Newton’s law, gravitational field, potential, satellites, escape velocity, Kepler’s laws (JEE Main focus).
1) Newton’s Law of Gravitation
F = G m₁ m₂ / r²
- G = 6.67 × 10⁻¹¹ N m² kg⁻²
- Force is always attractive.
2) Gravitational Field Intensity
g = F / m
g = GM / r²
- Direction is towards the attracting mass.
- At Earth’s surface, g ≈ 9.8 m/s².
3) Gravitational Potential
V = −GM / r
- Potential is negative because gravitational force is attractive.
4) Gravitational Potential Energy
U = −GMm / r
U = mV
- Reference position is at infinite separation.
5) Relation Between Field & Potential
g = − dV / dr
dV = −g · dr
6) Variation of g
- With height (h):
g' = g (1 − 2h/R) (for h ≪ R)
- With depth (d):
g' = g (1 − d/R)
- With latitude (λ): g is maximum at poles and minimum at equator.
7) Escape Velocity
vₑ = √(2GM / R)
- Independent of mass of the body.
- Atmosphere is ignored.
8) Orbital Motion of Satellites
Orbital velocity: v₀ = √(GM / r)
Time period: T = 2πr / v₀
Kinetic Energy = GMm / (2r)
Potential Energy = −GMm / r
Total Energy = −GMm / (2r)
9) Kepler’s Laws
- First Law: Planets move in elliptical orbits with the Sun at one focus.
- Second Law: Equal areas are swept in equal intervals of time.
- Third Law:
T² ∝ r³
10) Weightlessness in a Satellite
Apparent weight = 0
- Occurs because normal reaction becomes zero.
11) Gravitational Field & Potential – Special Bodies
- Hollow sphere: Field inside = 0
- Solid sphere (inside): g ∝ r
- Ring (on axis): Field is zero at centre, maximum at x = R/√2
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Last modified: December 14, 2025
