Distance and Time Measurement, Physics tutorial


In the study of astronomy and cosmology, distance is frequently represented by using the units termed as 'light-years'. A light-year is the distance which light travels in one year, and as light travels at around 3 x 108 m/s and there are approximately 3.15 x 107 seconds in one year, a light-year (that is, distance is the velocity multiplied by the time) is  just under 1016 m, or around 10 trillion kilometers.

The distance from the Sun to Pluto, that is the dimension of our solar system, is around 5.4 light-hours and the distance to the nearby star, Proxima Centauri, is around 4.25 light-years. Our solar system is a part of the Milky Way Galaxy that is a typical size galaxy and is around 100,000 light-years across. Andromeda, our nearest galactic neighbor, is positioned around 2,140,000 light-years away and the distance to the farthest object we can see is around of 10 to 20 billion light-years.

The universe is between 10 and 20 billion years old, and the general accepted age is 15 billion years. This is a very long time. To understand its depth, we will map the history of the universe into one of our 12-month calendar years. Our cosmic year starts with the formation of the universe at midnight. However a lot goes on in the first few months, our galaxy, the Milky Way, does not form until 1 May and our solar system is absent until around September 9. Earth forms on 14 September and life originates in late September or early October. The Eukaryotes, the first cells having nuclei, are flourishing through mid-November however most of what we recognize regarding the history of life takes place in December.

December opens via an increase in oxygen in our atmosphere, a by-product of oxygen-producing algae which destroy themselves through overproducing oxygen. The first worms appear in mid-December, and plants start colonizing the land around December 20. Life enters the middle age on Christmas and dinosaurs rule the next few days. The primary primates appear on the December 29th however the first humans don't grow until late evening on the last day of the year. Agriculture is discovered with just 40 seconds before midnight, Rome falls with three seconds remaining, and recent history makes up the last second. We are starting the second year as beginners to the universe.

The Big Bang:

Our present, best hypothesis for the origin of the universe is termed as the Big Bang. The cause of the Big Bang is unidentified and as well unknown is what, if anything, went on before it. However we have learned, and are continuing to learn much about how the universe developed since its birth. The existence of a universe-initiating explosion is supported through several lines of evidence, most remarkably are:

  • The observed motions of the galaxies.
  • The observed background electromagnetic hiss produced throughout the bang.
  • Evidence from the observed plenty of light chemical elements in the universe.

Everything we are familiar with is a composite of a mere 109 building blocks which we call elements. The atoms of 92 naturally occurring elements join to form the myriad of materials which we see and use on a daily basis. An atom is the collection of particles termed as protons, neutrons and electrons (that is, these particles are composites of still smaller particles; however we will keep it simple). We can assume an atom as a dense core of protons and neutrons termed as the nucleus, surrounded through a cloud of orbiting electrons and as protons and neutrons are much huger than electrons, most of the mass of an atom lives in the nucleus.

Origin of the elements and composition of universe:

All matter in the universe was produced during the Big Bang however much of it has been revised in the interior of stars.

Our understanding of the methods that made the solar system comes from our understanding of the physics of rotating bodies and examination into the chemical composition of the Sun, moons, planets and asteroids. However much exciting work remains to be done on several aspects of solar-system evolution, we encompass a robust hypothesis explaining the solar-system formation which gives a stable frame-work for research.

The kinds of Meteorites comprise: stony, iron and the processes for dating the age of rocks and meteorites are based on the spontaneous transition of some elements to other elements. This is termed as the radiometric dating method. The spontaneous transition is termed as radioactive decay and we name the isotopes that decay the 'parent' and the product of decay a 'daughter'.

The outcome of such analyses points out that meteorites have ages close to 4.56 Ga, and therefore so does Earth. The oldest rocks are just under 4 Ga; no rocks survived the earliest part of history of Earth.

The composition of Earth:

After gathering the original composition of the solar system from the sun and meteorites we can fill in gaps in our knowledge of the composition of Earth.

The radius of Earth is around 6,371 km and the radius of the core is around 3,486 km (that is, the inner core radius is around 1,217 km (that is, a little more than 2/3rd of the radius of the Moon). The mass of Earth is around 5.973 x 1024 kg, and its mean density is 5.515 g/cm3. The typical density of continental rocks is around 2.7 g/cm3. The crust accounts for less than one-half of one percent of the mass of the planet. The mantle accounts for around 84 percent of Earth's volume however the core consists of nearly 70 percent of the planet's mass.

Earth is hot due to three heat sources:

  • Heat of formation
  • Heat from freezing of inner core
  • Radioactive heat

The motions deep in Earth are much slower than such common at the surface.

The motion in the outer core carries on at a rate of around ten kilometers per hour. This is around six miles per hour that might seem slow, however which subjects the earth's material to huge pressure and that slow motion is the source of Earth's magnetic field. The mantle is much more sluggish; creeping all along at a rate of about 10 centimeters per year, around 100,000 times slower than the core. However these slow moving methods have had a remarkable impact on the nature of our planet.

The method of Trigonometric Parallaxes:

Nearby stars come out to move with respect to more distant background stars due to the motion of the Earth around the Sun. This apparent motion (that is, this is not true motion) is termed as Stellar Parallax.

1641_Parallax Measurements.jpg

In the figure above, the line of sight to the star in December is dissimilar than that in June if the Earth is on the other side of its orbit. As seen from the Earth, the close star comes out to sweep via the angle shown. Half of this angle is the parallax 'p'. It will be noted that the parallax reduces with distance.

As the distance to a star rises, the parallax reduces.

675_Parallax method.jpg

In the figure shown above, the star is around 2.5 times closer than the star in the lower figure, and consists of a parallax angle that is 2.5 times larger. This provides us a means to measure distances directly through measuring the parallaxes of close by stars. We term this direct distance procedure the Method of Trigonometric Parallaxes.

Stellar Parallax and Parallax Formula:

As the closest stars are still very far away, the largest measured parallaxes are extremely small generally less than an arc second. For illustration, the closest star, Proxima Centauri, consists of a parallax of 0.772-arcsec (that is, the largest parallax observed for any star). We make use of photography and digital imaging methods to measure parallaxes these days. Interestingly, we measure parallaxes from space to avoid blurring due to the atmosphere of Earth.

We have seen prior that the smaller the parallax, the larger the distance. We can deduce this as a simple formula:

d = 1/p


p = parallax angle in arc seconds

d = distance in Parsecs 

Parallax Second = Parsec (pc)

Fundamental unit of distance in Astronomy

 A star having a parallax of 1 arc second consists of a distance of 1 Parsec.

1 parsec (pc) is equal to:

206,265 AU

3.26 Light Years(ly)

3.086 x 1013 km

The alternative unit of astronomical distance is the Light Year (ly).

1 light year (ly) is equal to: 0.31 pc = 63,270 AU

Brightness of a Star:

There are two methods to recognize the brightness of a star quantitatively:

1) Intrinsic Luminosity: This is a measure of the net energy output of the star. This is distance independent and is a physical property of the star itself.

2) Apparent Brightness: This computes or measures how bright the star appears to be as seen from a distance it mainly depends on the distance to the star. 

Inverse Square Law of Brightness:

The Apparent Brightness of a source is a result of geometry. As light rays come out from a source, they spread out in area:

1279_Inverse Square Law of Brightness.jpg

Represented mathematically: B = 1/d

And in words: The Apparent Brightness (B) of a source is inversely proportional to the square of its distance (d)

The Implications of the statements above are as follows:

For a light source of given Luminosity the closer the source is the brighter it becomes that is if you move 2x closer to the light source it will appear 22 = 4 times brighter.

As well the farther is the light source the fainter is appears. This signifies that moving 2x further away from the light source it will appear 22 = 4 times fainter.

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