When astronomers discuss objects that give off light, such as the Sun, we discus

Question

When astronomers discuss objects that give off light, such as the Sun, we discuss a concept called "luminosity" which is measured in units of energy per unit time. Typically this is given in "Watts", the same unit of power that is used to rate lightbulbs. The luminosity of the Sun is L = 3.8 × 10 26 Watts. However, the brightness of a luminous object depends on how far away you are from it. This is called the "flux" by astronomers. Flux is calculated using the formula F = L 4 ? D 2 . The flux of light we receive from the Sun here at Earth (a distance of one astronomical unit or D = 1.5 × 10 8 km from the Sun) is called the "solar constant". It's measured to be F = 1362 Watts per square meter. Saturn is 10 AU from the Sun. What is the flux that Saturn receives from the Sun in Watts per square meter? (HINT: There is a very simple way to calculate this using "scaling" techniques and realizing that Saturn is 10 times further from the Sun than the Earth.)

Explanation / Answer

Stars brightness depends on two factors:
1. it's luminosity
2. it's distance

Brightness relation is an instance of an inverse square law. Since sSaturn is 9.5 times far way from the Sun than the Earth, the Sun will appear 9.52 which is equal to 90.25 times dimmer as viewed from the Saturn compared to the Sun as viewed from the Earth.

As the earth receives 1362 W/m2 from the sun , Saturn will receive only 15.0914 W/m2 from the sun, i.e,
   =>1362/90.25
   =>15.0914 W/m2

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