prepwalk

1. PHYSICS
GRAVITATIONAL FIELD
Short revision series

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

9. END