Question

Star 2 has a magnitude of m2 = 10.0. Star2 is one hundred times brighter than Star 1. What is the magnitude Star 1? Give your answer to the nearest integer.

Answer 1

The question requires the concept of magnitude used to measure the relative brightness of stars.

So A system is developed called system of apparent magnitude , in which brightness of a star is measured in terms of a unitless quantity called magnitude.

Higher the value of brightness , lower is the value of magnitude.

On this scale a unit increase in magnitude decreases the brightness of the star by a factor of

This means a star having a magnitude 2 has 2.512 times less brightness than star having magnitude 1 .

Now we can solve our question

Given'

Magnitude of star 2 (m₂) = 10.0

Star 2 is 100 times brighter than star 1.

We have to find magnitude of star 1 (m₁) = ?

Let us suppost the change in magnitude be n

Since the brightness of star 1 is less its magnitude should be more than star 2.

So m₁ can be written as  

m₁ = 10 + n where n is the increase in magnitude of star 1 wrt star 2

So we can use our basic deifinition of this scales as

  (2.152)ⁿ = 100

n = ln(100)/ ln(2.512) = 5

n = 5

So Now m₁ = 10 + 5 = 15.0

Hence magnitude of star 1 is 15.0 (i.e. it is 5 more than magnitude of star 2)

m₁ = 15.0

Hope the explanation would be helpful for you.