Question

The star sirius has an apparent magnitude of - 1. 46 and appears 95 times brighter compared to the more distant star Tau Ceti, which has an absolute magnitude of 5.69.

A) explains the terms apparent magnitude, absolute magnitude and bolometric magnitude.
B) calculate the apparent magnitude of the star Tau Ceti.
C) find the distance between the earth and Tau Ceti. ​

Answer 1

Answer:

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The star Sirius has an apparent magnitude of -1.46 and appears 95-times brighter compared to the more distant star Tau Ceti, which has an absolute magnitude of 5.69. (a) Explain the terms apparent magnitude, absolute magnitude and bolometric magnitude. (b) Calculate the apparent magnitude of the star Tau Ceti. (c) Find the distance between the Earth and Tau Ceti.

The star Sirius has an apparent magnitude of -1.46 and appears 95-times brighter compared to the more distant star Tau Ceti, which has an absolute magnitude of 5.69. (a) Explain the terms apparent magnitude, absolute magnitude and bolometric magnitude. (b) Calculate the apparent magnitude of the star Tau Ceti. (c) Find the distance between the Earth and Tau Ceti.

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Question

The star Sirius has an apparent magnitude of -1.46 and appears 95-times brighter compared to the more distant star Tau Ceti, which has an absolute magnitude of 5.69. (a) Explain the terms apparent magnitude, absolute magnitude and bolometric magnitude. (b) Calculate the apparent magnitude of the star Tau Ceti. (c) Find the distance between the Earth and Tau Ceti.

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Expert Answer

Step 1

(a) Apparent Magnitude is the magnitude of a star as observed on Earth.

Absolute magnitude is the apparent magnitude measured at a distance of 10 pc.

Bolometric magnitude is the measure of all radiation at all wavelength.

Step 2

(b) Apparent magnitude of Tau Ceti

Advanced Physics homework question answer, step 2, image 1

Answer 2

The apparent magnitude of the star Tau Ceti is 3.51 and the distance between the earth and Tau Ceti is $1.13$ × $10^{14}$.

Given:

The apparent magnitude of the star Sirius = - 1. 46

The absolute magnitude of Tau Ceti = 5.69

To Find:

(a) Explain the following terms - apparent magnitude, absolute magnitude and bolometric magnitude

(b) The apparent magnitude of the star Tau Ceti

(c) The distance between the earth and Tau Ceti

Solution:

(a) Apparent magnitude is an estimate of an astronomical object's brightness as the object is seen from the Earth.

The absolute magnitude  is the magnitude of an object that is viewed from a 32.6 light-years distance while having a constant transfer of its luminosity that is not interfered by cosmic dust and objects present in the line of sight.

The bolometric magnitude of a star is the total of the star’s radiation released overall electromagnetic spectrum wavelengths

(b) The apparent magnitude of the star Tau Ceti can be found using the following equation.

$m_{2} -m_{1}=-2.512$ × $log(\frac{B_{2} }{B_{1} } )$

Where,

m₁ = Apparent magnitude of Tau Ceti

m₂ = Apparent magnitude of the star Sirius

B₁ = Brightness of Tau Ceti

B₂ = Brightness of Sirius

$\frac{B_{2}}{B_{1} } =95$

Hence we have;

$-1.46-m_{1} =-2.512$ × $log(95)$

$m_{1} =3.51$

Therefore, the apparent magnitude of the star Tau Ceti is 3.51.

(c) The distance between the Earth and Tau Ceti can be found using the following equation.

$m-M=5$ × $log(\frac{d}{10})$

Where,

m = Apparent magnitude of Tau Ceti

M = Absolute magnitude of Tau Ceti

d = The distance between the Earth and Tau Ceti

We get,

$3.51-5.69=5$ × $log(\frac{d}{10} )$

$\frac{d}{10}=10^{-0.436}$

$d=10$ × $0.3664$

$d=3.664$ parsecs

$d=1.13$ × $10^{14}$ km

Therefore, the distance between the earth and Tau Ceti is $1.13$ × $10^{14}$.

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