Angular%20Separation%20is%20not%20enough!

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The Distance to the Stars!

• 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 Parallax by Alan Hirshfeld

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How far away are the Stars?
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Triangulation

• First mark position A directly opposite tree.
• Move a known distance along the baseline.
• Measure ?ABC
• Deduce unknown distance via trigonometry

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Trigonometry

• Can solve it graphically
• Or use tangent function

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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.

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Parallax Geometry (I)
From the perspective of the planet (i.e. the
object in space), the parallax angle is a
fraction of the full 360º - with a known baseline.
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Parallax and Baselines

• 2 Observers 1000km apart determine the Moons
  parallax to be 9.0' 0.15?

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Parallax Geometry (II)
If distance to an object is known, we can measure
its size if we know its angular diameter.
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Determination of Size

• If distance to an object is known, we can measure
  its size.
• Moons angular diameter is 31' 0.52?
• Diameter of Earth is 12800km

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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 Earths orbit 300,000,000km

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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!

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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) Barnards Star 6.0 L.Y.
• Parallax 0.55 arc seconds

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Distance Scale!

• Proxima Centauri 4.3 L.Y
• Barnards 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!
• Barnards Star would be 370km away!

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Stellar Neighbourhood

• 30 Closest Stars are all within
• 13 Light Years
• ( 4 Parsecs)