Not given in the exam, recall it.
What it is for
Gravitational acceleration (field strength) is used in Gravitation (SPM Physics Form 4). Keep the SI units in every line of working. Gravitation
Symbols and SI units
| Symbol | Meaning | SI unit |
|---|---|---|
| g | gravitational field strength | m s⁻² |
| G | gravitational constant | N m² kg⁻² |
| M | mass of planet | kg |
| r | distance from centre | m |
Rearrangements
M = gr² / Gr = √(GM / g)
Worked example
Common trap
Understanding Gravitational acceleration (field strength)
The gravitational field strength near a planet, which is also the acceleration of free fall, is g = GM / r².
Here g is the field strength in metres per second squared (m s⁻²), G is the gravitational constant 6.67 × 10⁻¹¹ N m² kg⁻², M is the mass of the planet in kilograms (kg), and r is the distance from the planet’s centre in metres (m). Notice g depends only on M and r, not on the mass of the object placed in the field, that is why all objects fall with the same acceleration.
To find a planet’s mass, rearrange to M = gr² / G; to find the distance at which the field has a given strength, use r = √(GM / g).
A worked example, step by step
Find the gravitational field strength at the Moon’s surface, given M = 7.35 × 10²² kg and radius r = 1.74 × 10⁶ m, with G = 6.67 × 10⁻¹¹ N m² kg⁻².
Write the formula and substitute with units:
g = GM / r² = (6.67 × 10⁻¹¹ × 7.35 × 10²²) / (1.74 × 10⁶)²
g = (4.90 × 10¹²) / (3.03 × 10¹²) = 1.62 m s⁻².
This confirms the Moon’s surface gravity is about one sixth of Earth’s (9.8 m s⁻²), which matches the value used when calculating weight on the Moon. The answer is given to three significant figures with the correct unit.
Common mistakes and how this is tested
The key point is that r is measured from the planet’s centre (radius plus altitude) and must be squared, and that g does not depend on the mass of the object placed in the field.
Other errors: confusing the planet’s mass M with the object’s mass; using the diameter instead of the radius; and mishandling the powers of ten in standard form. At a height above the surface, remember to add that height to the planet’s radius.
This is tested under define (state what gravitational field strength means), calculate (find g, M or r), and explain (why g falls with altitude, and why all objects have the same free-fall acceleration).
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)