Gravitation Cheatsheet

Key Concepts & Formulas

• Newton's Law of Gravitation: \( F = G \frac{m_1 m_2}{r^2} \), where \( G \) is the gravitational constant.
• Gravitational Constant: \( G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \)
• Weight: \( W = mg \), where \( g \) is acceleration due to gravity.
• Acceleration due to Gravity: \( g = \frac{GM}{R^2} \), where \( M \) is Earth's mass and \( R \) is Earth's radius.
• Gravitational Potential Energy: \( U = -G \frac{mM}{r} \)
• Escape Velocity: \( v_e = \sqrt{\frac{2GM}{R}} \)
• Orbital Velocity: \( v = \sqrt{\frac{GM}{r}} \)
• Kepler’s Third Law: \( T^2 \propto r^3 \) (period squared is proportional to radius cubed)

Quick Reference Table

Concept	Formula	Description
Newton's Law	\( F = G \frac{m_1 m_2}{r^2} \)	Force of gravity between two masses
Acceleration	\( g = \frac{GM}{R^2} \)	Gravitational acceleration at surface
Potential Energy	\( U = -G \frac{mM}{r} \)	Energy due to gravitational attraction
Escape Velocity	\( v_e = \sqrt{\frac{2GM}{R}} \)	Minimum velocity to escape gravity
Orbital Velocity	\( v = \sqrt{\frac{GM}{r}} \)	Velocity to maintain circular orbit
Kepler’s 3rd Law	\( T^2 \propto r^3 \)	Relation between orbit period & radius

Advice

Gravitation Quick Tips

• Universal Law: Contacts between all masses produce gravitational force.
• Vector Nature: Gravity acts along the line joining two masses.
• Shell Theorem: Spherical shells of mass behave as if all mass is concentrated at the center.
• Orbital Motion: Velocity depends on radius of orbit and central mass.
• Energy Conservation: Total mechanical energy in orbit = kinetic + potential.

Gravitation Speed Quiz

Test your speed with 5 gravitation questions! You have 30 seconds per question.