Universal Law of Gravitation Formula & Step-by-Step Derivation
Newton’s law of gravitation describes the fundamental force of attraction between any two particles of matter in the universe. According to this principle, every object attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance that separates them. This concept is essential for understanding the motion of planets, the behavior of objects on Earth, and the general structure of the cosmos.
Newton first formulated this law in 1687, establishing a basis for classical mechanics and modern physics. The law explains not just everyday phenomena, like why objects fall to the ground, but also how celestial bodies interact across vast distances.
Newton's Law of Gravitation: Explanation and Formula
Newton’s law states:
Any particle of matter in the universe attracts any other particle with a force. This force acts along the line joining their centers. The magnitude of this force (F) depends on the masses of the two objects (m1 and m2) and the distance between them (r).
The law is mathematically expressed as:
Where:
- F is the gravitational force between two objects
- G is the universal gravitational constant
- m1 and m2 are the masses of the objects
- r is the distance between the centers of the objects
This law is universal. It applies to all objects with mass, whether they are microscopic particles or massive planets.
Step-by-Step Problem-Solving Approach
To solve any problem using Newton’s law of gravitation, follow these steps:
- Identify the two masses (m1, m2) and measure or note the distance (r) between their centers.
- Write the formula: F = G × (m1 × m2) / r2.
- Substitute the known values, including the value of G.
- Calculate the value of F, ensuring correct units throughout (SI units recommended).
- Analyze the result—consider whether the value matches expectations based on the size and distance of the objects involved.
Example Calculation
Suppose two objects have masses of 3 kg and 7 kg, with their centers 5 meters apart. If the universal gravitational constant (G) is 6.674 × 10−11 N m2 kg−2, calculate the force between them.
Substitute into the formula:
The force is very small, illustrating that gravitational attraction is only strong for extremely large objects.
Key Formulas Table
| Formula | Expression | Physical Meaning |
|---|---|---|
| Universal Law of Gravitation | F = G (m1m2) / r2 | Force between any two masses |
| Gravitational Constant | G = 6.674 × 10−11 N m2 kg−2 | Constant value in the gravitational formula |
Applications of Newton's Law of Gravitation
- Explains why objects fall towards Earth’s surface.
- Describes the force that keeps planets in motion around the sun.
- Helps predict planetary orbits and satellite paths.
- Accounts for tides formed due to gravitational attraction.
Practice Questions
- Calculate the gravitational force between two 10 kg masses placed 2 meters apart.
- If the mass of one object is doubled, but the distance remains unchanged, how does the gravitational force change?
- What happens to the force if the distance between two objects is doubled?
Related Vedantu Resources for Deeper Learning
- Universal Law of Gravitation
- Gravitational Constant and Universal Law
- Gravitational Force and Escape Velocity
- Gravitation - Additional Concepts
- Value of G Explained
Next Steps
- Practice with more calculation-based questions using the universal law of gravitation.
- Explore how the law explains planetary motion and orbit formation by studying related resources.
- For advanced understanding, refer to the concept of escape velocity and orbits in astronomy.
| Concept | Summary |
|---|---|
| Universal Law of Gravitation | Any two objects attract each other with a force proportional to their masses and inversely proportional to the square of their distance. |
| Gravitational Force (F) | Fundamental force responsible for the structure and movement of the universe. |
FAQs on Universal Law of Gravitation Explained for Students (2025)
1. What is Newton's law of gravitation in simple terms?
Newton's law of gravitation states that every object in the universe attracts every other object with a force that is:
- Directly proportional to the product of their masses
- Inversely proportional to the square of the distance between them
This law helps explain why planets orbit the Sun and why objects fall to the ground.
2. What is the universal law of gravitation formula?
The universal law of gravitation formula is:
F = G × (m1 × m2) / r2
- F = Gravitational force (Newtons)
- G = Universal gravitational constant (6.674 × 10−11 N m2 kg−2)
- m1, m2 = Masses of objects (kg)
- r = Distance between centers of the two masses (meters)
3. What is gravitational constant G?
Gravitational constant (G) is a universal value used in the law of gravitation, defined as:
- G = 6.674 × 10−11 N m2 kg−2
- It quantifies the strength of gravity between two masses
- G remains constant everywhere in the universe
4. Why is it called the 'universal law' of gravitation?
It is called the 'universal law' because:
- It applies to all objects regardless of size, mass, or location
- The force acts everywhere in the universe, from tiny particles to massive planets and stars
5. Who gave the universal law of gravitation?
Sir Isaac Newton proposed the universal law of gravitation in 1687, revolutionizing our understanding of forces in the universe.
6. State universal law of gravitation with formula.
Universal law of gravitation: Every particle attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Formula: F = G × (m1 × m2) / r2
7. What is the importance of universal law of gravitation?
The universal law of gravitation is important because:
- It explains planetary orbits and celestial motion
- Describes falling objects and tides on Earth
- Is fundamental for space missions and satellite technology
- Lays the foundation for understanding forces in nature
8. What is the value of G? What are its SI units?
The value of the gravitational constant G is:
- 6.674 × 10−11 N m2 kg−2
Its SI unit is Newton metre2 per kilogram2 (N m2 kg−2).
9. If the distance between two objects is tripled, how does the gravitational force change?
If the distance (r) between two objects is tripled:
- Gravitational force decreases by a factor of 9 (since force is inversely proportional to r2)
- New force = Original force / 9
10. How does the universal law of gravitation explain the motion of planets around the Sun?
Universal law of gravitation explains planetary motion because:
- Sun attracts planets with a gravitational force
- This force provides the necessary centripetal acceleration for planets to revolve in orbits
- The law predicts planetary paths accurately based on mass and distance
11. What is the difference between mass and weight?
Mass is the amount of matter in an object and remains constant everywhere.
Weight is the gravitational force acting on mass and varies depending on the location.
- Mass: Measured in kilograms (kg); a scalar, does not change with gravity.
- Weight: Measured in newtons (N); weight = mass × acceleration due to gravity (W = m × g).
12. What are some real-life applications of the universal law of gravitation?
Real-life applications include:
- Satellite launching and orbits
- Artificial gravity in space stations
- Explaining tides, planetary motion, and falling objects
- Designing GPS and navigation systems
