Gravitational field strength is the gravitational force acting per unit mass at a point in a gravitational field. It is calculated using or, outside a spherical mass, .
Gravitational field strength is the gravitational force acting per unit mass at a point in a gravitational field. It is calculated using or, outside a spherical mass, .
This is part of D.1 Gravitational fields and is studied by both SL and HL students.
A mass placed in a gravitational field experiences a force. Gravitational field strength describes how strong that interaction is at a particular position:
Here, is the gravitational force in newtons and is the mass experiencing the force in kilograms. Therefore, the unit of is , which is equivalent to .
Because gravitational field strength is a vector, its direction must also be specified. Around an isolated spherical body, points radially inward, toward the body's centre. The equation gives its magnitude.
| Situation | Calculation |
|---|---|
| Force on a known mass | |
| Field produced by a spherical mass |
In the second equation, and is the distance from the centre of mass, not from its surface.
For Earth, using and :
Thus, a object near Earth's surface has weight .
Weight and mass are therefore different quantities: mass is measured in kilograms and does not depend on location, whereas weight is the gravitational force and is measured in newtons.
The inverse-square relationship means that increasing distance has a strong effect. If the distance from Earth's centre doubled, the field strength would become , not .
A common misconception is that is always . This value applies approximately at Earth's surface; decreases with distance according to the inverse-square relationship.
For a Calculate question, show the equation, substitution and final answer. Distinguish lowercase , gravitational field strength, from uppercase , the universal gravitational constant, and measure from the centre of the spherical mass. If direction is requested, state that the field points toward the attracting mass.