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Answer:
(a) Apparent magnitude is the perceived brightness of an astronomical object
Absolute magnitude is the luminosity based on viewing an object from a 32.6 light-years distance
Bolometric magnitude is the total emitted radiation of a star
(b) The apparent magnitude of the star Tau Ceti = 3.51
(c) The distance between the Earth and Tau Ceti is 1.13 × 10¹⁴ km
Explanation:
(a) Apparent magnitude is an estimate of an astronomical objects' brightness as the object is perceived from the Earth
The absolute magnitude is the magnitude an object appears to have when viewed from a 32.6 light-years distance while having constant transfer of its luminosity that is not affected by cosmic dust and objects present in the line of sight
The bolometric magnitude of a star is the sum total of the star's radiation released over all electromagnetic spectrum wavelengths
(b) The apparent magnitude of the star Tau Ceti is found using the following equation;
Where:
m₁ = Apparent magnitude of Tau Ceti
m₂ = Apparent magnitude of Sirius = -1.46
B₁ = Brightness of Tau Ceti
B₂ = Brightness of Sirius
Hence we have;
m₁ = -1.46 + 2.512 × log(95) = 3.51
The apparent magnitude of the star Tau Ceti = 3.51
(c) The distance between the Earth and Tau Ceti is found using the following equation;
Where:
m = Apparent magnitude of Tau Ceti
M = Absolute magnitude of Tau Ceti = 5.69
d = The distance between the Earth and Tau Ceti
Which gives;
d = 10 × 0.3664 = 3.664 parsecs = 3.664 × 3.0857 × 10¹⁶ m
d = 1.13 × 10¹⁴ km.