Gravity

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• Gravity is a force of mutual attraction between any and all mass in the universe, and extends to the limits of the universe (long range force), and which decreases with distance as per the inverse square law
• A field is the region of space around an object possessing a particular property (e.g. mass) and within which another object possessing the appropriate property (e.g. mass) will experience a force (e.g. gravity)

Universal law of gravitation

$F_g=\frac{GMm}{r^2}$

• units of G is $6.67\times 10^{-11}{\text{ N m}}^2{\text{ kg}}^{-2}$

Gravitational Field Strength/

$g=\frac{F}{m}$

• in $Nk{g}^{-1}$

Definitions stuff

• Geostationary: Located above 1 position of the earth, equatorial orbit
  • Period is one day
• Polar: Polar orbit
• Sun - synchronises: it is above the same position on earth at the same time each day

Work in Gravity

$W=Fs$

• If an object is moving in the direction appropriate to the acting force (i.e. mass towards larger mass, positive charge to negative charge, positive charge away from positive charge), then we say that the field is doing work on the object
• Or if mass is moving away from a larger mass, then we say that the object is doing work on the field

What is the altitude of a geostationary object?

$F_c=F_g$

$\frac{m{v}^2}{r}=\frac{GMm}{r^2}$

$\frac{\frac{2\pi r^2}{T}}{r}=\frac{GM}{r^2}$

$\frac{4{\pi }^2{r}^2}{T^{2}r}=\frac{GM}{r^2}$

$r^3=\frac{GM{T}^2}{4{\pi }^2}$

Kepler’s Law

$\frac{T^2}{r^3}=\frac{4{\pi }^2}{GM}$