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Star a and b have the same luminosity, but star b is 10 times farther from earth than star

a. how much brighter will star a appear?

User Leff
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2 Answers

3 votes

100 times brighter

Further Explanation

Stars are celestial bodies that emit light. There are pseudo stars and real stars. Pseudo stars are stars that do not produce their own light but reflect light that is received from other stars. The real star is the star that produces their own light. In general, the designation of stars is an outer space object that produces its own light (real stars).

The stars have become a part of every culture. The stars are used in religious practices, in navigation, and farming. The Gregorian calendar, which is used in almost all parts of the world, is the Sun calendar, basing itself on the position of the Earth relative to the nearest star, the Sun.

The stars have become a part of every culture. The stars are used in religious practices, in navigation, and farming. The Gregorian calendar, which is used in almost all parts of the world, is the Sun calendar, basing itself on the position of the Earth relative to the nearest star, the Sun.

Star luminosity is the amount of light and other forms of radiation energy emitted by the star per unit time. The luminosity of a star is measured in units of power (watts). The luminosity of a star is determined by the size of the radius and its surface temperature. Assuming that a star is a perfect black body.

L = 4 \ pi R ^ {2} \ sigma T_ {e} ^ {4}

where L is luminosity, σ is the Stefan-Boltzmann constant, R is the radius of the star and Te is the effective temperature of the star.

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luminosity luminosity

Details

Grade: High School

Subject: Physics

keywords: luminosity

User Andrew Johns
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5.8k points
4 votes

Answer:

100 times brighter

Step-by-step explanation:

The apparent luminosity of a star follows the inverse square law, which means that the luminosity is inversely proportional to the square of the distance:


L \sim (1)/(r^2)

where r is the distance.

In this problem, star A and star B have same intrinsec luminosity, but star B is 10 times farther than star A:


r_B = 10 r_A

We can write the luminosity of star A as follows:


L_A = k (1)/(r_A^2)

While the luminosity of star B will be:


L_B = k (1)/(r_B^2)

Substituting
r_B = 10 r_A:


L_B = k (1)/(r_B^2)=k (1)/((10 r_A)^2)=k (1)/(100 r_A^2)=(1)/(100)L_A

So, star A will appear 100 times brighter than star B.

User Nanndoj
by
5.5k points