Gravitation
I.
Useful constant: G = 6.6710-11 Nkg-2m2, me  61024 kg, re  6400 km
II. Gravitational force, F 
Gm 1 m 2
r
2
(the inverse square law); field strength, g 
F GM
 2
m
r
III. Shell Theorem
1. Outside: all the shell’s masses were concentrated at its center.
2. Inside: the net attraction by the shell is zero.
IV. Apparent weight
1. The density of the Earth crust is not uniform.
2. The Earth is not a perfect sphere.
3. The Earth is rotating.
V. Variation of g with height and depth
1. Outside the Earth: g  g o
Re2
r
2
 2h 
1

 g o 1 
 r2
R
e 

2. Below the Earth’s surface: g 

go
d
r  g o 1 
Re
R
e


r


VI. Gravitational Potential Energy
1. Zero PE is defined at infinity. WD is negative when moving an object from infinity to that point.
UP  
GM e m
r
. When there is more than one “reference mass”, the total PE = the sum of all the PE
2GM
GM
 goR
 2 g o R ; where orbital speed, v o 
R
R
U
3. Gravitational potential, V 
m
dV
4. Potential V and field strength g, g  
. Earth-Moon system, Fig.16
dr
2. Escape speed, v e 
VII. Orbital Motion
1. Kepler’s Laws:
(i) The Law of orbits: all planets move in elliptical orbits, with the Sun at one focus.
(ii) The Law of areas: the area swept out in a given time by the line joining any planet to the
sun is always the same.
(iii) The Law of Periods: the square of the period T of any planet about the Sun is proportional
to the cube of their mean distance r from the Sun. T2  r3.
2. Satellites: natural satellites Vs artificial satellite; geosynchronous satellite Vs polar satellite.
3. Energy and Satellite Motion
1
2
(i)
KE: U k  mv 2 
(ii)
PE: U p  
GM e m
2r
GM e m
r
(iii) Eo: U  U k  U p  
GM e m
2r
VIII. Reminders
1. The gravitational force is an action and reaction pair.
2. T2 = kR3, k is valid only for the same mass centre.
3. Density  = m/V  m/r3