Not given in the exam, recall it.
What it is for
Orbital velocity of a satellite 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 |
|---|---|---|
| v | orbital velocity | m s⁻¹ |
| G | gravitational constant | N m² kg⁻² |
| M | mass of planet | kg |
| r | orbital radius | m |
Rearrangements
v² = GM / rr = GM / v²M = v²r / G
Worked example
Common trap
Understanding orbital velocity of a satellite
The formula v = √(GM / r) gives the speed a satellite must keep to stay in a circular orbit. Here v is the orbital velocity in metres per second (m s⁻¹), 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 orbital radius in metres (m) measured from the planet's centre.
The relation comes from setting gravity equal to the centripetal force, which is why the satellite's own mass cancels out. To find other quantities, square both sides to get v² = GM / r, then rearrange to r = GM / v² or M = v²r / G.
A larger radius always means a slower orbit.
A worked example, step by step
A satellite orbits Earth (M = 6.0 × 10²⁴ kg) at a radius r = 4.2 × 10⁷ m, near geostationary height. Take G = 6.67 × 10⁻¹¹ N m² kg⁻².
Write the formula: v = √(GM / r). Substitute with units: v = √((6.67 × 10⁻¹¹ N m² kg⁻² × 6.0 × 10²⁴ kg) / 4.2 × 10⁷ m).
Work the top first: GM = 4.00 × 10¹⁴. Divide by r: 4.00 × 10¹⁴ / 4.2 × 10⁷ = 9.53 × 10⁶.
Take the square root: v = √(9.53 × 10⁶) = 3.09 × 10³ m s⁻¹. So the satellite travels at about 3090 m s⁻¹, quoted to three significant figures.
Common mistakes and how this is tested
The main trap is measuring r from the planet's surface. It must be from the centre, so add the planet's radius to the altitude.
The orbital speed also does not depend on the satellite's own mass, a fact examiners like to test with a distractor value.
Other errors: forgetting to take the square root at the end and leaving the answer as v²; dividing before multiplying G and M; and mixing up r in kilometres with r in metres. Always convert to metres first.
Under the command word calculate you show the substitution and units. Under explain you may be asked why a higher orbit means a slower satellite, or why mass cancels.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)