Gravitational Force Calculator

Calculate gravitational force between masses, weight on different celestial bodies, and orbital velocity. Uses Newton's law of universal gravitation for physics and astronomy applications.

**Newton's Law of Universal Gravitation:** F = G × m₁ × m₂ / r² Where: • F = Gravitational force (N) • G = Gravitational constant = 6.674×10⁻¹¹ N·m²/kg² • m₁, m₂ = Masses (kg) • r = Distance between centers (m) **Weight Formula:** W = m × g Where: • W = Weight (N) • m = Mass (kg) • g = Gravitational acceleration (m/s²) **Gravitational Field:** g = G × M / r² **Orbital Velocity:** v = √(G × M / r) **Orbital Period:** T = 2πr / v = 2π√(r³ / GM) **Planetary g values:** • Earth: 9.81 m/s² • Moon: 1.62 m/s² • Mars: 3.71 m/s² • Jupiter: 24.79 m/s²
**Example 1 (Earth-Moon Force):** Earth mass = 5.972×10²⁴ kg, Moon mass = 7.342×10²² kg Distance = 3.844×10⁸ m (center to center) • F = 6.674×10⁻¹¹ × 5.972×10²⁴ × 7.342×10²² / (3.844×10⁸)² • F = 1.98×10²⁰ N (this keeps Moon in orbit!) **Example 2 (Weight on Moon):** Person mass = 70 kg • Weight on Earth = 70 × 9.81 = 686.7 N • Weight on Moon = 70 × 1.62 = 113.4 N • Moon weight = 16.5% of Earth weight **Example 3 (ISS Orbital Velocity):** Earth mass = 5.972×10²⁴ kg ISS altitude = 400 km above surface Orbital radius = 6,371,000 + 400,000 = 6,771,000 m • v = √(6.674×10⁻¹¹ × 5.972×10²⁴ / 6,771,000) • v = 7,669 m/s = 7.67 km/s • Period = 92.7 minutes (~16 orbits per day) **Example 4 (Surface Gravity of Mars):** Mars mass = 6.39×10²³ kg Mars radius = 3.39×10⁶ m • g = 6.674×10⁻¹¹ × 6.39×10²³ / (3.39×10⁶)² • g = 3.71 m/s² (38% of Earth's gravity) **Example 5 (Geostationary Orbit):** Earth mass = 5.972×10²⁴ kg Period must be 24 hours = 86,400 s • r = ∛(GMT² / 4π²) = 4.22×10⁷ m • Altitude = 35,786 km above equator • v = 3.07 km/s **Example 6 (Two People Attraction):** Two 80 kg people standing 1 m apart • F = 6.674×10⁻¹¹ × 80 × 80 / 1² • F = 4.27×10⁻⁷ N (negligible!)

What is Newton's law of universal gravitation?

Newton's law states that every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: F = Gm₁m₂/r². G is the gravitational constant.

What is the gravitational constant G?

The gravitational constant G = 6.674×10⁻¹¹ N·m²/kg² (or m³/kg·s²). It's one of the fundamental constants of nature, discovered by Henry Cavendish in 1798, and relates mass to gravitational force.

How does distance affect gravitational force?

Gravitational force follows an inverse square law: F ∝ 1/r². If you double the distance, the force becomes 1/4 as strong. Triple the distance, force drops to 1/9. This is why gravity weakens rapidly with distance.

What is the difference between mass and weight?

Mass is the amount of matter (kg), which is constant everywhere. Weight is the gravitational force on that mass: W = mg, where g is local gravitational acceleration. Your mass is the same on Earth and Moon, but weight differs.

How do I calculate orbital mechanics?

For circular orbits, gravitational force provides centripetal force: GMm/r² = mv²/r. This gives orbital velocity v = √(GM/r) and period T = 2πr/v. The orbital speed decreases with altitude.

What is gravitational field strength (g)?

Gravitational field g = GM/r² is force per unit mass (m/s² or N/kg). At Earth's surface, g ≈ 9.81 m/s². It's the acceleration a free-falling object experiences. Calculate using g = F/m.

Why don't we feel gravitational attraction to nearby objects?

We do, but it's incredibly weak! G is very small (6.67×10⁻¹¹), so gravitational force between everyday objects is negligible. You need planetary masses for significant gravity. Two 100 kg people 1 m apart attract with only ~0.0000007 N force!

What is escape velocity?

Escape velocity is the minimum speed to escape a body's gravity: v_escape = √(2GM/r). For Earth, it's 11.2 km/s at the surface. This velocity decreases with altitude since r increases.

How does gravitational force work in space?

Gravity works the same in space! Astronauts aren't weightless because there's no gravity - they're in free fall, continuously falling around Earth. At ISS altitude (~400 km), Earth's gravity is still ~90% of surface strength.

What is the difference between g and G?

G is the universal gravitational constant (6.674×10⁻¹¹ N·m²/kg²), same everywhere in the universe. g is local gravitational acceleration (9.81 m/s² on Earth's surface), which varies by location and altitude.

Can I calculate gravity between Earth and Moon?

Yes! Earth mass = 5.972×10²⁴ kg, Moon mass = 7.342×10²² kg, average distance = 3.844×10⁸ m. F = GMₑMₘ/r² = 1.98×10²⁰ N. This force keeps the Moon in orbit and causes tides.

How does altitude affect weight?

Weight decreases with altitude because r increases. At height h above Earth's surface: g(h) = g₀(R/(R+h))², where R is Earth's radius. At 400 km (ISS), weight is about 88% of surface weight.

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