Retrieval Practice
Gravitational Fields & Orbits — AQA A-Level Physics
Q1. Define a gravitational field.
A region of space where a mass experiences a force due to the gravitational attraction of another mass.
Q2. State the equation for gravitational field strength and define the unit.
- g = F/m.
- Gravitational field strength is the force per unit mass.
- Measured in N kg⁻¹ (equivalent to m s⁻²).
Q3. State Newton's law of gravitation in words and as an equation.
- The gravitational force between two point masses is proportional to the product of their masses and inversely proportional to the square of their separation.
- F = GMm/r².
Q4. What happens to the gravitational force when the distance between two masses is doubled?
- It reduces to (1/2)² = 1/4 of its original value.
- This is the inverse square law.
Q5. Write the equation for gravitational field strength in a radial field and state how it is derived.
- g = GM/r².
- Derived by combining g = F/m with F = GMm/r².
- The test mass m cancels.
Q6. Define gravitational potential and state why it is always negative.
- The work done per unit mass in bringing a test mass from infinity to a defined point.
- It is always negative because it is defined as zero at infinity, and since gravitational force is attractive, work must be done on the mass to reach infinity.
Q7. State the equation for gravitational potential and its units.
- V = -GM/r.
- Measured in J kg⁻¹.
Q8. How is g related to a V-r graph? How is ΔV related to a g-r graph?
g equals the negative gradient of a V-r graph: g = -ΔV/Δr. ΔV equals the area under a g-r graph.
Q9. State the equation for work done moving a mass through a gravitational potential difference.
ΔW = mΔV, where ΔW is the work done (J), m is the mass (kg), and ΔV is the change in gravitational potential (J kg⁻¹).
Q10. Derive the orbital speed equation for a circular orbit.
- Set gravitational force equal to centripetal force: GMm/r² = mv²/r.
- Cancel m and one r: v² = GM/r.
Q11. State Kepler's third law and write the equation.
- T² ∝ r³.
- For objects orbiting the same central body, T² = 4π²r³/GM.
Q12. How do KE and GPE change when a satellite moves to a lower orbit?
- KE increases (faster speed), GPE decreases (becomes more negative).
- Total energy remains constant.
Q13. Define escape velocity and derive the equation.
- The minimum speed to escape a gravitational field with no further energy input.
- Equate KE to GPE magnitude: ½mv² = GMm/r.
- Cancel m: v = √(2GM/r).
Q14. State three defining features of a geostationary orbit.
- 1.
- Orbits in the equatorial plane. 2.
- Moves west to east (same direction as Earth's rotation). 3.
- Has an orbital period of exactly 24 hours.
Q15. What are equipotential surfaces and how are they related to field lines?
- Surfaces joining points of equal gravitational potential.
- They are always perpendicular to the field lines.
- No work is done moving along an equipotential.