OCR A-Level Physics B H557
Planning
Implementing
Analysis
Evaluation
Practical Skills
Use of Apparatus and Techniques
Fundamental Data Analysis
Imaging and Signalling
Sensing
Mechanical Properties of Materials
Waves and Quantum Behaviour
Space, Time and Motion
Creating Models
Out Into Space
Our Place in the Universe
Matter: Very Simple
Matter: Hot or Cold
Electromagnetism
Charge and Field
Probing Deep Into Matter
Ionising Radiation and Risk
Out Into Space
Gravitational potential energy in a radial field
- 3 things to know
- Components 01, 02 and 03
Overview
Recall questions on E = −GMm/r and why it is negative, the zero at infinite separation, how potential energy changes with distance, satellite and spacecraft calculations, constant energy in a circular orbit, when mgh is enough, escape velocity v = √(2GM/r) and why it does not depend on mass, negative total energy in a bound orbit, and the energy–distance graph.
What you need to know
Answer each one before you reveal it.
Why can mgh be used near the surface while −GMm/r is needed for a rocket leaving the Earth?
What is the gravitational potential energy of a mass m at a distance r from a mass M?
Questions from this subtopic
Each one with the model answer underneath.
- 1
What is the gravitational potential energy of a mass m at a distance r from a mass M?
Model answer
The energy is E = −GMm/r.
- 2
Why is gravitational potential energy defined as negative?
Model answer
The zero is taken at infinite separation, and work must be done against the attraction to reach infinity, so the energy at any finite separation is less than zero.
- 3
What is the gravitational potential energy of two masses infinitely far apart?
Model answer
It is zero, which is the chosen reference level.
- 4
How does the gravitational potential energy of a satellite change as it moves further from a planet?
Model answer
It increases towards zero, in other words it becomes less negative.
- 5
A 1200 kg satellite is 4.22 × 10⁷ m from the Earth's centre, where GM is 3.98 × 10¹⁴ N m² kg⁻¹. What is its gravitational potential energy?
Model answer
E = −GMm/r = −3.98 × 10¹⁴ × 1200 / 4.22 × 10⁷ = −1.13 × 10¹⁰ J.
- 6
A 2000 kg spacecraft moves from 2.0 × 10⁷ m to 4.0 × 10⁷ m from the Earth's centre, where GM is 3.98 × 10¹⁴ N m² kg⁻¹. What is the change in its gravitational potential energy?
Model answer
The energy rises from −3.98 × 10¹⁰ J to −1.99 × 10¹⁰ J, an increase of 1.99 × 10¹⁰ J.
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