Question

Stars can be described using many different parameters: mass, color, temperature, luminosity, radius, single or binary. What are the qualities of the closest stars? What are the qualities of the brightest stars?  Do you think we have a skewed perspective due to what we observe in the night sky? Why/why not?

Answer 1

Qualitites of the closest stars :

We need to determine the distance between the star to our planet to understand which one is closer than another. There are various characteristics we can observe in a star which concludes the star to be a closer one than others.

Parallax :

The most famous and direct method is to measure the parallx in a star's position. We can observe a small shift in the star's position due to the earth's motion around the sun. This shift is usually in the order or less than one arcsec and this parallax only happens in case of the closest stars.

If the distance of the star is referred by R and the angle of the parallax is found to be N, Then the distance of the star is measured as,

R = 1/N

where the distance is measured in Parsec.

Proper Motion :

One more property of a closer star that is observed is known as as Proper Motion. As all we know all the stellar objects are in motion in the universe. Any star is not an exception to this phenomenon. Usually these star move with very high velocities in the sky but due to their very large distance from us we can not detect it. Still with very accurate observation through mdern telescopes we can detect it. In case of a closer star this proper motion is resulting in a shift of no more than one arc second per year and as it is a very small quantity, the stars appears to be fixed to our naked eye. Hence this proper motion can be concluded as a significant property to detect nearby stars.

Diagram :

N.B. The absolute luminiousity of a star can vary at a long range. Hence we can never conclude that the brightest star is the nearby star.

Qualitites of the brightest stars :

The term itself is very much concluding. The brightest stars are those stars which appear to be very bright in the night sky. As I mentioned in the last part that it is not mandatory that the closest stars are the only candidates to be brightest as it can be very much possible that a distant star is also appearing to be very bight in the night sky, though distance also play a keyrole in apparent brightness. This coins two terms which are Apparent magnitude and Absolute magnitude. It is also important to remember that not all the stars emits energy in our visible spectrum rather some are present in infrared, Ultraviolet regions too and the astronomers are required to observe those frequencies which are invisible to our naked eye.

Apparent Magnitude : The apparent magnitude of luminiousity of a star is mostly dependent on its distance. Any star which is less luminous but at a small distance appears to be brighter than a highly luminous star at a large distance. This term apparent magnitude refers to the brightness that we observe from our planet which is dependent on our position and distance from the stellar body.

Absolute Magnitude : Absolute magnitude refers to the true luminiousity of the stellar object. This factor is independent of its distance. It is basically the measurement of stellar power radiated from the object i.e the energy radiated by the star pe unit time. This can be calculated if we know the size of the and its temperature.

The power radiated by the star is calculated like

Power Radiated= (stefan boltzman constant) X (Surface area of the body) X (Temperature in K)

From here we can measure luminiousity of the star like with respect to the sun like :

L / L☉ = (R / R☉)² * (T / T☉)⁴

where ,

L is the luminiousity of the star

L☉ is the luminiousity of the sun.

R is the radius of the star.

R☉ is the radius of Sun.

T is the temperature of the star.

T☉ is the temperature of the Sun.

The absolute magnitude of the star can be calculated from the following formula from our luminiousity calculation like the following :-

Absolute magnitude, M = -2.5 * log₁₀(L / L₀)

The apparent magnitude of the star can be calculated from the following formula from our luminiousity calculation like the following :-

Apparent Magnitude, m = M - 5 + 5*log₁₀(D)

where D is the distance between the star and the earth in Parsec.

FOR THE THIRD QUERY, The answer is no. We dont get any skewed perspectie due to our observation at night.

First of all we are bound to observe in the night sky beacuse of the prensence of Sun during daytime that outshines the the other stellar bodies. Moreover ther is no apparent change in the night sky that will bias our our propotions of observed values. If anything was observed by the astronomers then we would simply choose the two poles for our observation where we will have the luxury of 6 months of contionious darkness.