Two celestial objects have the same apparent magnitudes and their radiation is not influenced by extinction. Object 1 is at a distance of 10^3pc, object 2 at a distance of 10^6pc. Calculate the ratio of the luminosities of both objects.
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If
m = apparent magnitude
M = absolute magnitude (measure of luminosity)
d = distance in parsecs
m - M = 5 [log d - 1].
since for both stars m is same,
M1+5 [log d1 - 1] = M2+5 [log d2 - 1]
M1-M2 = 5 [log d2 - log d1] = 5[6-3] = 15.
A difference of 5 in magnitude indicates a luminosity ratio of 100; 15 corresponds to
100X100X100 = 1,000,000 (or a million).
Since the magnitude scale is in the reverse direction of luminosities; M2 is 1 million times of M1, in luminosity terms.
m = apparent magnitude
M = absolute magnitude (measure of luminosity)
d = distance in parsecs
m - M = 5 [log d - 1].
since for both stars m is same,
M1+5 [log d1 - 1] = M2+5 [log d2 - 1]
M1-M2 = 5 [log d2 - log d1] = 5[6-3] = 15.
A difference of 5 in magnitude indicates a luminosity ratio of 100; 15 corresponds to
100X100X100 = 1,000,000 (or a million).
Since the magnitude scale is in the reverse direction of luminosities; M2 is 1 million times of M1, in luminosity terms.