Question

Polaris has an apparent and absolute magnitudes 2 and −3.64 respectively

1. What is the distance in ly of Polaris to Earth?
2. What is the luminosity of Polaris in Watts?
3. What is the brightness (flux) in pW/cm² of Polaris on Earth?
4. Using the same magnitudes, find the distance of Polaris by considering extinction in space for average opacity constant of α = 2 kpc^-1.
5. Consider Polaris is observed in a location close to our Physics & Optics Department where average atmospheric extinction is k = 0.15. What will be the apparent magnitude of Polaris in this place?

Answer 1

Given :Apparent magnitude of Polaris(m) = 2 Absolute magnitude of Polaris(M) = - 3.64

a). m - M = 5 log (d/10)

m - M = 5logd - 5log10

m - M + 5 = 5logd

logd = (m - M + 5)/5

d = 10^(m - M +5)/5

(m - M +5 )/5 = 10.64/5 = 2.128

distance (d) =10^2.128 = 134.276m

Luminosity = power output of a star (watt)

Intensity is the power emitted by a source divided by the area of a sphere over which the energy is spread equally, Intensity . = Power /Area

In astrophysics terminology,

Intensity =appernt brightness

Power =luminosity

So, brightness =. Luminosity /area

b =. L/4 pi d^2

b =. L/ 4 ×3.14× (134.276)^2

b =. L/ 226457.354 watt/m^2