🌌 Classical Mechanics & Universal Gravitation
Newton's Gravitational Force Calculator
Calculate the mutual gravitational attraction force ($F = G \frac{m_1 m_2}{r^2}$), gravitational potential energy ($U$), and acceleration between two bodies in the universe.
☀️ Sun & 🌍 Earth ($3.54 \times 10^{22}\text{ N}$)
🌍 Earth & 🌕 Moon ($1.98 \times 10^{20}\text{ N}$)
🧍 Human on Earth ($686\text{ N}$)
🤝 Two Humans at 1m ($3.27 \times 10^{-7}\text{ N}$)
Masses & Separation
kg
kg
Gravitational Attractive Force (F)
686.9 N
Potential Energy ($U$)
-4.38 GJ
Acceleration on $m_2$
9.814 m/s²
Separation ($r$)
6,371 km
💡 Gravitational Constant ($G$):
$$G = 6.67430 \times 10^{-11}\text{ N}\cdot\text{m}^2/\text{kg}^2$$
Newton's Law of Universal Gravitation
Sir Isaac Newton established that gravity is an inverse-square central force:
$$F = G \frac{m_1 m_2}{r^2}, \quad U = -G \frac{m_1 m_2}{r}, \quad g = \frac{F}{m_2} = \frac{G m_1}{r^2}$$
- Gravitational Constant ($G$): $6.67430(15) \times 10^{-11}\text{ m}^3\text{kg}^{-1}\text{s}^{-2}$.
- Inverse Square Law: Doubling separation distance reduces gravitational attraction by a factor of 4 ($1/2^2$).