Measuring the distance to the stars?

--------- #1310 - Using Parallax to Measure Distance to the Stars

- Attachment: Constellation of stars.

- By using precision parallax methods the Hipparcos Satellite has measured the distances to 22,396 stars to an accuracy of better than 10%. Before the launch of this spacecraft only the distances to 1,000 stars were known using parallax methods. ( See note 1 to learn how parallax measurements work.)

- Today Hipparcos measurements to the stars extends out to 300 lightyears. The brightness was measured for 1,058,332 stars. 23,900 of these stars belong to multiple star systems. 118,000 of these stars were measured in brightness over 100 times. As a result 11,597 stars were discovered to be variable stars. Nearly 10% are “variables” and 8,237 of these were not known before Hipparcos discovered them. Much of this data needs continual study to determine why the stars are variable in brightness. They could be “ Irregular Variables”, Large-amplitude Variables”, “Unsolved Variables”, “ Eclipsing Binary” stars, or something else yet to be discovered. So far 273 were determined to be Cepheids. 917 are eclipsing binaries. There is still more to learn.

- Distance precision varies. Brighter stars can be measured more accurately than fainter ones. More precise measurements can be made at the ecliptic poles. Stars within 30 lightyears like Vega and Formalhaut can be measured to within 1% accuracy.

- In 200 B.C. Hipparchus Nicea , an astronomer using only his naked eyes measured the position and brightness of 1,080 stars. Today the science he started is called “ astrometry” In August 8, 1989 the High Precision Parallax Collecting Satellite was launched, “Hipparcos”, to carry on the science of astrometry. To achieve parallax measurements Hipparcos measured the angle in the sky of stars at 6 month intervals when the Earth was viewing from opposite sides of its orbit about the Sun. The closer stars would shift by a small angle compared to the distant stars in the foreground. The separation of the two measurements is the base of a triangle 186,000,000 miles at its base. The Earth-Sun distance is one astronomical unit of 93,000,000 miles.

- For the 118,000 closer stars the measurements included distance, motion, luminosity, mass, size, and age.

-------------------------- 400 stars were measured to within 1% accuracy

------------------------- 7,000 stars were measured to within 5% accuracy. Ground based telescopes could measure only 100 stars to this precision accuracy.

------------------------ some measurements extended out to 500 lightyears. The Milky Way Galaxy disk of stars is 120,000 lightyears in diameter.

----------------------- Star Clusters were measured:

-------------------------------------- Hyades ------------------ 120 stars

-------------------------------------- Coma Berenices ------ 120 stars

--------------------------------------- Pleiades ----------- 80 stars at 385 lightyears distance. This was 10% closer than previous measurements that had put the distance at 440 lightyears. The difference meant that the stars were emitting 20% less light than expected.

- Hipparcos not only measured the distances to the stars it measured how gravity bent space-time and consequently bent the light that passed near the Sun. Einstein’s equations predicted that the gravitational deflection of starlight passing by the Sun would be 1.7 arc seconds. Measurements confirmed this calculation to one part in one thousand. Light travels in a straight line in curved space-time. Mass tells space-time how much to curve. Space-time tells light how much to bend.

- The Sun and stars quiver, or ring, at a unique resonant frequency of oscillations. These oscillation modes depend on star’s diameter and the different compositions of the different layers that make up the star. Using this data science can create a model that predicts the precise luminosity of the star. Hipparcos measurements exactly confirmed these predictions of the star’s brightness.

- An example of some numbers that calculated the distance to the star Eta Bootes. The parallax angle measured was 88.17 + or - 0.75 milli-arc seconds. The corresponding distance was calculated to be 40.0 lightyears with an uncertainty of less than 1%.

- Footnote (1): The parallax angle is a very small angle. But, once you have it simple trigonometry is used to calculate distances. Every six months the Earth moves from one side of its orbit about the Sun to the other side that is separated by a distance of 186,000,000 miles. This separation allows a different line of sight to nearby stars compared to the distant background stars. This is like holding your thumb at arm’s length and seeing it move back and forth as you close one eye than the other. If you measured the change in the line of sight angle that would be the parallax angle.

To illustrate further, When I was a Boy Scout I learned to use the parallax method to measure the distance across the river. We walked along the bank of the river and lined up two trees on the opposite side. On tree near the opposite bank and another tree in the far distance. (rocks or mountain tops work just as well as trees, duh). We wrote down the angle for the line of sight to each. We then walked along the bank of the river stepping off say 100 yards. We then sighted the same distant tree and the original spot we started from. This angle should be the same. Now we sight to the near tree. This angle changed and this is the angle due to parallax. The parallax angle plus the original angle is the same as the angle at the triangle’s vertex at the near tree. (Trigonometry rule about intersecting angles to parallel lines.) We sighted back to the original spot to give us two angles of the triangle, minus 180 degrees to get the third angle. Trigonometry is used again to calculate the side of the triangle represented by the distance across the river.
　
Example: The parallax angle change, 10 degrees, plus the original angle ,20 degrees, calculates the vertexes angel to be 30 degrees. The angle back to the original spot is measured at 60 degrees. The third angle in the triangle must be 90 degrees. The base of the 90 degree triangle was 100 yards. The distance across the river is the tangent 30 degrees = 100 / distance = 0.577 The distance across the river was 175 yards. That is some wide river. Better not try to swim across.
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707-536-3272, Thursday, October 13, 2011