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?
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 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
Baseline
2  Distance

Parallax
360

2 Observers 1000km apart determine the
Moon’s parallax to be 9.0' = 0.15
Dis tan ce 
1000km  360
2  0.15

 382,000km
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 its size.
Diameter
2  Dis tan ce

Angular Diameter
360

• Moon’s angular diameter is 31' = 0.52
Diameter 

0.52  2  382,000km
360 
• Diameter of Earth is ~12800km
 3467km
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)