1. 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!

2. How far away are the Stars?

3. Triangulation First mark position A directly opposite tree. Move a known distance along the ‘baseline’. Measure  ABC Deduce unknown distance via trigonometry

4. Trigonometry Can solve it graphically Or use tangent function:

5. 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.

6. 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.

7. Parallax and Baselines 2 Observers 1000km apart determine the Moon’s parallax to be 9.0' = 0.15 

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

9. 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

10. 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

11. 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!

12. 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

13. 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!

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