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Newton's Law of Universal Gravitation
Newton’s law of universal gravitation states that every two masses attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
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Newton's Law of Universal Gravitation
What is it?
Newton’s law of universal gravitation states that every two masses attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
In simple words
- Gravity is attractive.
- Acts between masses.
- Inverse-square law.
Scientists connected to this topic
Known for: Three laws of motion and universal gravitation (Principia, 1687).
Wikimedia Commons — Godfrey Kneller, 1689 (public domain).
Recommended for Class 12
Full school-level explanation
Newton’s law of universal gravitation states that every two masses attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
Direct Dependence on Mass
Consider two masses `m₁` and `m₂` separated by centre-to-centre distance `r`. The gravitational force is: F = Gm₁m₂/r² where: `F` = gravitational force `G` = universal gravitational constant `m₁, m₂` = interacting masses `r` = distance between their centres If either mass increases while all other quantities stay unchanged, gravitational force increases. For example: If `m₁` doubles: F doubles
Inverse-Square Dependence
Force varies as: F ∝ 1r² Therefore: if distance doubles: F becomes F/4 if distance triples: F becomes F/9
Direction
Gravitational force acts along the line joining the centres of the two masses. The forces on the two bodies have equal magnitude and opposite direction, in agreement with Newton’s third law.
Universal Gravitational Constant
G ≈ 6.67 × 10⁻¹¹ N m² kg⁻² It is called universal because the same gravitational law applies to masses throughout the universe in the Newtonian model.
Formula / Key Relation
**F = Gm₁m₂/r²**
Remember
- F doubles
- F ∝ 1r²
- F becomes F/4
- F becomes F/9
- G ≈ 6.67 × 10⁻¹¹ N m² kg⁻²
- F = Gm₁m₂/r²
Scientists connected to this topic
Known for: Three laws of motion and universal gravitation (Principia, 1687).
Wikimedia Commons — Godfrey Kneller, 1689 (public domain).
Deeper understanding
Go deeper on Newton's Law of Universal Gravitation: connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
GRAVITY
Exam focus
Quick revision
- F doubles
- F ∝ 1r²
- F becomes F/4
- F becomes F/9
- Direct Dependence on Mass: Consider two masses `m₁` and `m₂` separated by centre-to-centre distance `r`. The gravitational for
- Inverse-Square Dependence: Force varies as: F ∝ 1r² Therefore: if distance doubles: F becomes F/4 if distance tri
For long answers on Newton's Law of Universal Gravitation: define clearly → explain the main parts → give one example → state one exam caution.
Scientists connected to this topic
Known for: Three laws of motion and universal gravitation (Principia, 1687).
Wikimedia Commons — Godfrey Kneller, 1689 (public domain).
Exam Focus
Exam Focus
Important points
- F doubles
- F ∝ 1r²
- F becomes F/4
- F becomes F/9
Important formulas
- F doubles
- F ∝ 1r²
- F becomes F/4
Common exam traps
- Do not use surface-to-surface separation when spherical-body problems require centre-to-centre distance.
- Do not write:
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not use surface-to-surface separation when spherical-body problems require centre-to-centre distance.
- Mistake
Do not write:
- Mistake
`F ∝ 1r`
- Mistake
The correct dependence is:
- Mistake
`F ∝ 1r²`
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
F doubles
F ∝ 1r²
F becomes F/4
F becomes F/9
**Newton’s law of universal gravitation states that every two masses attract each other with a force directly proportional to the product of their masses and in
F = Gm₁m₂/r²
- Definition
- **Newton’s law of universal gravitation states that every two masses attract each other with a force directly proportional to the product of their masses and in
- Formula
- F = Gm₁m₂/r²
- Critical warning
- Do not use surface-to-surface separation when spherical-body problems require centre-to-centre distance.
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Exam Practice
Define
Q1. Define Newton's Law of Universal Gravitation.
Explain
Q2. Explain: Direct Dependence on Mass.
Example
Q3. Give one clear example of Newton's Law of Universal Gravitation and say why it fits.
Mistake
Q4. State one common mistake students make about Newton's Law of Universal Gravitation.
Exam note
Q5. Write a short exam note on Newton's Law of Universal Gravitation: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.