Edexcel A Level (IAL) Physics-5.36 Orbital Motion- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -5.36 Orbital Motion- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -5.36 Orbital Motion- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
- be able to apply Newton’s laws of motion and universal gravitation to orbital motion
Applying Newton’s Laws of Motion and Universal Gravitation to Orbital Motion
Orbital motion occurs when an object moves in a curved path under the influence of a central force. For satellites and planets, this central force is provided by gravity.
Orbital Motion and Newton’s First Law
- An object moving in a straight line at constant speed will continue to do so unless a force acts.
- In orbit, the object does not move in a straight line.
- This means a force must be acting on it.
Conclusion: A satellite remains in orbit because a force continuously changes its direction of motion.
Centripetal Motion and Newton’s Second Law
An object moving in a circular orbit undergoes centripetal acceleration.
Centripetal acceleration: \( a = \dfrac{v^2}{r} \)
Using Newton’s second law:
Centripetal force: \( F = m\dfrac{v^2}{r} \)
- The force is always directed towards the centre of the orbit.
- The speed may be constant, but velocity changes direction.
Gravitational Force as the Centripetal Force
For orbital motion, the centripetal force is provided by gravity.
Newton’s law of universal gravitation:
\( F = \dfrac{G M m}{r^2} \)
Equating centripetal force and gravitational force:
\( \dfrac{G M m}{r^2} = m\dfrac{v^2}{r} \)
Cancel \( m \):
\( v^2 = \dfrac{G M}{r} \)
Meaning of the Result
- Orbital speed depends on the mass of the central body.
- Orbital speed decreases with increasing orbital radius.
- Satellite mass does not affect orbital speed.
Key idea: Gravity provides exactly the force needed to keep the object in circular motion.
Orbital Motion and Newton’s Third Law
- The satellite exerts a gravitational force on the planet.
- The planet exerts an equal and opposite force on the satellite.
- The satellite accelerates more because it has much smaller mass.
Condition for Circular Orbit
- The gravitational force must act perpendicular to velocity.
- The object must have sufficient tangential speed.
- If speed is too low → object falls back.
- If speed is too high → object escapes orbit.
Example (Easy)
Why does a satellite in orbit not fall straight down to Earth?
▶️ Answer / Explanation
It has sufficient horizontal velocity, so gravity causes it to follow a curved path rather than falling vertically.
Example (Medium)
State the force that provides the centripetal acceleration for a satellite in circular orbit.
▶️ Answer / Explanation
The gravitational force between the satellite and the planet.
Example (Hard)
Explain why a satellite closer to Earth must move faster than one further away.
▶️ Answer / Explanation
- Gravitational force is stronger at smaller radius.
- Greater centripetal force is required.
- Therefore a higher orbital speed is needed.
Escape Velocity and Orbital Period (Kepler’s Third Law)
Gravitational fields determine both whether an object can escape from a planet and how objects move in stable orbits.
Escape Velocity
Escape velocity is the minimum speed an object must have to escape completely from a gravitational field without further propulsion.
Key condition:
- Final kinetic energy at infinity = 0
- Gravitational potential energy at infinity = 0
Derivation using energy conservation:
Initial KE = increase in gravitational potential energy
\( \dfrac{1}{2}mv^2 = \dfrac{GMm}{r} \)
Cancel \( m \):
\( v = \sqrt{\dfrac{2GM}{r}} \)
Escape velocity equation:
- Independent of mass of object
- Depends on mass and radius of planet
Meaning of Escape Velocity
- Object continues slowing but never returns
- Speed tends to zero at infinity
- No further force or thrust required
Important: Escape velocity is not the same as escape acceleration.
Orbital Motion and Orbital Period
For a satellite in a circular orbit, gravitational force provides centripetal force.
Gravitational force: \( F = \dfrac{GMm}{r^2} \)
Centripetal force: \( F = m\dfrac{v^2}{r} \)
Equating:
\( \dfrac{GMm}{r^2} = m\dfrac{v^2}{r} \)
\( v = \sqrt{\dfrac{GM}{r}} \)
Orbital Period
Orbital period \( T \) is the time taken for one complete orbit.
\( v = \dfrac{2\pi r}{T} \)
Substitute orbital speed:
\( \dfrac{2\pi r}{T} = \sqrt{\dfrac{GM}{r}} \)
Rearranging:
\( T^2 = \dfrac{4\pi^2 r^3}{GM} \)
Kepler’s Third Law
Kepler’s third law states:
The square of the orbital period is proportional to the cube of the orbital radius
\( T^2 \propto r^3 \)
- Applies to planets and satellites
- Same central mass → same constant
Comparison: Orbit vs Escape
- Orbital speed: \( v = \sqrt{\dfrac{GM}{r}} \)
- Escape speed: \( v = \sqrt{\dfrac{2GM}{r}} \)
- Escape speed is √2 times orbital speed
Example (Easy)
Does escape velocity depend on the mass of the object?
▶️ Answer / Explanation
No. The mass cancels out during derivation.
Example (Medium)
If orbital radius increases, what happens to orbital period?
▶️ Answer / Explanation
Orbital period increases since \( T^2 \propto r^3 \).
Example (Hard)
Explain why a satellite must have less speed than escape velocity to remain in orbit.
▶️ Answer / Explanation
- Escape velocity gives zero KE at infinity
- Lower speed keeps object bound
- Gravity bends path into orbit