The Distance to the Stars Angular Separation is

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The Distance to the Stars! • Angular Separation is not enough! • We want

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

How far away are the Stars?

How far away are the Stars?

Triangulation • First mark position A directly opposite tree. • Move a known distance

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:

Trigonometry • Can solve it graphically • Or use tangent function:

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

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) From the perspective of the planet (i. e. the object in

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.

Parallax and Baselines 2 Observers 1000 km apart determine the Moon’s parallax to be

Parallax and Baselines 2 Observers 1000 km apart determine the Moon’s parallax to be 9. 0' = 0. 15

Parallax Geometry (II) If distance to an object is known, we can measure its

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

Determination of Size • If distance to an object is known, we can measure

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 ~12800 km

Technical Difficulties in Triangulation • For a fixed baseline, angle 90 as object gets

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

Parallax Angle is Small! • The closer the object the larger the parallax. •

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

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 ~

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 1 m, then Proxima Centauri would be 270 km away! Barnard’s Star would be 370 km away!

Stellar Neighbourhood” 30 Closest Stars are all within 13 Light Years (~ 4 Parsecs)

Stellar Neighbourhood” 30 Closest Stars are all within 13 Light Years (~ 4 Parsecs)