Question

If parallax of a star is 0.1 and three times luminosity than sun, find apparent magnitude

Answer 1

d=1/p

where: d = distance measured in parsecs (pc), p = parallax shift measured in arc seconds (")

d=1/0.1 = 10 pc

We use
m - M = -5 + 5 log (d)

where: m = apparent magnitude, M = absolute magnitude
lg L/LS = 0.4 (MS – M)
where MS = 4.77 absolute magnitude of the sun.

lg 3 LS /LS = 0.4 (MS – M)

lg 3 = 0.4 (MS – M)

- M = (lg 3 / 0.4) - MS

- M = 1.1925 – 4.77

- M = -3.58

M = 3.58

m - M = -5 + 5 log (d)
m – 3.58 = -5 + 5 log (10)
m - 3.58 = -5 + 5 x 1 (the log of 10 = 1)
m – 3.58 = -5 + 1
m – 3.58 = 4
m = 4 + 3.58
m = 7.58