Gravitation

GravitationNEET Physics · Class 11 · NCERT Chapter 7

Overview Notes NEET Questions Interactive Learning

7 interactive concept widgets for Gravitation. Drag any slider, change any number, and watch the formula and the answer update live. Built so you understand how each NEET problem actually works, not just the final number.

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Gravitational force calculator (F = G m₁m₂/r²)

Variation of g with altitude and depth

Kepler's third law (T² ∝ r³)

Orbital satellite simulator

Geostationary orbit visualiser

Gravitational potential energy and work

Escape velocity calculator

Universal law and the value of g

Newton's law of gravitation plus the variation of g with altitude or depth — both NEET regulars.

Universal law

Gravitational force calculator (F = G m₁m₂ / r²)

Adjust two masses and the distance between them. Watch the inverse-square scaling at work.

Mass m₁: 1 kg

Mass m₂: 1 kg

Distance r: 1.0 m

Gravitational force

F = 6.674e-11 N

F = \frac{G m _{1} m _{2}}{r ^{2}} = \frac{6.67 \times 1 0 ^{- 11} \times 1 \times 1}{1. 0 ^{2}}

G = 6.67 × 10⁻¹¹ N·m²/kg² is tiny, so gravity is weak unless one of the masses is very large.

Try this

Two 1 kg masses 1 m apart attract with about 7 × 10⁻¹¹ N — far too small to feel.
Increase m₁ to 1000 kg → force goes up by 1000×. Still tiny on a human scale.
Doubling r drops F by 4× (inverse-square). Halving r raises F by 4×.

Variation of g

Variation of g with altitude and depth

Two formulas, two behaviours: at altitude g falls as 1/(R+h)², at depth it falls linearly with d/R.

Altitude h: 0 km

LEO ≈ 400 km · GPS ≈ 20,000 km · Geostationary ≈ 36,000 km

Local gravity

g = 9.800 m/s²

That is 100.0% of the surface value.

g_{h} = g \frac{R ^{2}}{( R + h ) ^{2}} = 9.8 \times \frac{6. 4 ^{2}}{( 6.4 + 0.00 ) ^{2}} = 9.800 m/s^{2}

Try this

At LEO altitude (400 km), g is still ~89% of surface gravity. Astronauts feel weightless because of free fall, not lack of gravity.
At geostationary altitude (36,000 km), g drops to about 0.22 m/s² — about 2.3% of surface gravity.
Going down: at d = R/2, g halves. At the centre, g = 0 (no net pull from a uniform shell).

Orbits and Kepler's third law

Same central body ⇒ T² ∝ r³. Pair the orbital satellite simulator with Kepler's law to see the scaling for any orbit.

Kepler

Kepler's third law (T² ∝ r³)

A unitless calculator. Pick reference orbit's r and T, then change the new orbit's radius to see its period.

Kepler's third law: T² ∝ r³. Same central body for both orbits. Set the first orbit's radius and period, then read off the period of any other orbit you choose.

Reference orbit

r₁: 1.00 (any unit, e.g. AU or R_E)

T₁: 1.00 (matching unit, e.g. years or hours)

New orbit

r₂: 4.00

New period

T₂ = 8.000

\frac{T _{2}}{T _{1}} = (\frac{r _{2}}{r _{1}})^{3/2} = (\frac{4.00}{1.00})^{3/2} = 8.000

T_{2} = 8.000 \times 1.00 = 8.000

Try this

Set r₂ = 4 r₁ → T₂ = 8 T₁. The famous "fourth power × eighth period" relation.
Try Earth orbit (1 AU, 1 year) → Mars at 1.52 AU has T = 1.88 years. Saturn at 9.5 AU has T = 29.4 years.
For a satellite at LEO (~6,800 km, T = 90 min) → at GEO (42,000 km), T = 90 × (42000/6800)^1.5 ≈ 90 × 15.7 = 1413 min ≈ 23.6 hours.

Satellite

Orbital satellite simulator

A satellite in a circular orbit around Earth. The widget shows orbital velocity, period and total energy as you slide altitude.

Altitude h: 400 km (orbit radius 6771 km)

ISS ≈ 400 km · GPS ≈ 20,200 km · Geostationary ≈ 35,800 km

Satellite mass m: 1000 kg

Orbital velocity

7.67 km/s

Period

1.54 h

Kinetic energy

29.43 GJ

Total energy

-29.43 GJ

(negative = bound)

v_{orb} = \frac{GM}{R + h}, T = \frac{2 π ( R + h )}{v _{orb}}, E = - \frac{GM m}{2 ( R + h )}

Try this

ISS at h = 400 km → v ≈ 7.67 km/s, T ≈ 92 min. About 16 orbits per day.
Geostationary at h = 35,800 km → T = 24 h, v ≈ 3.07 km/s. The unique orbit that stays above one spot.
Doubling the orbital radius drops v by √2 (≈ 30%) and multiplies T by 2√2 (≈ 2.83×).

Geostationary

Geostationary orbit visualiser

Pick a target period and see the orbit radius that satisfies Kepler's third law for Earth. T = 24 h gives the unique geostationary orbit.

Target period: 24.00 hours

Drag toward 24 h to find the geostationary radius. ISS = 1.5 h · GPS = 12 h · GEO = 24 h

Altitude

35.9k km

Orbital speed

3.07 km/s

Geostationary orbit found. Stays above one point on Earth.

r = 3 \frac{GM T ^{2}}{4 π ^{2}} = 42.24 \times 1 0^{6} m

Try this

Slide to T = 24 h → r ≈ 4.22 × 10⁷ m, altitude ≈ 35,800 km. The unique GEO orbit.
T = 12 h → GPS-style orbit at altitude ≈ 20,200 km, with v ≈ 3.87 km/s.
T = 1.5 h (90 min) → low Earth orbit at ≈ 380 km, v ≈ 7.7 km/s. Where the ISS lives.

Energy and escape velocity

Gravitational PE is always negative; escape velocity is what brings the total energy back to zero.

Gravitational PE

Gravitational potential energy and work

The PE of a mass m at distance r from Earth's centre. The work to raise it equals ΔU.

Gravitational PE relative to infinity = 0. Always negative for a bound mass; less negative as you move away from Earth. The work done in raising a body equals the change in its PE.

Mass m: 10 kg

Initial altitude h₁: 0 km

Final altitude h₂: 1000 km

U at h₁

-625.602 MJ

U at h₂

-540.729 MJ

Work to raise from h₁ to h₂

W = 84.873 MJ

W = U_{2} - U_{1} = - \frac{GM m}{r _{2}} + \frac{GM m}{r _{1}}

Try this

Set h₁ = 0, h₂ small → W ≈ m·g·h. Recovers the textbook formula for low altitudes.
Set h₂ = 36,000 km → big leap in PE. Lifting to geostationary height costs many MJ even for a small mass.
Set h₂ very large → U₂ → 0. Work needed approaches G·M·m/R, exactly the energy that defines escape.

Escape velocity

Escape velocity calculator

Vary the mass and radius of a planet (or click a preset) to see escape velocity. The orbital velocity at the surface is √2 times smaller.

Mass: 1.00 × Earth (5.97e+24 kg)

Radius: 1.00 × Earth (6371 km)

Quick presets

Escape velocity

11.19 km/s

v_{esc} = \frac{2 GM}{R} = 11.19 km/s

Orbital velocity (low orbit)

7.91 km/s

v_esc / v_orb = √2 ≈ 1.414 (always, at the same r)

Try this

Click Earth → 11.18 km/s. Click Moon → 2.38 km/s (light enough that it cannot hold an atmosphere).
Click Jupiter → 59.5 km/s. The most massive planet has the largest escape velocity in our system.
NEET classic: doubling M and doubling R leaves v_esc unchanged — the M/R ratio is what matters.

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