Physics IGCSE 0625.

[Moleko Moeketsi]

What does the equation g = 4π²/G define? It is found in the IGCSE Physics Course Book 0625 at the section of 'key equations'- page 496. Albeit, it is not in the Physics 0625 IGCSE syllabus for 2025-2026.

 

[badrobot14]

What does the equation g = 4π²/G define? It is found in the IGCSE Physics Course Book 0625 at the section of 'key equations'- page 496. Albeit, it is not in the Physics 0625 IGCSE syllabus for 2025-2026.

The equation [imath]g = \frac{4\pi^2}{G}[/imath] as written in that specific textbook section is actually a mathematical definition of a constant used for a specific derivation, rather than a fundamental law of physics you need to memorize.

What it Defines​

In the context of the IGCSE 0625 "Key Equations" summary, this specific [imath]g[/imath] is often used as a proportionality constant to simplify the relationship between a planet's orbital period ([imath]T[/imath]) and its orbital radius ([imath]r[/imath]).

It is derived from Kepler’s Third Law, which states that for a circular orbit:

[math]T^2 \propto r^3[/math]When you combine the centripetal force formula with Newton’s Law of Gravitation, you get:

[math]\frac{T^2}{r^3} = \frac{4\pi^2}{GM}[/math]In some older textbook editions or specific exam board contexts, authors use a lowercase [imath]g[/imath] (not to be confused with [imath]9.8 \text{ m/s}^2[/imath]) to represent the constant [imath]\frac{4\pi^2}{G}[/imath] to make the math look cleaner:

[math]T^2 = \left( \frac{g}{M} \right) r^3[/math]
The equation [imath]g = \frac{4\pi^2}{G}[/imath] is a "textbook artifact." It’s a derivation tool that helps explain why planets move the way they do, but the syllabus coordinators likely removed it to prevent students from confusing this mathematical "constant [imath]g[/imath]" with the "gravitational field strength [imath]g[/imath]."

If you are prepping for the 2025 or 2026 exams, you can safely ignore that specific formula. Just stick to knowing that orbital speed [imath]v = \frac{2\pi r}{T}[/imath].