportional to the cube of its average distance r from the sun   

T²  ∝  r³ 

Modeling Planetary orbits as circles

centripetal force = gravitational force on planet

mv² / r = GMm / r²

v² = GM / r

• Only force acting upon them is gravitational force due to the earth
• All satellites must be given correct height and speed for a stable orbit 

v = √(GM / r)

Types of Orbits

• Polar Orbits: Circles the poles, covers the whole globe over a number of orbits ( Mapping, Reconnasaince)
• Low Earth Orbit: Orbits are close to earth surface and are very quick ( K's 3rd Law) (GPS)
  • GPS: 32 satellites send message of time of transmission and location, needs four satellites, software determines position on earth by calculating tiny delay
• Equatorial Orbit: Orbits placed above the equator (Geostationary satellites)

Geostationary Satellites

• Possible to choose satellites period by height above earth
• A satellite that remains in the same point above the earth as the earth rotates
• Must have an orbital rotation of 24 hours

Gravitational Potential energy 

E = m V