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

(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.

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s