Express mass of the Earth in unit of M. Take ME = 6 x 1024kg. The apparent magnitude of the sun is £¡ 26.81 and that of another star is£¡1.81. How much brighter the sun is with respect to that star ?
To compare the brightness of the Sun to that of another star, we can use the concept of apparent magnitude. The difference in apparent magnitude between two objects is related to the ratio of their brightness.
The formula to calculate the difference in apparent magnitude (Δm) is:
Δm = m1 - m2
where m1 is the apparent magnitude of the first object (in this case, the Sun) and m2 is the apparent magnitude of the second object (the other star).
In this question, m1 = -26.81 (apparent magnitude of the Sun) and m2 = -1.81 (apparent magnitude of the other star).
Therefore, the difference in apparent magnitude (Δm) is:
Δm = (-26.81) - (-1.81)
Δm = -26.81 + 1.81
Δm = -25
Now, to determine how much brighter the Sun is compared to the other star, we can use the equation:
Brightness ratio = 10^(0.4 * Δm)
Let's substitute the value of Δm into the equation:
Brightness ratio = 10^(0.4 * (-25))
Now, using the exponentiation rule:
Brightness ratio = 10^(-10)
Using the property that 10^(-x) = 1/10^x:
Brightness ratio = 1 / 10^10
Hence, the Sun is approximately 10 billion times brighter than the other star.