Gravitation Notes for NEET — Class 11 NCERT

Introduction

Gravity holds you to the Earth, the Earth to the Sun, the Sun to the galaxy. Newton wrote down a single law in the 1680s that explains all of these — and Einstein, three centuries later, refined it but did not replace it for everyday distances.

For NEET 2027, expect 1 to 3 questions from this chapter. Kepler's third law, escape velocity, orbital velocity, the variation of $g$ with altitude or depth, and the total energy of a satellite are the heavy hitters. Most questions are formula-driven — memorise the six formulas in the cheat sheet and you can lock in full marks.

Newton's universal law of gravitation

Every pair of point masses attracts each other with a force directed along the line joining them, with magnitude:

F = G \frac{m _{1} m _{2}}{r ^{2}} .

Here $G = 6.674 \times 1 0^{- 11} N m^{2} / kg^{2}$ is the universal gravitational constant. The law applies to spherical bodies as well — you can treat each sphere as if all its mass were concentrated at its centre (the shell theorem).

Properties of the gravitational force:

Always attractive (no negative masses).
Acts along the line joining the centres.
Obeys Newton's third law — the two bodies pull on each other equally.
Inverse-square: doubling $r$ drops $F$ by a factor of four.
Independent of the medium between the masses.

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.

Kepler's three laws

Kepler discovered three empirical laws of planetary motion before Newton explained them. NEET tests all three.

Law 1 — Law of orbits

Every planet moves in an elliptical orbit with the Sun at one focus.

Law 2 — Law of areas

The line joining a planet to the Sun sweeps equal areas in equal times. Areal velocity is constant. This is equivalent to conservation of angular momentum (the Sun's gravity is a central force, so torque about the Sun is zero).

Law 3 — Law of periods

T^{2} = \frac{4 π ^{2}}{GM} r^{3} \Rightarrow T^{2} \propto r^{3} .

For any two satellites of the same central body: $T_{1}^{2} / T_{2}^{2} = r_{1}^{3} / r_{2}^{3}$ . For elliptical orbits, $r$ is the semi-major axis.

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

Acceleration due to gravity at Earth's surface

Setting the universal law equal to $m g$ for an object of mass $m$ at the surface of Earth (mass $M$ , radius $R$ ):

g = \frac{GM}{R ^{2}} .

Take $g \approx 9.8 m/s^{2}$ , $M \approx 6 \times 1 0^{24} kg$ , $R \approx 6.4 \times 1 0^{6} m$ .

Variation of g

With altitude (height h above surface)

g_{h} = g \frac{R ^{2}}{( R + h ) ^{2}} .

For $h ≪ R$ , this reduces to $g_{h} \approx g (1 - 2 h / R)$ .

With depth (depth d below surface)

g_{d} = g (1 - \frac{d}{R}) .

At the centre of the Earth ( $d = R$ ), $g = 0$ . The mass outside a shell at radius $R - d$ exerts no net force on a body inside it.

With latitude (rotation of Earth)

Effective gravity decreases as you move from the poles to the equator because of Earth's rotation:

g_{eff} = g - R ω^{2} cos^{2} λ,

where $λ$ is the latitude. Difference between equator and poles is about $0.034 m/s^{2}$ .

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}

Practice these on the timed test

Try a free 10-question NEET mock test on Gravitation — instant results, no sign-up needed.

Gravitational potential and potential energy

Gravitational potential

The gravitational potential at distance $r$ from a point mass $M$ (taking zero at infinity):

V = - \frac{GM}{r} .

Gravitational potential energy

The PE of a mass $m$ at distance $r$ :

U = mV = - \frac{GM m}{r} .

Always negative (because we choose $U = 0$ at infinity), and it gets less negative — that is, increases — as $r$ increases.

Near Earth's surface

For small heights, $Δ U = m g h$ (the formula you have used since Class 11 mechanics). It is a special case of the universal formula expanded near the surface.

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}}

Escape velocity

The minimum speed at which a projectile must be launched to escape a planet's gravity (and never come back) is found by setting the total mechanical energy at the surface to zero:

\frac{1}{2} m v_{esc}^{2} - \frac{GM m}{R} = 0 \Rightarrow v_{esc} = \frac{2 GM}{R} = 2 g R .

For Earth, $v_{esc} \approx 11.2 km/s$ . Independent of the mass of the projectile and of the angle of projection (energy is a scalar).

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)

Earth satellites — orbital velocity and period

For a satellite of mass $m$ in a circular orbit of radius $r = R + h$ around Earth, the gravitational pull provides the centripetal force:

\frac{GM m}{r ^{2}} = \frac{m v _{orb}^{2}}{r} \Rightarrow v_{orb} = \frac{GM}{r} .

Time period:

T = \frac{2 π r}{v _{orb}} = 2 π \frac{r ^{3}}{GM} .

For low Earth orbit ( $h ≪ R$ , so $r \approx R$ ), $v_{orb} \approx 7.9 km/s$ and $T \approx 84 min$ .

Two useful relations:

v_{esc} = 2 v_{orb} (at the surface) .

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 )}

Energy of an orbiting satellite

For a satellite in a circular orbit of radius $r$ :

K = \frac{1}{2} m v_{orb}^{2} = \frac{GM m}{2 r} .

U = - \frac{GM m}{r} .

E = K + U = - \frac{GM m}{2 r} = - K .

Total energy is negative — the satellite is bound. Its magnitude equals the kinetic energy. To unbind the satellite (set $E = 0$ ), you must add energy equal to $\frac{GM m}{2 r}$ .

Geostationary and polar satellites

Geostationary satellite

A satellite is geostationary if its orbital period equals one sidereal day ( $\approx 24$ h), so it appears fixed in the sky from Earth. Conditions:

Orbits in the equatorial plane.
Orbits in the same direction as Earth's rotation.
Has the unique radius computed from Kepler's third law: $r \approx 4.2 \times 1 0^{7} m$ from the centre of Earth, i.e. $\approx 36, 000 km$ above the equator.

Used for communication, TV broadcast and weather.

Polar satellite

Polar (or sun-synchronous) satellites orbit at low altitudes ( $\sim 500$ – $800 km$ ) passing close to both poles. They cover the entire surface as Earth rotates beneath them. Used for remote sensing, mapping and meteorology.

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

Weightlessness

An astronaut in orbit feels weightless not because there is no gravity (gravity at $400 km$ is still about $89%$ of surface gravity) but because the astronaut and the spacecraft are both in free fall — gravity is the only force, and it accelerates everything together. With no normal force, there is no apparent weight. Same effect inside a freely falling lift, or at the top of a parabolic plane manoeuvre.

Worked NEET problems

NEET-style problem · Variation of g

Question

Find the height above Earth's surface at which

g

is reduced to

1/4

of its surface value. Take Earth's radius

R

Solution

g_{h} = g \frac{R ^{2}}{( R + h ) ^{2}} = \frac{g}{4} \Rightarrow \frac{R ^{2}}{( R + h ) ^{2}} = \frac{1}{4} .

Take square roots: $R / (R + h) = 1/2 \Rightarrow R + h = 2 R \Rightarrow h = R$ .

NEET-style problem · Escape velocity

Question

The escape velocity at the surface of Earth is

11.2 km/s

. The escape velocity from a planet whose mass is

9

times that of Earth and whose radius is

4

times that of Earth is:

Solution

v_{esc} = \frac{2 GM}{R} \Rightarrow \frac{v ^{'}}{v} = \frac{M ^{'} / R ^{'}}{M / R} = \frac{9}{4} = \frac{3}{2} .

$v^{'} = \frac{3}{2} \times 11.2 = 16.8 km/s$ .

NEET-style problem · Kepler third law

Question

A satellite revolves around the Earth at a radius

r_{1}

with time period

T_{1}

. Another satellite revolves at

r_{2} = 4 r_{1}

. Find its time period.

Solution

By Kepler's third law:

\frac{T _{2}^{2}}{T _{1}^{2}} = \frac{r _{2}^{3}}{r _{1}^{3}} = 64 \Rightarrow T_{2} = 8 T_{1} .

NEET-style problem · Orbital velocity

Question

A satellite of mass

m

orbits Earth at a height equal to Earth's radius

R

. The orbital velocity (in terms of

g

and

R

) is:

Solution

At height $R$ , orbit radius $r = 2 R$ .

v_{orb} = \frac{GM}{r} = \frac{GM}{2 R} = \frac{g R}{2} .

(Used $GM = g R^{2}$ .)

NEET-style problem · Total energy

Question

The total energy of a satellite of mass

m

in a circular orbit of radius

r

is:

Solution

E = - \frac{GM m}{2 r} .

Negative means the satellite is bound. Half-magnitude of the potential energy $U = - GM m / r$ .

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Summary cheat sheet

Universal law: $F = G m_{1} m_{2} / r^{2}$ , $G = 6.67 \times 1 0^{- 11} N m^{2} / kg^{2}$ .
Surface gravity: $g = GM / R^{2}$ .
g at altitude: $g_{h} = g R^{2} / (R + h)^{2}$ , small h: $g (1 - 2 h / R)$ .
g at depth: $g_{d} = g (1 - d / R)$ . Zero at the centre.
Kepler III: $T^{2} \propto r^{3}$ for any orbit around a fixed central body.
Gravitational PE: $U = - GM m / r$ .
Escape velocity: $v_{esc} = 2 GM / R = 2 g R$ , Earth: 11.2 km/s.
Orbital velocity: $v_{orb} = GM / r$ , low Earth orbit: 7.9 km/s.
Useful link: $v_{esc} = 2 v_{orb}$ at the same radius.
Satellite energy: $E = - GM m / (2 r) = - K = U /2$ .
Geostationary: equatorial, prograde, period 24 h, altitude ≈ 36,000 km.

Next: try the interactive widgets for variation of g, escape velocity, orbital satellites and Kepler's third law, or work through the 30+ NEET PYQs with full solutions. To time yourself, take the free 10-question mock test.

Frequently asked questions

How many questions come from Gravitation in NEET 2027?

You can expect 1 to 3 questions from Gravitation in NEET 2027. The chapter has high PYQ frequency. Kepler's third law, escape velocity, orbital velocity, the variation of g with altitude or depth, and total energy of a satellite are tested almost every year.

What is the universal law of gravitation?

Every two point masses attract each other with a force F equals G m1 m2 over r squared, directed along the line joining them. G is the universal gravitational constant, equal to 6.67 times 10 to the minus 11 N m squared per kg squared. The law works for spherical bodies treating them as if all mass were at the centre.

How does the value of g change with altitude and depth?

At height h above the surface, g_h equals g times R squared over (R plus h) squared, smaller than the surface value. At depth d below the surface, g_d equals g times (1 minus d over R), also smaller. At the centre of Earth, g equals zero. NEET asks both of these almost every year.

What is escape velocity and what is its value on Earth?

Escape velocity is the minimum speed an object needs to leave the gravitational pull of a planet without further propulsion. It equals square root of (2 G M over R), or equivalently square root of (2 g R). For Earth, v_esc is approximately 11.2 km per second. It does not depend on the mass of the escaping object.

What is orbital velocity for an Earth satellite?

For a satellite in a circular orbit at height h, the orbital velocity is v_orbital equals square root of (G M over (R plus h)). For low Earth orbit (h is much smaller than R), this simplifies to about 7.9 km per second. The orbital velocity equals escape velocity divided by square root of 2, regardless of orbit radius near Earth.

What does it mean for a satellite to be geostationary?

A geostationary satellite has its orbital period equal to one sidereal day (24 hours), so it appears stationary above one point on Earth. This requires it to orbit in the equatorial plane at a height of about 36,000 km, where v_orbital equals about 3.07 km per second. Used for communications and TV broadcasting.

What is Kepler's third law and why does it work?

Kepler's third law says T squared is proportional to r cubed for any planet or satellite around a central body. The constant of proportionality is 4 pi squared over G M, where M is the mass of the central body. NEET problems often give T and r for one orbit and ask for the other, which only requires this proportionality.

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GravitationNEET Physics · Class 11 · NCERT Chapter 7

Introduction

Newton's universal law of gravitation

Kepler's three laws

Law 1 — Law of orbits

Law 2 — Law of areas

Law 3 — Law of periods

Acceleration due to gravity at Earth's surface

Variation of g

With altitude (height h above surface)

With depth (depth d below surface)

With latitude (rotation of Earth)

Gravitational potential and potential energy

Gravitational potential

Gravitational potential energy

Near Earth's surface

Escape velocity

Earth satellites — orbital velocity and period

Energy of an orbiting satellite

Geostationary and polar satellites

Geostationary satellite

Polar satellite

Weightlessness

Worked NEET problems

Summary cheat sheet

Frequently asked questions

How many questions come from Gravitation in NEET 2027?

What is the universal law of gravitation?

How does the value of g change with altitude and depth?

What is escape velocity and what is its value on Earth?

What is orbital velocity for an Earth satellite?

What does it mean for a satellite to be geostationary?

What is Kepler's third law and why does it work?

Continue with the next chapter notes

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