Not given in the exam, recall it.
What it is for
Kepler's third law 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 |
|---|---|---|
| T | orbital period | s |
| r | orbital radius | m |
Rearrangements
T₁²/r₁³ = T₂²/r₂³T² = (constant) × r³r³ = T² / (constant)
Worked example
Common trap
Understanding Kepler's third law
Kepler’s third law says the square of a planet’s orbital period is proportional to the cube of its orbital radius: T² ∝ r³, so T² / r³ = constant for every body orbiting the same central mass.
Here T is the orbital period in seconds (s) and r is the orbital radius in metres (m). Because the ratio T²/r³ is fixed, two orbits around the same star or planet can be compared directly.
The most useful form is the ratio T₁²/r₁³ = T₂²/r₂³. To find an unknown period, rearrange to T₂² = T₁² (r₂/r₁)³; to find a radius, use r³ = T² / (constant).
Keep the same units on both sides.
A worked example, step by step
Planet A orbits a star with period T₁ = 2 years at radius r₁. Planet B orbits the same star at r₂ = 9r₁.
Find the period of planet B.
Use the ratio form and substitute:
T₂² / r₂³ = T₁² / r₁³, so T₂² = T₁² (r₂/r₁)³ = 2² × 9³
T₂² = 4 × 729 = 2916, so T₂ = √2916 = 54 years.
Because the radius is 9 times larger, the period grows by a factor of √(9³) = 27, giving 54 years. The ratio method avoids needing the value of the constant, and it works as long as both planets orbit the same central body.
The answer keeps two significant figures.
Common mistakes and how this is tested
The core rule is to square the period and cube the radius; swapping the powers (cubing T or squaring r) is the most frequent error.
Other slips: forgetting to cube the radius ratio when using T₂² = T₁²(r₂/r₁)³; taking the square root of only one side; and mixing units (using years on one side and seconds on the other). The law also only compares bodies orbiting the same central mass.
It appears under state (write the law), calculate (find an unknown period or radius from another orbit), and explain (why outer planets take much longer to orbit than inner ones).
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)