Gravitation - Formula Sheet
1. Universal Law of Gravitation
F = G * (m₁ * m₂) / r²
Where:
F = Gravitational force (N)
G = Gravitational constant = 6.674 × 10⁻¹¹ N·m²/kg²
m₁, m₂ = Masses of the two bodies (kg)
r = Distance between the centers of the two bodies (m)
2. Acceleration due to Gravity
g = G * M / R²
Where:
g = Acceleration due to gravity (m/s²)
M = Mass of Earth (5.972 × 10²⁴ kg)
R = Radius of Earth (6.371 × 10⁶ m)
3. Relation between g and G
g = G * M / R²
4. Variation of g with Height
g_h = g * (R / (R + h))²
Where h is the height above the Earth's surface.
5. Variation of g with Depth
g_d = g * (1 - d / R)
Where d is the depth inside the Earth.
6. Gravitational Potential Energy
U = - G * (m₁ * m₂) / r
7. Escape Velocity
v_e = √(2 * G * M / R)
For Earth, v_e ≈ 11.2 km/s
1. Universal Law of Gravitation
F = G * (m₁ * m₂) / r²
Where:
F = Gravitational force (N)
G = Gravitational constant = 6.674 × 10⁻¹¹ N·m²/kg²
m₁, m₂ = Masses of the two bodies (kg)
r = Distance between the centers of the two bodies (m)
2. Acceleration due to Gravity
g = G * M / R²
Where:
g = Acceleration due to gravity (m/s²)
M = Mass of Earth (5.972 × 10²⁴ kg)
R = Radius of Earth (6.371 × 10⁶ m)
3. Relation between g and G
g = G * M / R²
4. Variation of g with Height
g_h = g * (R / (R + h))²
Where h is the height above the Earth's surface.
5. Variation of g with Depth
g_d = g * (1 - d / R)
Where d is the depth inside the Earth.
6. Gravitational Potential Energy
U = - G * (m₁ * m₂) / r
7. Escape Velocity
v_e = √(2 * G * M / R)
For Earth, v_e ≈ 11.2 km/s
