ly = light years
Stars P and Q have the same luminosity, but P is 30 ly from Earth and Q is 40 ly from Earth. What is the ratio of their brightness as viewed from Earth?
their brightness ratio is the ratio of the inverse of the square of their distances
bP / bQ = (dQ / dP)^2
So it would be 900:1600
= 9:16?
To find the ratio of the brightness of stars P and Q as viewed from Earth, we need to understand the concept of luminosity and how it affects the brightness of stars.
Luminosity refers to the total amount of energy a star emits per unit of time. It is often measured in units like watts or, in astronomy, in terms of the Sun's luminosity (Lā). However, for this problem, we are given that stars P and Q have the same luminosity, so we can consider them to have equal values.
The brightness of a star, on the other hand, is the amount of light received from the star per unit of area at a specific location, like on Earth. The brightness of a star decreases as the distance between the star and the observer increases. This relationship is described by the inverse square law, which states that the brightness is inversely proportional to the square of the distance.
Let's use this information to find the ratio of the brightness of stars P and Q as viewed from Earth.
1. Start by defining the variables:
- Lp: Luminosity of star P (equal to the luminosity of star Q)
- dp: Distance between star P and Earth (30 ly)
- dq: Distance between star Q and Earth (40 ly)
- Bp: Brightness of star P as viewed from Earth
- Bq: Brightness of star Q as viewed from Earth
2. Apply the inverse square law to relate the brightness of each star with its distance from Earth:
Bp ā Lp/dp^2
Bq ā Lp/dq^2
3. Substitute the values given:
Bp = Lp/(30^2)
Bq = Lp/(40^2)
4. Calculate the ratio of their brightness:
Ratio = Bp/Bq = (Lp/(30^2)) / (Lp/(40^2))
5. Simplify the expression:
Ratio = (40^2) / (30^2)
Ratio = 1600 / 900
Ratio = 16/9
Hence, the ratio of the brightness of stars P and Q as viewed from Earth is 16/9.