Question

1) Star A has an apparent magnitude of 0.5, and star B has an apparent magnitude of 3.0. Which star is brighter and how much brighter is that star than the dimmer star?

2) A star has an apparent magnitude of 2.5 but an absolute magnitude of -0.5. what is the distance to the star?

Answer 1

1) Apparent magnitude of Star A = 0.5

Apparent magnitude of Star B = 3.0

  The apparent magnitude of a Star is the apparent brightness of a star observed in the sky from the Earth.

  Star A is brighter than star B because it has a lower apparent magnitude.

Star A is brighter than Star B by the magnitude of (3.0 - 0.5) = 2.5

  In terms of intensity star A is 2.512^(3-0.5) = (2.512)^2.5 = 10 = > Star A is 10 times brighter than star B.

2) Apparent magnitude of star = 2.5

Absolute magnitude of star = - 0.5

To find: Distance to the star

  The absolute magnitude is the magnitude the star would have if viewed from a distance of 32.6 light years or 10 parsecs

To find the distance, we have the equation:

(Apparent magnitude - Absolute magnitude) = 5 log₁₀ (d / 10 parsecs)

[2.5 - (-0.5)] = 5 log₁₀ (d / 10 parsecs)

log₁₀ (d / 10 parsecs) = 3 / 5 = 0.6

  (d / 10 parsecs) = (10)^0.6 = 3.98

d = 3.98 x (10 parsecs)

  d = 39.8 parsecs

   = 39.8 x (3.086 x 10 ¹³) Kms

= 39.8 x (3.086 x 10 ¹³) Kms

d = 122.82 x 10 ¹³ Kms

d In terms of light years = 39.8 parsecs x (3.26)

d = 129.74 light years