Astronomy Assignment: Cosmic Distance, Variable Stars, and Life Cycle

This astronomy assignment explores two key areas: measuring cosmic distances and understanding stellar evolution. The assignment begins by examining the parallax method for determining the distance to nearby stars, providing a table with data on the first five nearest stars to the sun, including parallax values, errors, and calculated distances. The assignment also discusses variable stars, differentiating between intrinsic and extrinsic types and providing examples like Polaris and Cepheid variables. Furthermore, it delves into the standard candle technique, explaining its importance in measuring distances to galaxies, especially using Cepheid variables. The assignment outlines the relationship between a star's absolute magnitude, apparent magnitude, and distance. Finally, the assignment covers the life cycle of stars, explaining how a star's mass determines its ultimate fate, from high-mass stars that end as supernovae to low-mass stars that become white dwarfs. The assignment also briefly touches on the formation of the first stars in the early universe.

Running head: ASTRONOMY 1
Astronomy
Student’s Name
Institution’s Name

ASTRONOMY 2
Question 1 (b)
The distance of the first five nearest stars to the sun
Star Parallax
Error(arcsec)
Parallax
(arcsec)
Distance
(ly)+
Distance(pc) Distance
Error
*Proxima
Centauri 0.00242 0.77233 4.2231 1.2948 0.31%
*Alpha-
Centauri A 0.00140 0.74212 4.3950 1.3475 0.19%
*Alpha-
Centauri B 0.00140 0.74212 4.3950 1.3475 0.19%
Barnard's Star 0.00158 0.54901 5.9409 1.8215 0.29%
Lalande 21185 0.00091 0.39240 8.3120 2.5484 0.23%
Fig 1. (Bradt, 2015).
Question 1b
While millions of starts have a consistent brightens, over hundreds of thousands are
cataloged variables stars (Bradt, 2015). These stars include the sun, which usually varies its
output energy by approximately 0.1%. Variable stars can be intrinsic implying that features
including contraction, expansion, pulsation or expansion change the stars ‘luminosity. Besides,
variable stars can be extrinsic implying that a planet or a star has blocked the light or because of
stellar rotation (Bradt, 2015).
Certain stars also gradually change their luminosity. For instance, the Polaris or North
Star was believed to be 4.6 times brighter long time ago, than it is currently (De & Falanga,
2019). Based on the latest studies, the star dimmed in the last few decades; however radically
brightened once more (Lasota, 2014). Polaris belongs to Cepheid variables class, which are very
luminous starts with short pulsation periods. Intrinsic variable stars types also include eruptic
variables with a brightness that varies as it erupts on the surface or combines with interstellar
matter (De & Falanga, 2019). Cataclysmic variable brightens because of outburst including

ASTRONOMY 3
supernovae explosions. Extrinsic variables types consist of rotating stars and binary stars. For
instance, pulsars with electromagnetic radiation that is visible when the ray is directed at the
planet earth.
Stars have a different degree of apparent brightness from an observer on earth. This
variation in brightness is due to both distance and luminosity difference. A nearby star which is
intrinsically faint can appear very bright by an observer on earth just like a very distant star
which is intrinsically luminous (De & Falanga, 2019).
Question 2
Standard candles: Method of measuring cosmic distance
Standard candles technique is a very instrumental method for measuring the distance of
galaxies which are very distant from the earth. Cepheid variable stars are sued to measure
distances in the milky way (Lasota, 2014). Variable stars generally change their brightness and
there might even change their mass, luminosity and there could be even blockage in the path of
the photon as it travels toward the planet earth. Such variation in luminosity occurs over a long
period of time as well as can occur within no minute. Standard candles employ natural brightness
of a given object. Due to the fact that scientists have calculated the luminosity of certain
astronomical objects, this provides a reference point to calculate their distance. Because the
brightness of a star from the earth is a function of both absolute magnitude (actual output of
light) and the observer distance, it possible to calculate the cosmic distance.
In the field of astronomy, a standard candle has definite luminosity. Luminosity is
defined as total output power in watts or solar luminosities. 1 L⊙¿ 3.84 ×1026 watts (Lasota,
2014).

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Very far distanced stars cannot be measured using parallax methods, hence standard
candles are employed. Light sources far distance appear fainter due to the fact that light is
dispersed in a very large surface area. Having the luminous of an object would make it possible
to estimate its distance from the earth. The light reaching the earth spread on a sphere with the
area given as 4 π r2
Where r is the radius of the sphere, which is equivalent to the earth radius. On the
surface of the earth, the power received by the unit area will be given by source luminousity
areaof the sphere
(Lasota, 2014).
The distance varies with power, the larger the power the shorter the distance and vise-
versa.
Fig 2. (De, 2015).
There are different types of standard candles used by astronomers. This includes a
Cepheid variable.

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Cepheid variables are a particular type of stars, which have varying luminosity based on
different cycles. Variability period is closely associated with the star luminosity (De, 2015).
Thus, timing the Cepheid variability can help to approximate its luminosity and knowing
luminosity as well as its brightness from the earth, the calculation of distance becomes possible
(Webb, 2016).
Standard candle, therefore, can be assumed as an astronomical object with a definite
absolute magnitude. Measuring the apparent magnitude of these objects will make it possible
calculating the distance of the object from earth (Shu,2014).
m−M=5lgd−5
Where m=apparent magnitude
M = Absolute Magnitude
d=distance of the astronomical object ∈ parsecs
m-M = 5 log d – 5
.

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References
Bradt, H. (2015). Astronomy methods: A physical approach to astronomical observations.
Cambridge, UK: Cambridge University Press.
De, G. R. (2015). An introduction to distance measurement in astronomy. Chichester, West
Sussex: John Wiley and Sons.
De, G. R., & Falanga, M. (2019). Astronomical distance determination in the space age.
Dordrecht, The Netherlands: Springer.
Lasota, J.-P. (2014). Astronomy at the frontiers of science. Dordrecht: Springer.
Shu, F. H. (2014). The physical universe: An introduction to astronomy. Sausalito, Calif:
University Science Books.
Webb, S. (2016). Measuring the universe: The cosmological distance ladder. London: Springer.