JEE · Physics

Gravitation

Connect gravitational force, field, potential, energy, and orbital motion without mixing vector and scalar quantities.

Subject: Physics
Syllabus unit: Gravitation
Updated: 8 September 2026

Mapped to JEE Main 2026 and JEE Advanced 2026
Formulas carry their conditions
No invented weightage, question counts or trend percentages

Content status: draft. Verified academic content for this page has not been loaded yet, so the page is excluded from search indexing and the sitemap.

In short

Gravitation is an attractive inverse-square interaction. Gravitational field is force per unit test mass and points toward the source. Gravitational potential is potential energy per unit mass and is negative when zero is chosen at infinity.

Circular orbits result when gravity supplies centripetal acceleration; escape is an energy condition, not a powered climb at constant speed.

Syllabus mapping

Syllabus mapping
Unit	Topics
Gravitation	Universal law of gravitation, Acceleration due to gravity and its variation with altitude and depth, Kepler's laws of planetary motion, Gravitational potential and potential energy, Escape velocity, Satellite motion, orbital velocity, time period, and energy, Geostationary orbits

Unit
Gravitation
Topics
Universal law of gravitation, Acceleration due to gravity and its variation with altitude and depth, Kepler's laws of planetary motion, Gravitational potential and potential energy, Escape velocity, Satellite motion, orbital velocity, time period, and energy, Geostationary orbits

What this chapter contains and why it matters

What this chapter contains and why it matters
Question	Direct answer
What is the chapter about?	How gravitational force, field, potential, potential energy, orbital motion, and escape velocity connect, and how g varies with altitude and depth.
What is the central method choice?	Use field and vector superposition for force or acceleration at a point, potential difference for work between two radii, gravity-equals-centripetal-requirement for circular satellites, total orbital energy for transfers between orbits, and energy conservation for escape.
Where do most mistakes begin?	Using altitude instead of centre-to-centre radius, giving potential a vector direction, and confusing total orbital energy with potential energy.
What should come before Gravitation?	Vectors, circular-motion acceleration, work-energy reasoning, and graph reading.
What comes after it?	Electrostatics reuses the same inverse-square field and potential structure, and Rotational Motion extends circular-motion reasoning.

Question
What is the chapter about?
Direct answer
How gravitational force, field, potential, potential energy, orbital motion, and escape velocity connect, and how g varies with altitude and depth.
Question
What is the central method choice?
Direct answer
Use field and vector superposition for force or acceleration at a point, potential difference for work between two radii, gravity-equals-centripetal-requirement for circular satellites, total orbital energy for transfers between orbits, and energy conservation for escape.
Question
Where do most mistakes begin?
Direct answer
Using altitude instead of centre-to-centre radius, giving potential a vector direction, and confusing total orbital energy with potential energy.
Question
What should come before Gravitation?
Direct answer
Vectors, circular-motion acceleration, work-energy reasoning, and graph reading.
Question
What comes after it?
Direct answer
Electrostatics reuses the same inverse-square field and potential structure, and Rotational Motion extends circular-motion reasoning.

The official JEE documents define content scope. They do not publish chapter weightage, so none is asserted here.

Official JEE syllabus mapping for Gravitation

Verified against the current JEE Main 2026 syllabus and JEE Advanced 2026 syllabus on 8 September 2026. This is a wording and scope mapping, not a claim about question difficulty or frequency.

Official JEE syllabus mapping for Gravitation
Concept group	JEE Main 2026	JEE Advanced 2026	Preparation note
Law of gravitation and g variation	Universal gravitation and acceleration due to gravity with variation with altitude and depth are explicitly listed.	Law of gravitation and acceleration due to gravity are explicitly listed.	Name the model, spherical Earth or uniform-density Earth, before applying a variation formula.
Kepler's laws	Kepler's laws are explicitly listed.	Kepler's law is explicitly listed.	Distinguish equal-area, period-cubed-radius, and elliptical-orbit statements.
Field, potential, and energy	Gravitational potential and potential energy, and escape velocity are explicitly listed.	Gravitational field and potential are explicitly listed.	Keep field as a vector and potential as a scalar throughout.
Satellite and orbital motion	Satellite motion, orbital velocity, time period, and energy are explicitly listed.	Geostationary orbits and circular planetary and satellite motion are explicitly listed.	Main and Advanced scope should not be assumed identical from a combined coaching outline. Keep both official documents available.

Concept group
Law of gravitation and g variation
JEE Main 2026
Universal gravitation and acceleration due to gravity with variation with altitude and depth are explicitly listed.
JEE Advanced 2026
Law of gravitation and acceleration due to gravity are explicitly listed.
Preparation note
Name the model, spherical Earth or uniform-density Earth, before applying a variation formula.
Concept group
Kepler's laws
JEE Main 2026
Kepler's laws are explicitly listed.
JEE Advanced 2026
Kepler's law is explicitly listed.
Preparation note
Distinguish equal-area, period-cubed-radius, and elliptical-orbit statements.
Concept group
Field, potential, and energy
JEE Main 2026
Gravitational potential and potential energy, and escape velocity are explicitly listed.
JEE Advanced 2026
Gravitational field and potential are explicitly listed.
Preparation note
Keep field as a vector and potential as a scalar throughout.
Concept group
Satellite and orbital motion
JEE Main 2026
Satellite motion, orbital velocity, time period, and energy are explicitly listed.
JEE Advanced 2026
Geostationary orbits and circular planetary and satellite motion are explicitly listed.
Preparation note
Main and Advanced scope should not be assumed identical from a combined coaching outline. Keep both official documents available.

Sources: JEE Main 2026 syllabus and JEE (Advanced) 2026 syllabus, both linked in the sources section below.

Before this chapter

Prerequisites: what you should know before Gravitation

Prerequisites: what you should know before Gravitation
Prerequisite	You are ready if you can…	If not, repair this first
Vectors	Add and resolve vectors, and superpose forces or fields from multiple sources.	Review vector addition and components in Kinematics.
Circular motion	Identify centripetal acceleration and its direction in uniform circular motion.	Review radial acceleration in Kinematics.
Work and energy	Relate work done against a force to a change in potential energy.	Review work-energy reasoning in Work, Energy and Power.
Graphs	Read variation graphs, such as g against height or depth.	Review slope and trend reading from motion graphs in Kinematics.

Prerequisite
Vectors
You are ready if you can…
Add and resolve vectors, and superpose forces or fields from multiple sources.
If not, repair this first
Review vector addition and components in Kinematics.
Prerequisite
Circular motion
You are ready if you can…
Identify centripetal acceleration and its direction in uniform circular motion.
If not, repair this first
Review radial acceleration in Kinematics.
Prerequisite
Work and energy
You are ready if you can…
Relate work done against a force to a change in potential energy.
If not, repair this first
Review work-energy reasoning in Work, Energy and Power.
Prerequisite
Graphs
You are ready if you can…
Read variation graphs, such as g against height or depth.
If not, repair this first
Review slope and trend reading from motion graphs in Kinematics.

This is a readiness check, not a weightage or scoring-priority list.

Concepts in this chapter

1. A source creates a field

A mass distribution creates a gravitational field around it.

A mass distribution creates a gravitational field around it. Every other mass placed in that field experiences a force.

2. Field is a vector

The field g gives the acceleration of a test mass and points toward the source.

The field g gives the acceleration a test mass would experience at a point. It is a vector and points toward the source mass.

3. Potential is a scalar

The scalar V makes energy changes easier: U equals m times V.

The scalar potential V makes energy changes easier to compute. Potential energy of a mass m in the field equals m times V.

4. Zero at infinity is the standard reference

For isolated masses, choosing V equal to zero at infinity makes bound-state potential and total energy negative.

For isolated masses, V equal to zero at infinity is the standard choice, so bound-state potential and total energy come out negative.

5. Circular orbit keeps speed constant, direction changing

In a circular orbit, gravity changes the direction of velocity while speed remains constant. Gravity supplies exactly the centripetal force required.

6. Escape is an energy condition

Minimum escape speed makes the final total energy at infinity zero.

Minimum escape speed makes the final total energy at infinity zero, neglecting atmosphere and other bodies. Escape is not a constant force climbing at constant speed.

Method selector: choose the model before calculating

Six decisions cover most Gravitation questions. Select the model before any algebra.

Method selector: choose the model before calculating
Question signal	First model	First check
Force or acceleration at a point	Field and vector superposition	Direction and distance from source centre
Work between two radii	Potential difference	Reference and endpoint radii
Circular satellite	Gravity equals centripetal requirement	Orbit radius is from the planet's centre
Transfer between circular orbits	Total orbital energy	A transfer path is not itself a circular orbit
Escape from a radius	Energy conservation	Final speed at infinity and neglected resistance
g below a surface	Enclosed-mass model	Density assumption if using a linear depth result

Question signal
Force or acceleration at a point
First model
Field and vector superposition
First check
Direction and distance from source centre
Question signal
Work between two radii
First model
Potential difference
First check
Reference and endpoint radii
Question signal
Circular satellite
First model
Gravity equals centripetal requirement
First check
Orbit radius is from the planet's centre
Question signal
Transfer between circular orbits
First model
Total orbital energy
First check
A transfer path is not itself a circular orbit
Question signal
Escape from a radius
First model
Energy conservation
First check
Final speed at infinity and neglected resistance
Question signal
g below a surface
First model
Enclosed-mass model
First check
Density assumption if using a linear depth result

Formula sheet

Gravitational force equals G times the product of the two masses, divided by the square of the separation between their centres.
Mutual force magnitude between point masses.
F
gravitational force magnitude (N)
G
universal gravitational constant (N m^2/kg^2)
m1, m2
interacting masses (kg)
r
centre-to-centre separation (m)
Use when — Point masses, or spherically symmetric bodies evaluated outside their surface.
Common trap — Using altitude instead of centre-to-centre r.
Gravitational field equals minus G times M divided by r squared, directed toward the source along the radial unit vector.
Field of an isolated spherical mass M, at distance r, directed toward the mass.
g
gravitational field (m/s^2)
M
source mass (kg)
r-hat
unit vector pointing away from the source
Use when — Outside a spherically symmetric source.
Common trap — Dropping the inward direction and treating the field as a positive scalar.
Gravitational potential equals minus G M over r, and potential energy equals mass times potential.
Potential and potential energy with zero chosen at infinity.
V
gravitational potential (J/kg)
U
potential energy of mass m (J)
Use when — Outside an isolated spherical source, with V equal to zero at infinity.
Common trap — Treating potential as a vector, or making it positive.
Orbital speed equals the square root of G M divided by r.
Circular-orbit speed.
v_o
orbital speed (m/s)
r
orbit radius from the centre (m)
Use when — Circular orbit of a satellite with negligible mass compared to a dominant central source.
Common trap — Using surface radius when the orbit altitude is nonzero.
Orbital period equals two pi times the square root of r cubed divided by G M.
Circular-orbit period.
T
orbital period (s)
Use when — Same conditions as the circular-orbit speed relation.
Common trap — Applying it directly to a noncircular trajectory.
Total orbital energy equals minus G M m divided by two r.
Total energy in a circular orbit.
E
total mechanical energy (J)
m
satellite mass (kg)
Use when — Circular orbit, zero potential chosen at infinity.
Common trap — Confusing total energy with potential energy, which is minus G M m over r.
Escape speed equals the square root of two G M divided by r.
Minimum local escape speed.
v_e
escape speed (m/s)
Use when — No atmosphere, no propulsion after launch, other bodies neglected.
Common trap — Assuming the object reaches infinity with nonzero speed.
Gravity at height h equals surface gravity times the square of R over R plus h.
Variation of g above a spherical body at height h.
g_h
gravity at height h (m/s^2)
g_0
gravity at the surface (m/s^2)
R
planetary radius (m)
h
height above the surface (m)
Use when — Outside a spherical Earth model.
Common trap — Using the small-height approximation g_0 times (1 minus 2h/R) when h is not small.
Gravity at depth d equals surface gravity times one minus d over R, for a uniform-density model.
Textbook depth result for g below the surface, at depth d.
g_d
gravity at depth d (m/s^2)
d
depth below the surface (m)
Use when — Uniform-density spherical Earth model.
Common trap — Treating the linear result as an exact real-Earth law.

Worked examples

A satellite of mass m moves in a circular orbit of radius r. How much energy must be added, at minimum, to let it escape, and by what factor does its speed change?

Answer: The least added energy is G M m divided by two r, and the speed changes from the orbital speed to the square root of two times the orbital speed.

The satellite's initial total energy in the circular orbit is E_i = minus G M m divided by two r.
The minimum escape condition is that the final total energy at infinity equals zero.
The least added energy is therefore delta E = G M m divided by two r.
At the injection point, this changes the speed from the orbital speed v_o = square root of (G M / r) to the escape speed v_e = square root of (2 G M / r), which equals the square root of two times v_o.

Common mistakes and what they actually indicate

Using altitude as r instead of adding the planetary radius
Execution error
Why it happens
Force, field, and orbit formulas use the centre-to-centre distance, not height above the surface.
How it is corrected
Add the planetary radius to the altitude before substituting r.
Giving gravitational potential a vector direction
Knowledge gap
Why it happens
Potential is a scalar, energy per unit mass; only the field is a vector.
How it is corrected
Keep potential as a signed scalar and reserve direction for the field.
Forgetting that circular-orbit total energy is half the potential energy
Recall gap
Why it happens
Total energy in a circular orbit is minus G M m over two r, while potential energy is minus G M m over r.
How it is corrected
Derive total energy from kinetic plus potential energy rather than recalling it in isolation.
Using the uniform-density depth formula without naming its model
Needs review
Why it happens
The linear depth result assumes a uniform-density spherical Earth, which is not exact for the real Earth.
How it is corrected
State the uniform-density assumption whenever the depth formula is used.
Calling escape speed an acceleration or assuming a constant upward force is required
Knowledge gap
Why it happens
Escape speed is a velocity threshold set by energy conservation, not a description of a powered climb.
How it is corrected
Treat escape as reaching zero total energy at infinity, independent of the launch method.
Applying geostationary conditions to any orbit with a 24-hour period without checking plane and direction
Decision / selection error
Why it happens
A geostationary orbit also requires the equatorial plane and a direction matching Earth's rotation.
How it is corrected
Check period, plane, and direction together before naming an orbit geostationary.

PI v1.1 diagnosis: find the first wrong layer

PI v1.1 diagnosis: find the first wrong layer
Primary label	Evidence	Corrective action
Knowledge Gap	Cannot distinguish field, potential, and potential energy	Rebuild vector-versus-scalar and per-unit-mass meanings
Recall Gap	Correct orbit model, but speed, period, or energy relation is unavailable	Retrieve the relation with its circular-orbit condition
Execution Error	Wrong sign, radius, or square-root algebra	Write centre-to-centre radius before substitution
Decision / Selection Error	Uses force integration when endpoint potential is enough, or circular formulas for a transfer path	Classify trajectory and requested quantity first
Needs Review	Uses an unstated Earth-density model or ambiguous orbit condition	Escalate the assumption for academic review

Primary label
Knowledge Gap
Evidence
Cannot distinguish field, potential, and potential energy
Corrective action
Rebuild vector-versus-scalar and per-unit-mass meanings
Primary label
Recall Gap
Evidence
Correct orbit model, but speed, period, or energy relation is unavailable
Corrective action
Retrieve the relation with its circular-orbit condition
Primary label
Execution Error
Evidence
Wrong sign, radius, or square-root algebra
Corrective action
Write centre-to-centre radius before substitution
Primary label
Decision / Selection Error
Evidence
Uses force integration when endpoint potential is enough, or circular formulas for a transfer path
Corrective action
Classify trajectory and requested quantity first
Primary label
Needs Review
Evidence
Uses an unstated Earth-density model or ambiguous orbit condition
Corrective action
Escalate the assumption for academic review

Official-paper handling

Official-paper handling
Question	Direct answer
How are official questions used here?	Official questions may be classified by field, potential, g variation, circular orbit, Kepler relation, geostationary condition, or escape only after academic review.
What is published about a linked question?	The source year and paper link, not invented chapter counts or trend conclusions.

Question
How are official questions used here?
Direct answer
Official questions may be classified by field, potential, g variation, circular orbit, Kepler relation, geostationary condition, or escape only after academic review.
Question
What is published about a linked question?
Direct answer
The source year and paper link, not invented chapter counts or trend conclusions.

Official repositories: JEE Advanced paper archive and NTA JEE Main question papers.

FAQ

Gravitation — questions

Straight answers about how Rank Sarthi fits into serious exam preparation.

With zero potential chosen at infinity, positive work is required to separate a bound mass to infinity, so its potential at a finite radius is negative.

Sources and provenance

Evidence boundary: the syllabus mapping is tied to the official 2026 JEE Main and JEE Advanced documents. No chapter weightage, question frequency, or forecast is asserted. Official papers are linked for evidence-safe practice, and any question classified by chapter, field, potential, g variation, circular orbit, Kepler relation, geostationary condition, or escape, requires human academic review first.

Syllabus for JEE (Main) 2026 — National Testing Agency (NTA) · official · checked 27 August 2026
JEE (Advanced) 2026 Syllabus (PDF) — JEE (Advanced) 2026, organising institute IIT Roorkee · official-pdf · checked 27 August 2026
JEE (Advanced) official past question-paper archive — JEE (Advanced), organising institute · official · checked 27 August 2026
JEE (Main) official site, Question Papers section — National Testing Agency (NTA) · official · checked 27 August 2026

Last updated: 8 September 2026

Contributor requirements for this page

Written by: Unassigned. Ideal author type: a JEE Physics educator experienced in gravitation, energy methods, and orbital mechanics.
Academically reviewed by: Unassigned. Required expertise: classical mechanics and Newtonian gravitation. Required qualification: postgraduate degree in Physics or a closely related discipline, or an engineering degree with documented JEE Physics teaching expertise.
Last reviewed: pending completion of academic review.
Sources checked: NTA JEE Main syllabus, JEE Advanced syllabus, NCERT Gravitation, and official paper archives.
Review scope: potential signs, radius definitions, orbit conditions, the depth-model caveat, formulas, worked reasoning, links, metadata, and schema-content parity.
No contributor is named on this page until their identity and qualification are verified, so no author, reviewer or rating is displayed yet.