Chapter 18- Gravitational fields

All objects with mass create a gravitation field
1. This field extends to infinity
2. The force that masses would feel in a gravitational field can be represented using 'lines of force'
  1. Planets or spherical masses form a radial field
  2. Close to the surface of a planet it appears as a uniform field
(g) Gravitational field strength- "the gravitational force exerted per united mass at a point within a gravitational field"
1. g=F/M
  1. ms^-2
  2. Nkg^-1
Newton's law of gravitation- "The force between 2 point masses is directly proportional to the product of the masses and inversely proportional to the square of the separation between them
1. F=-(GMm)/r^2
  1. G-Gravitational constant (6.67x10^-11)
Combining Newton's law of gravitation and g=F/m allows us to calculate gravitational field strength in a radial field
1. g=-(GM)/r^2
Kepler's laws of planetary motion
1. 1st Law- The orbit of a planet is an elipse with the sun at one of the 2 foci
  1. The sum of the distances to the 2 foci is constant for every point on the curve
    1. 'Eccentricity' is a measure of how elongated the circle is
2. 2nd law- A line joining the sun to a planet will sweep out equal areas in equal time
3. 3rd 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
  1. (T^2/r^3) =k
4. Most planets in the solar system have 'nearly' circular orbits
  1. We can therefore combine Gravitation force and centripetal force equations
    1. v^2=(GM)/r
    2. T^2=((4π^2)/GM)r^3
5. Satellites orbitng the Earth obey these laws
  1. The speed of a satellite remains constant due to no air resistance
  2. Geostationary orbit
    1. Specific orbit where it remains directly above the same point of the Earth whilst the Earth rotates
    2. 1) Must be in orbit above the Earth's equator
    3. 2) Must rotate in the same direction as Earth's rotation
    4. 3) Must have an orbital period of 24 hours
  3. Height or satellite is directly proportional to its period
Gravitational potential (Vg)
1. "the work done per unit mass to move an object to that point from infinity"
  1. Jkg^-1
  2. When r=∞, Vg=0
2. Vg=-(GM)/r
  1. Moving towards a point mass results in a decrease in gravitation potential
  2. Moving towards a point mass results in a n increase in gravitation potential
Gravitation potential energy (E)
1. "the work done to move the mass from infinity to a point in a gravitational field"
2. E=mVg
3. In a radial field
  1. E=-(GMm)/r
4. Escape velocity is the velocity needed so an object has just enough kinetic energy to escape a gravitational field
  1. v^2=(2GM)/r

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Chapter 18- Gravitational fields

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