JEE Physics — Gravitation Complete Chapter Guide

Chapter Overview & Weightage

Gravitation is a high-reward chapter in JEE Physics. The concepts are tightly interconnected — once you understand orbital mechanics, everything from escape velocity to satellite energy falls into place.

Gravitation contributes 1–2 questions per paper in JEE Main, typically worth 4–8 marks. In JEE Advanced, it appears in multi-concept problems combined with mechanics or SHM. The chapter has shown up every single year since 2015.

Year	JEE Main (Questions)	JEE Advanced	Key Topic Tested
2024	2	1	Orbital velocity, gravitational PE
2023	1	2	Kepler’s 3rd law, escape velocity
2022	2	1	Satellite energy, binding energy
2021	2	1	Variation of g, gravitational field
2020	1	2	Geostationary orbit, shell theorem
2019	2	1	Circular orbit, potential energy

The weightage sits consistently at 4–6% of JEE Main. For a 30-mark Physics section, you’re looking at 4–8 marks — worth every hour you put in.

Key Concepts You Must Know

Ranked by frequency in PYQs:

Newton’s Law of Gravitation — $F = \frac{Gm_1 m_2}{r^2}$ . The foundation. Know the vector form and understand that G is universal (same in vacuum, water, or space).
Gravitational Field and Potential — $g = \frac{GM}{r^2}$ outside a sphere; variation inside (linear with r) and outside (inverse square). This variation is JEE’s favourite trap zone.
Shell Theorem — field inside a uniform spherical shell is zero. Field outside is as if all mass is at the centre. This appears in almost every set of PYQs in some form.
Orbital Velocity — $v_o = \sqrt{\frac{GM}{r}}$ . Independent of the satellite’s mass — this surprises students every exam season.
Escape Velocity — $v_e = \sqrt{\frac{2GM}{R}}$ . Note that $v_e = \sqrt{2} \cdot v_o$ at the surface.
Kepler’s Three Laws — Law of orbits (ellipse), law of areas (equal areas in equal time = conservation of angular momentum), law of periods ( $T^2 \propto a^3$ where a is semi-major axis).
Gravitational Potential Energy — $U = -\frac{GMm}{r}$ . The negative sign is not cosmetic — it drives most energy questions.
Satellite Energy — total energy of a satellite is $E = -\frac{GMm}{2r}$ . KE = $\frac{GMm}{2r}$ , PE = $-\frac{GMm}{r}$ .
Geostationary and Polar Satellites — qualitative understanding plus numerical on time period.

Important Formulas

F = \frac{Gm_1 m_2}{r^2}

When to use: Any force calculation between two point masses or spherical bodies. Also the starting point for deriving orbital velocity and escape velocity.

Outside a sphere ( $r > R$ ): $\quad g = \frac{GM}{r^2}$

Inside a uniform solid sphere ( $r < R$ ): $\quad g = \frac{GMr}{R^3}$

Inside a spherical shell: $\quad g = 0$

When to use: Any question on variation of g with depth, height, or position. For height $h$ above surface: $g_h = g\left(1 + \frac{h}{R}\right)^{-2} \approx g\left(1 - \frac{2h}{R}\right)$ for $h \ll R$ .

v_o = \sqrt{\frac{GM}{r}} \qquad v_e = \sqrt{\frac{2GM}{R}}

Relationship: $v_e = \sqrt{2} \cdot v_o$ (only valid when comparing at the surface, $r = R$ ).

When to use: Orbital velocity for any circular orbit at radius r. Escape velocity to find the minimum launch speed to leave a planet’s gravity.

E = K + U = \frac{GMm}{2r} - \frac{GMm}{r} = -\frac{GMm}{2r}

When to use: Binding energy = $|E| = \frac{GMm}{2r}$ . When a satellite moves to a higher orbit, its KE decreases and total energy increases (becomes less negative). This counter-intuitive fact is JEE gold.

T^2 \propto a^3 \quad \Rightarrow \quad \frac{T_1^2}{T_2^2} = \frac{a_1^3}{a_2^3}

For circular orbit: $T = \frac{2\pi r}{v_o} = 2\pi\sqrt{\frac{r^3}{GM}}$

When to use: Comparing time periods of planets or satellites. Also to find orbital radius when time period is given.

V = -\frac{GM}{r}

Potential due to a shell (outside): $V = -\frac{GM}{r}$

Potential due to a shell (inside): $V = -\frac{GM}{R}$ (constant)

When to use: Work done by gravity = $-\Delta U = -m\Delta V$ . Potential energy $U = mV$ .

Solved Previous Year Questions

PYQ 1 — JEE Main 2024 (Shift 1)

Q. A satellite of mass $m$ is orbiting the Earth in a circular orbit of radius $2R$ , where $R$ is Earth’s radius. The minimum energy required to move the satellite to an orbit of radius $3R$ is:

Solution:

The total energy at radius $r$ is $E = -\frac{GMm}{2r}$ .

Energy at $r = 2R$ :

E_1 = -\frac{GMm}{2(2R)} = -\frac{GMm}{4R}

Energy at $r = 3R$ :

E_2 = -\frac{GMm}{2(3R)} = -\frac{GMm}{6R}

Energy required:

\Delta E = E_2 - E_1 = -\frac{GMm}{6R} + \frac{GMm}{4R} = GMm\left(\frac{1}{4R} - \frac{1}{6R}\right) = \frac{GMm}{12R}

Since $GM = gR^2$ :

\Delta E = \frac{mgR}{12}

Answer: $\frac{mgR}{12}$

Students often subtract the wrong way: $E_1 - E_2$ instead of $E_2 - E_1$ . Remember — higher orbit = higher (less negative) total energy. You must supply energy to move a satellite outward.

PYQ 2 — JEE Main 2023

Q. The ratio of the escape velocity to the orbital velocity of a satellite orbiting just above the Earth’s surface is:

Solution:

At the surface ( $r = R$ ):

v_o = \sqrt{\frac{GM}{R}}, \qquad v_e = \sqrt{\frac{2GM}{R}}

\frac{v_e}{v_o} = \frac{\sqrt{\frac{2GM}{R}}}{\sqrt{\frac{GM}{R}}} = \sqrt{2}

Answer: $\sqrt{2}$

This is a direct formula result, but it only holds when both are evaluated at $r = R$ . If the orbital radius is $2R$ but you’re asked for escape from the surface, you need to be careful.

PYQ 3 — JEE Advanced 2022 (Paper 1)

Q. A planet of mass $M$ moves in an elliptical orbit around the Sun. At aphelion (farthest point) the distance is $r_a$ and velocity is $v_a$ . At perihelion (closest point) the distance is $r_p$ . Find the velocity at perihelion.

Solution:

We use conservation of angular momentum (Kepler’s Second Law in disguise). At any point in the orbit, the angular momentum about the Sun is constant:

L = mv_a r_a = mv_p r_p

Since $m$ cancels:

v_p = \frac{v_a r_a}{r_p}

Why angular momentum? The gravitational force is always directed toward the Sun (central force), so torque about the Sun is zero, making $L$ conserved.

For JEE Advanced ellipse questions, always write two equations: (1) conservation of angular momentum ( $mv r$ = constant at any two points where velocity ⊥ radius), and (2) conservation of energy. Two equations, two unknowns — it always works.

Difficulty Distribution

For JEE Main Gravitation questions, here’s the realistic split from analysing 2019–2024 papers:

Difficulty	Percentage	What It Looks Like
Easy	40%	Direct formula: orbital velocity, escape velocity, g variation
Medium	45%	Two-concept: energy + orbit change, Kepler + velocity
Hard	15%	JEE Advanced style: multi-body, elliptical orbits, shell combinations

The medium-difficulty questions are where most marks are won or lost. If you can handle energy conservation + orbital mechanics in one problem, you’re in the top bracket for this chapter.

Expert Strategy

Week 1 — Build the conceptual core. Understand the shell theorem physically before memorising anything. Draw the field-vs-distance graph for a solid sphere and a shell. If you can draw it from scratch, you own the concept.

Week 2 — The energy framework. Derive $E = -\frac{GMm}{2r}$ yourself from scratch using $F = ma$ for circular motion. Once you’ve derived it once, you’ll never forget the sign or the factor of 2.

Toppers treat Gravitation as a pure energy chapter. 70% of JEE Main problems here reduce to: write initial energy, write final energy, find the difference. The conceptual layer (what’s a satellite, what’s an orbit) just tells you which formula to use.

For JEE Advanced: Elliptical orbit problems always come down to two conservation laws — angular momentum and energy. Practice identifying the aphelion and perihelion, and applying both laws simultaneously. This is a 5-mark question type you can reliably score.

PYQ revision plan: Solve the last 5 years of JEE Main Gravitation questions in one sitting (roughly 8–10 questions). You’ll notice the same 4–5 concepts recycled. That’s the exam telling you exactly what to prepare.

Integration with other chapters: Gravitation problems in JEE Advanced often combine with:

SHM — a particle oscillating through a tunnel in the Earth
Circular motion — satellite in orbit is uniform circular motion
Energy conservation — any orbit change or escape problem

Common Traps

Trap 1 — Orbital velocity depends on the satellite’s mass. It does not. $v_o = \sqrt{GM/r}$ — the satellite’s mass $m$ cancels from $\frac{GMm}{r^2} = \frac{mv^2}{r}$ . Examiners put satellite masses in the question specifically to see if you’ll use them.

Trap 2 — “g is zero at the centre of the Earth.” Wrong — g is zero at the centre, but gravitational potential energy is at its minimum (most negative). Students confuse g = 0 with “no gravity” and make energy errors. The field is zero; the potential is not.

Trap 3 — Escape velocity depends on the direction of launch. It does not. You need the same $v_e = \sqrt{2GM/R}$ whether you launch straight up or at an angle (ignoring atmosphere). As long as the initial KE equals $|U|$ at the surface, the object escapes.

Trap 4 — Higher orbit means higher kinetic energy. Completely backwards. As $r$ increases, $v_o = \sqrt{GM/r}$ decreases. Higher orbit = lower KE, lower |PE|, higher total energy. The satellite slows down as it moves outward. This entire triplet is reversed from intuition, and JEE exploits it every year.

Trap 5 — Applying $T^2 \propto a^3$ using radius instead of semi-major axis. For circular orbits, $a = r$ , so it works fine. But in an elliptical orbit, $a$ is the semi-major axis, not the orbital radius at any particular point. If a question gives perihelion and aphelion distances, first find $a = \frac{r_p + r_a}{2}$ .

The cleanest way to avoid sign errors in energy problems: always write $U = -\frac{GMm}{r}$ with the negative sign first, then substitute numbers. Never “figure out the sign at the end” — that’s how marks disappear.