Field Strength of a Point Mass
Field Strength of a Point Mass
- Start from force per unit mass, then substitute Newton's law of gravitation.
- The result tells you how field strength changes with the central mass and distance.
Field strength of a point mass
- Substitute Newton's force law into the definition of field strength. The mass placed in the field cancels.
Symbols
- = field strength at the point (N kg⁻¹)
- = gravitational constant (N m² kg⁻²)
- = mass making the field (kg)
- = distance from the centre of M (m)
- g depends only on the mass M that makes the field and the distance r, not on the mass placed there (9702/41/O/N/25 Q3(b)(i)).
- Same inverse square as the force: at 2R from the centre g is a quarter; at 3R it is a ninth.
Worked example
Make M the subject and find a planet's mass
A planet has surface field strength g and radius R. Make M the subject, then find the Earth's mass from g = 9.81 N kg⁻¹ and R = 6.4 × 10⁶ m.
- Use the surface field-strength equation and make M the subject.
- Substitute the values.
Answer
- If the next part asks for , use the mass M that you have just found. Divide it by the volume of the planet. Here, ρ is the mean density in kg m⁻³.
Why g is almost constant near the surface
- Near the surface r changes very little compared with the planet's radius, so changes very little. The field lines are also nearly parallel (9702/41/O/N/23 Q1(a)(ii)).
- Climbing 9 km up Everest changes g by only about 0.3%.
- So for normal heights we treat g as constant and use weight = mg.
Field strength is force per unit mass and falls with the square of the distance. Its unit is N kg⁻¹, the same as m s⁻². It uses the mass that makes the field, not the mass placed in the field.