25.1.1 Luminosity & Radiant Flux

• Luminosity L is defined as:

The total power output of radiation emitted by a star

• It is measured in units of Watts (W)
• Radiant flux intensity F is defined as:

The observed amount of intensity, or the radiant power transmitted normally through a surface per unit of area, of radiation measured on Earth

• The best way to picture this is:
  • The luminosity is the total radiation that leaves the star
  • The radiant flux intensity is the amount of radiation measured on Earth
  • By the time the radiation reaches the Earth, it will have spread out a great deal, therefore, it will only be a fraction of the value of the luminosity

The luminosity is the total power output of the star, whereas the radiant flux is what is measured on Earth

• Light sources which are further away appear fainter because the light it emits is spread out over a greater area
• The moment the light leaves the surface of the star, it begins to spread out uniformly through a spherical shell
  • The surface area of a sphere is equal to 4πr²

• The radius r of this sphere is equal to the distance d between the star and the Earth
• By the time the radiation reaches the Earth, it has been spread over an area of 4πd²
• The inverse square law of flux can therefore be calculated using:

• Where:
  • F = radiant flux intensity, or observed intensity on Earth (W m^-2)
  • L = luminosity of the source (W)
  • d = distance between the star and the Earth (m)

• This equation assumes:
  • The power from the star radiates uniformly through space
  • No radiation is absorbed between the star and the Earth

• This equation tells us:
  • For a given star, the luminosity is constant
  • The radiant flux follows an inverse square law
  • The greater the radiant flux (larger F) measured, the closer the star is to the Earth (smaller d)

Inverse square law; when the light is twice as far away, it has spread over four times the area, hence the intensity is four times smaller

Step 1: Write down the known quantities

• • Luminosity, L = 9.7 × 10²⁷ W
  • Radiant flux intensity, F = 114 nW m^–2 = 114 × 10^–9 W m^–2

 Step 2: Write down the inverse square law of flux

Step 3: Rearrange for distance d, and calculate

Distance, d = 8.2 × 10¹⁶ m