Gravitational force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them. Kepler's first law states that planets orbit the sun in ellipses. Kepler's second law states that planets sweep out equal areas in equal times. Kepler's third law states that the square of a planet's orbital period is proportional to the cube of its average distance from the sun. Centripetal force is the force directed towards the center of an object's circular motion, such as an electron orbiting an atom's nucleus. Escape velocity is the minimum speed an object must achieve to escape a planet or moon's gravitational pull entirely.

1. Kepler’s Laws
Gravitational force, F is ________________
___________________________________
and ________________________________
___________________________________
F α and F α
Thus F =
Where G = gravitational constant
G = 6.67 x 10-11 N kg
m1 m2 = masses
r = distance between center of masses
*As m increases, gravitational force ________
*As r increases, gravitational force _________
Newton’s Law of Gravitation
Gravitational Acceleration, g
Weight = gravitational force on surface of Earth
W = = Fg
=
g =
On surface of Earth r = Radius of earth, R,
m1= Mass of earth, M
g =
g = 9.81 ms-1
R
Radius of Earth
g/ms-2
r/m
r < R
g α
r > R
g =
g α
h
R
r = distance between masses
r = R+h
Thus, g =
Centripetal Force, Fc
A resultant force that is always acted towards the
center of the circular motion.
Example, Electron orbiting nucleus of atom.
Moon orbiting Earth.
Force = mass x acceleration
Acceleration is the ________________________
Velocity is a vector that has __________ and
_______
An object moves in circular motion has the same
magnitude (speed) but always changing direction.
The change in direction is always directed towards
the center of the circular motion.
F = ma but a = v2/r
Centripetal force, F =
Kepler’s 1st Law; _______________________
_____________________________________
_____________________________________
Kepler’s 2nd Law; _______________________
_____________________________________
_____________________________________
Kepler’s 3rd Law; _______________________
_____________________________________
_____________________________________
Fc = Fg
v = 2πr/T
T2 =

2. Escape velocity, vesc is the minimum velocity of an object
needed to completely move away from the surface of the
Earth.
Kinetic energy = Gravitational potential energy
KE = GPE
vesc =
1. Earth able to maintain a layer of atmosphere around it.
Air molecules has velocity less than the Earth’s escape
velocity
2. Aeroplanes won’t escape to outer space
3. Rockets to be launched into outer space needs a lot of
fuels to produce large thrust and high velocity that is
bigger than the Earth’s escape velocity.
Cg Ann
Man-made satellite
Geostationary
Satellite
Non-geostationary
Satellite
Orbits the Earth Orbits the Earth
Speed of satellite Speed of satellite
Period of satellite Period of satellite
Direction of orbit is
the same as the direc-
tion of Earth’s rota-
tion
Direction of orbit is
NOT the same as the
direction of Earth’s
rotation
Period, T = 24 hours
same as Earth’s rota-
tion
Period is NOT 24
hours, can be less or
more.
Located at equator,
above the same
geographical location
Located anywhere on
the sky at any time of
the day
i.e.: Communication
satellite, MEASAT
i.e.: Military satellite,
ISS
Escape velocity, vesc
Benefits and implication of vesc