Edexcel A Level (IAL) Physics-5.32 Newton’s Law of Universal Gravitation- Study Notes- New Syllabus

Newton’s Law of Universal Gravitation

Newton’s law of universal gravitation states that every mass attracts every other mass with a gravitational force.

The Gravitational Force Equation

The magnitude of the gravitational force between two point masses is given by:

\( F = \dfrac{G m_1 m_2}{r^2} \)

• \( F \) = gravitational force between the masses (N)
• \( G \) = gravitational constant \( = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}} \)
• \( m_1, m_2 \) = masses (kg)
• \( r \) = distance between the centres of the masses (m)

 Meaning of the Equation

• The force is proportional to the product of the two masses.
• The force is inversely proportional to the square of the distance between them.
• The force acts along the line joining the centres of the two masses.
• The force is always attractive.

Key idea: This is an inverse-square law.

 Direction of the Gravitational Force

• Each mass experiences a force.
• The forces are equal in magnitude and opposite in direction.
• This is consistent with Newton’s third law of motion.

 Using the Equation in Calculations

• Convert all values to SI units.
• Use the distance between the centres of the masses.
• Substitute carefully and calculate.

Common rearrangements:

\( m_1 = \dfrac{F r^2}{G m_2} \)

\( r = \sqrt{\dfrac{G m_1 m_2}{F}} \)

Applications of Newton’s Law of Gravitation

• Calculating gravitational attraction between planets.
• Explaining planetary motion and orbits.
• Deriving gravitational field strength around a planet.
• Understanding satellite motion.