Luminosity & Radiant Flux
A telescope detects radiation arriving at Earth. That received signal is not the same quantity as the total power emitted by the star.
Separate what the star emits from what Earth receives
Definition
2 marksWhat is meant by the luminosity of a star?
Model answer: The total power of radiation emitted by the star.
| Quantity | Meaning | Unit |
|---|---|---|
| luminosity L | total emitted radiation power | W |
| radiant flux intensity F | received power per unit area | W m⁻² |
Key idea
A star can look bright because it is very luminous or because it is close. Apparent brightness alone cannot separate those causes.
The same power spreads over a growing sphere
Swipe left or right to see the whole diagram →
If radiation spreads equally in every direction, the luminosity passes through a spherical surface whose area grows with the square of distance.
Symbols
- = radiant flux intensity at Earth (W m⁻²)
- = luminosity of the source (W)
- = distance from source to observer (m)
- Double the distance: the flux becomes one quarter.
- Triple the distance: the flux becomes one ninth.
- The equation assumes isotropic emission and ignores absorption between the source and observer.
Your turninverse-square relationship check
The distance to a star is increased by a factor of 5 while its luminosity is unchanged. By what factor does the radiant flux intensity decrease?
Show worked answer
Flux is inversely proportional to distance squared, so it becomes 1/25 of its original value. It decreases by a factor of 25.
Common mistake
Do not use watts for radiant flux intensity. Watts measure luminosity; watts per square metre measure the received flux.