2. Newton’s law of universal gravitation
Every particle in the universe attracts other
particles with a force that is directly proportional
to the product of the masses of the particles and
inversely proportional to the sq of the distance
between them
F = G m1 m2
r2
F = gravitational force on either particles
m1 m2 = masses of the particles
r = distance between them
G = universal gravitation constant = 6.67 x 10-11
Nm2 kg-2
3. Relating G with force of gravity g
Consider a small object with mass m in our
big earth of mass M and radius R
F = GMm/ R2 F is also = mg
So mg = GMm/R2
g = GM/R2
g α 1/R
* g will increase`where the earth’s radius
decreases
4. Gravitation potential
Work done in bringing a unit mass from
infinity to a point on the earth under the
influence of gravitational field
V = - GM/r
The negative sign indicates that potential at
infinity is greater than potential close to the
earth
5. Escape Velocity
Minimum velocity required of a body to
escape the earth’s gravitational force
Work = m x GM/R
½ v2 = m x GM/R
v = √(2GM/R) ............ Escape velocity
g = GM/R2 .....substitute into the eqn above
V = √(2gR)
6. Satelites in orbits
Consider a satelite of mass m, circling earth
of mass M; assuming earth is perfectly
spherical
mv2/r = GMm/r2 = mg
From this eqn v2 = rg
v = √rg
7. Parking orbits
Orbit a satelite will be`on and stay at the
same place above the earth as the earth
rotates if the period of the satelite = period of
the earth about its own axis)
mv2/R = GMm/R2
remember GMm/r2 = mg
So GMm = mgr2
mv2/R = mgr2/R2
v2 = gr2/R
v = √gr2/R
8. Period
v = 2πR/T1
Square both sides
V2 = 4π2 R2
T1
2
Remember v2 = gr2/R
gr2 = 4π2 R2 T2 = 4π2 R3
R T1
2 gr2
• T =√ 4π2 R3
gr2