Newton's law of universal gravitation describes how every particle in the universe attracts other particles with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The gravitational constant G relates this gravitational force to the masses and distance. For objects on Earth, like satellites, the force of gravity g can be expressed using the mass of the Earth, the radius of the Earth, and the gravitational constant G. Escape velocity is the minimum velocity needed for an object to escape Earth's gravity and can be calculated using g and the radius of the Earth. The velocity of satellites in orbit around Earth is the square root of the product of the radius of the orbit and g. Parking

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