Tuesday, April 17, 2012

Parsec and the cosmic patience of God of Israel (1)

In the Book of Jeremiah there is a text of cosmic dimensions where God of Israel is thinking aloud something truly scary. He says - through prophet Jeremiah - that under certain conditions God may completely and finally abandon His chosen people Israel and they will never more be His nation.

But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD,
I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people. And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
Thus saith the LORD, which giveth the sun for a light by day, and the ordinances of the moon and of the stars for a light by night, which divideth the sea when the waves thereof roar; The LORD of hosts is his name:

If those ordinances depart from before me, saith the LORD, then the seed of Israel also shall cease from being a nation before me for ever. 

Thus saith the LORD; If heaven above can be measured, and the foundations of the earth searched out beneath, I will also cast off all the seed of Israel for all that they have done, saith the LORD.
Jeremiah 31:33-37 KJ

The prophecy contains what must certainly looked like an impossible condition for the ancients assuring the people of Israel that they can break even this covenant - the writing of the law in their hearts - God will never abandon them.

Unfortunately, today heaven above can be measured, and the foundations of the earth searched out.

This makes this word of God of Israel through prophet Jeremiah both relevant and rather scary. Even God's patience has limits - measured in parsec. The Hippocrates and Gaia projects are currently on way to use space-based telescopes to measure as accurately as possible the heaven above.


Measuring the heaven above
The parsec is equal to the length of the adjacent side of an imaginary right triangle in space. The two dimensions on which this triangle is based are the angle (which is defined as 1 arcsecond), and the opposite side (which is defined as 1 astronomical unit, which is the distance from the Earth to the Sun). Using these two measurements, along with the rules of trigonometry, the length of the adjacent side (the parsec) can be found.

One of the oldest methods for astronomers to calculate the distance to a star was to record the difference in angle between two measurements of the position of the star in the sky.

The first measurement was taken from the Earth on one side of the Sun, and the second was taken half a year later when the Earth was on the opposite side of the Sun. The distance between the two positions of the Earth for the measurements was known to be twice the distance between the Earth and the Sun. The difference in angle between the two measurements was known to be twice the parallax angle, which is formed by lines from the Sun and Earth to the star at the vertex. Then the distance to the star could be calculated using trigonometry.

The first successful direct measurements of an object at interstellar distances were undertaken by German astronomer Friedrich Wilhelm Bessel in 1838, who used this approach to calculate the distance of 61 Cygni.

The parallax method is the fundamental calibration step for distance determination in astrophysics; however, the accuracy of ground-based telescope measurements of parallax angle is limited to about 0.01 arcseconds, and thus to stars no more than 100 pc distant. This is because the Earth’s atmosphere limits the sharpness of a star's image.

Space-based telescopes are not limited by this effect and can accurately measure distances to objects beyond the limit of ground-based observations.

Between 1989 and 1993, the Hipparcos satellite, launched by the European Space Agency (ESA), measured parallaxes for about 100,000 stars with an astrometric precision of about 0.97 milliarcseconds, and obtained accurate measurements for stellar distances of stars up to 1,000 pc away.

NASA's FAME satellite was to have been launched in 2004, to measure parallaxes for about 40 million stars with sufficient precision to measure stellar distances of up to 2,000 pc. However, the mission's funding was withdrawn by NASA in January 2002.

ESA's Gaia satellite, due to be launched in late 2012, is intended to measure one billion stellar distances to within 20 microarcseconds, producing errors of 10% in measurements as far as the Galactic Center, about 8,000 pc away in the constellation of Sagittarius.

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