Angular Separation is not enough!



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tarix08.01.2018
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#19910


Angular Separation is not enough!

  • Angular Separation is not enough!

  • We want to know the answer to the ‘age old question’:

  • How far away are the stars?

  • Ans: A lot farther than anyone imagined!

  • See: “Parallaxby Alan Hirshfeld


How far away are the Stars?



Triangulation

  • First mark position A directly opposite tree.

  • Move a known distance along the ‘baseline’.

  • Measure ABC

  • Deduce unknown distance via trigonometry



Trigonometry

  • Can solve it graphically

  • Or use tangent function:



Parallax

  • Consider a planet as seen against the background stars (very far away).

  • View from A and B are different –the planet moves with respect to the background stars

  • Apparent angular displacement is Parallax.



Parallax Geometry (I)



Parallax and Baselines

  • 2 Observers 1000km apart determine the Moon’s parallax to be 9.0' = 0.15



Parallax Geometry (II)



Determination of Size

  • If distance to an object is known, we can measure its size.

  • Moon’s angular diameter is 31' = 0.52

  • Diameter of Earth is ~12800km



Technical Difficulties in Triangulation

  • For a fixed baseline, angle   90 as object gets further away.

  • Hence error in distance value increases.

  • How big a baseline can you get?

  • Diameter of Earth : 13,000km

  • Size of Earth’s orbit : 300,000,000km



Parallax Angle is Small!

  • The closer the object the larger the parallax.

  • Parallaxes are usually very small.

  • Parallax of Venus at closest approach (45 million km) is 1 arc minute!

  • Parallax of nearby (25 light years) stars not observed/measured until 1839!



Stellar Parallax

  • Measurements require largest baseline possible!

  • Nearest stars are:

  • (a) “Proxima Centauri”, in the Alpha Centauri Triplet ~4.3 L.Y.

  • Parallax ~ 0.76 arc seconds

  • (b) Barnard’s Star ~ 6.0 L.Y.

  • Parallax ~ 0.55 arc seconds



Distance Scale!

  • Proxima Centauri ~ 4.3 L.Y

  • Barnard’s Star ~ 6.0 L.Y.

  • If the earth was a grain of sand orbiting a small marble-sized Sun with a radius of 1m, then

  • Proxima Centauri would be 270km away!

  • Barnard’s Star would be 370km away!



Stellar Neighbourhood”

  • 30 Closest Stars are all within

  • 13 Light Years

  • (~ 4 Parsecs)




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