Are formulas given in the exam?

No. You must recall SPM Physics formulas.

Is a formula sheet given for these calculations?

No. SPM Physics (4531) provides no formula sheet, recall each formula and write units on every line.

What does the medium band mean?

Mid-level items usually need one rearrangement and a unit conversion.

Can a tutor mark my working?

Yes, in a one-to-one lesson the teacher checks each line and fixes the exact step that loses marks. From RM50/hr, paid trial available.

Gravitation Calculations (Medium), SPM Physics

How to approach

These need a rearrangement or two steps, often finding one quantity before the one asked for.

The method

List what is given, with units.
Choose the formula and rearrange for the unknown.
Substitute with units on every line.
Round to the correct significant figures.

Worked examples

Newton's universal law of gravitation

F = G m₁m₂ / r²

Two masses m₁ = 5 kg and m₂ = 10 kg are r = 2 m apart (G = 6.67 × 10⁻¹¹ N m² kg⁻²). F = G m₁m₂ / r² = (6.67 × 10⁻¹¹ × 5 × 10) / 2² = 8.34 × 10⁻¹⁰ N.

Gravitational acceleration (field strength)

g = GM / r²

Earth: M = 6.0 × 10²⁴ kg, r = 6.4 × 10⁶ m (G = 6.67 × 10⁻¹¹). g = GM / r² = (6.67 × 10⁻¹¹ × 6.0 × 10²⁴) / (6.4 × 10⁶)² = 9.77 m s⁻².

Kepler's third law

T² ∝ r³ (T²/r³ = constant)

Planet A has period T₁ = 1 yr at radius r₁; planet B orbits at r₂ = 4r₁. T₂² / r₂³ = T₁² / r₁³ → T₂² = T₁² (r₂/r₁)³ = 1² × 4³ = 64, so T₂ = 8 yr.

Orbital velocity of a satellite

v = √(GM / r)

A satellite orbits Earth (M = 6.0 × 10²⁴ kg) at r = 7.0 × 10⁶ m (G = 6.67 × 10⁻¹¹). v = √(GM / r) = √((6.67 × 10⁻¹¹ × 6.0 × 10²⁴) / 7.0 × 10⁶) = 7.56 × 10³ m s⁻¹.

Where marks are lost

Skipping units, rounding too early, and writing only the final answer (which loses method marks in Paper 2).

Practise these

Try each formula above with your own numbers, showing every line. Bring anything you get stuck on to a one-to-one lesson.

Formulas you use for Gravitation calculations

These mid-level problems draw on the 4 relationships in Gravitation. None is printed in the exam, so recall each and write its symbols with units before substituting:

F = G m₁m₂ / r², Newton's universal law of gravitation
g = GM / r², Gravitational acceleration (field strength)
T² ∝ r³ (T²/r³ = constant), Kepler's third law
v = √(GM / r), Orbital velocity of a satellite

A worked example, with units on every line

Using T² ∝ r³ (T²/r³ = constant) (T = orbital period (s); r = orbital radius (m)):

Planet A has period T₁ = 1 yr at radius r₁; planet B orbits at r₂ = 4r₁.
T₂² / r₂³ = T₁² / r₁³ → T₂² = T₁² (r₂/r₁)³ = 1² × 4³ = 64, so T₂ = 8 yr.

Where the marks are, and the common mistakes

In Paper 2, calculation marks are awarded line by line: the formula, the substitution with units, and the final answer with its unit and sensible significant figures. Watch this trap: Square the period and cube the radius.

Use the ratio form T₁²/r₁³ = T₂²/r₂³ to compare two orbits; keep units consistent on both sides. For mid-level items, expect one rearrangement and a unit conversion.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)

Written by the spmphysics.com.my editorial team.· Updated 5 Sept 2026