• 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)