SPM Physics 2026: AHA! Kepler’s Third Law Explained

 

Students often ask: how do we derive Kepler’s Third Law from the Sun’s mass equation? The secret is to freeze the constants and focus only on the changing variables.

From

$$M=\frac{4{\pi }^2{r}^3}{G{T}^2}$$

we rearrange to

$$T^2=\frac{4{\pi }^2}{GM}{r}^3$$

Since M, G, and π are constants, we group them into one constant k. Therefore,

$$T^2=k{r}^3\Rightarrow T^2\propto r^3$$

Exam tip: Don’t just memorize. Rearrange, lock the constants, and state the proportionality. That’s how you secure marks in SPM Physics.

AHA! Freeze constants, unlock Kepler’s Law. Not by sight, but by INSIGHT!

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