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• 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
The Distance to the Stars!
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 and Baselines
2 Observers 1000km apart determine the Moon’s parallax to be 9.0' = 0.15
km000,38215.02
360km1000cetanDis
360
Parallax
Distance2
Baseline
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
360
DiameterAngular
cetanDis2
Diameter
km3467360
km000,382252.0Diameter
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)