Question

Can someone define these?
Light-year
Parsec
Parallax
Absolute magnitude
Apparent magnitude
Redshift

Answer 1

A light-year is a unit of distance. It is the distance that light can travel in one year.
1 light year = 9.4605284 × 1015 meters

Answer 2

10^15 in above statement

Answer 3

light year - distrance covered by light in an year in vaccum.
Parsec - A parsec is a distance a star would be from earth, to have a parallax of 1 arc second at earth.
parallax - parallax is defined as half the anglular shift that occurs in a stars position in the sky with respect to distant stars as seen from earth between the 2 positions of earth corresponding to perihelion and apohelion
\[p (\in arcseconds) = 1(parsec)/stellar distance(\in parsecs)\]

Apparant magnitude = This defines how bright a star 'appears' because of its distance from earth.
\[Mapp = -2.5 \log(I) + K1\], here K1 is a suitably chosen constant

Absolute magnitude = This defines the actual brightness of the star. it can also be defined as the apparant magnitude of that star, if it was placed at a distance of 10 parsecs from earth.
absolute magnitude only depends on the stellar luminosity, which is independent of distance.
\[Mabs = -2.5\log(L) + k2\], where k2 is a suitably chosen constant

This is the relation between absolute and apparant magnitude

\[Mabs = Mapp - 5*\log(d) + 5\]

hence, as per the above definition, if you put d = 10 parsecs in the above relation, you will see Mabs = Mapp , at d = 10 parsecs

Redshift
When a body moves relative to another body, the light rays travelling from one body to another get doppler shifted. This means, that the observed frequency of the light increases if the bodies are moving towards each other and decreases if they are moving away. Thus, when 2 bodies are moving away from each other at high velocites, this effect gets pronounced and noticeable by current human technology. hence, light from bodies moving apart appears to be 'redshifted' i.e. decreased in frequency.

Answer 4

1) LIGHT YEAR
Defn: The distance travelled by light (with c) in 1 year (in terms of seconds)
(I am using approx. values here)
\[1LY=365 (\approx. days/yr)*24(\approx. hrs/day)*60(\min/hr)*60 (\sec/\min)*3*10^{8} (\approx. c)\]So, \[1 Light Year \approx 9.4608*10^{15} m\]
2) PARALLAX
Defn: It is the angular distance between two points (two points of the same object or two different objects) with reference to an assumed origin (may vary depending on the problem).
Finding the parallax is similar to finding the angle of a right- angled triangle trignometrically.

Parallax = Distance between the two points / Distance of the line joing the points to the assumed origin.

You may find many examples for understanding parallax, like finding the distance/diameter of moon using parallax methods, finding the distance of a star, etc.

In the first case, you have to assume the Center of Earth as the origin and the two points are ends of the diameter of the Moon. If you knoe the diameter of the moon, you can find its distance from the Earth and vice versa.

3) PARSEC
Defn: The distance of an object which measures 1 arc second of parallax.

Practical method:
So to find the distance of an object from the sun, the parallax should be measured. It can be done by measuring the position of the object at an interval of six months and dividing the difference in the position over the six months (mentioned as 2p in the diagram) by 2 gives the parallax angle p. Using the distance between Earth and Sun (1 Astronomical Unit), the distance of the object can be found.

Here if the value of p=1, the distance of the object from Sun gives 1 parsec. Thus
Distance in parsec = 1 / Parallax in seconds.

The greater the parallax, shorter is the distance.

1parsec = 206,265 AU = 3.26 LY

4) Apparent Magnitude and Absolute Magnitude:

Apparent Magnitude of a star is a measure of the relative(logarithmic) brightness of the star with respect to a standard star.

Absolute Magnitude is the intrinsic brightness of the surface of the star.

The explanation for the magnitudes are mentioned in the post above.

5) Redshift
\[z=\frac{ \lambda _{observed} - \lambda _{emitted} }{ \lambda _{emitted} }\]
There are three types of redshifts:
a) Doppler redshift: Result of relative radial motion between emitter and observer. This can give the radial velocity of a star.
b) Gravitational Redshift: Result of loss of energy of the emitting body's photons while overcoming a strong gravitational field.
c) Cosmological Redshift: Caused by the relativistic expansion of the Universe, quantified by Hubble's constant.

The actual observed redshift of an object is the sum of all the types of redshift.