February – Orion’s Stellar Distances

by Pat Browne

Orion’s Sword contains the Trapezium – an asterism containing 4 Stars embedded in Nebulousity


 Constellation of Orion - Line below the Belt Stars contains Orion Nebula


Closeup view in a telescope of the Orion Nebula - Image taken by Stephen J. McIntyre http://denholmobservatory.ca/?p=822

Observing the Orion Nebula in the Sword of Orion is probably one of the easiest and rewarding (and quick) star tours you can do in the winter months. Small scopes can easily resolve the 4 stars which make up the ‘Trapezium’. Last year, during one of our astronomy classes, someone asked how close are these four stars to each other? What’s the interstellar distance. This give us an appreciation of the beauty of starlight and the understanding that we can actually see across our field of view in the eyepiece and see a distance in landmarks (well “starmarks” ) in the sky.

A Field Guide to the Stars and Planets (Peterson Field Guide Series) explains the reason for the appearance of such beautiful wisps of stardust.The Orion nebula is a ‘blister’ in the side of the great Orion Molecular Cloud which shields the molecules from ultraviolet radiation, (otherwise they would be broken apart) and thus preserves the glorious, celestial nebulosity for us to view.

Distance Determination to the Nebula

Distance determination through good ‘old fashioned’ parallax… with a new twist!trig-anim

Courtesy http://www.astronomynotes.com/starprop/s2.htm#A1.1

The new twist is the use of fixed star radio sources so that the technique of trigonometric parallax could be used at a much larger distance and much tinier angle. The distance to the star(s) is the dotted line from our location to the star, and is expressed as d = 1/p (where p is in arc-secs)

“After locating four compact radio-bright stars within the nebula, the astronomers also found a very remote (extragalactic) radio source nearby, just 1.6° to the southeast. Using the VLBA [Very Large Baseline Array Radio Telescope] allowed them to measure the angular separation … of this “fixed” source from each of those in the nebula. By repeating their measurements during 2005–07 … — that is, from opposite sides of Earth’s orbit — they detected enough of a parallax shift to deduce a distance of 414 ± 7 parsecs, or very nearly 1,350 light-years.” http://www.skyandtelescope.com/news/11853711.html

Note: A parsec is a measure of distance equal to 3.2 light years. It is defined as the distance to a star when the parallax angle measured is 1 arc-sec. … ‘par-sec’

The region of interest on the field map is the 4 stars represented by Θ (Theta 1) Orionis is shown in the detailed map made by Stellarium below:


Distances between the Stars : INTER-STELLAR distance

So the question is:

When we look in a telescope and see 4 tiny stars in a tight cluster surrounded by stardust and gas, what are the distances in fractions of a light year are we seeing?

(This could make us feel a bit claustrophobic as we know that we live in a much roomier stellar system where the nearest start to us (Proxima Centauri is about 4.2 light years distant) .

Angles in the Sky

When we measure relative distances in the sky, we express them as angles on our celestial sphere. You can think of the celestial sphere as the sphere expanding outwards from the equator above the terrestrial equator. Typical angular measures that you can see naked eye look like this:

Angles in the sky naked eye

Angles Recorded in A Telescope with A Digital Camera

But when we need to measure very small angles between stars in a telescope eyepiece, we are looking at very small angles measured in units of arc-seconds or 1/3600 degree! If we mount a digital camera on the eyepiece we can figure out how many pixels in the camera image correspond to the measure of the angle. For example, my digital camera has a ‘field of view’ in the eyepiece of roughly 1/2 degree or the width of the moon. The camera has a resolution of roughly 750 pixels in width. This means that we have 1800 arc-secs (remember 1 arc second is 1/3600 degree so 1/2 of that is 1800 arc-seconds). That amounts to 1800/750 arc-seconds/pixel or 2.4 arc-seconds /pixel. With Stephen McIntyre’s Camera, there are 3465 pixels across so he can actually see the individual stars in his image – the same way we can see them in a small telescope.

Angles between stars in a telescope view

Number of Pixels measured using the Results from ImageJ


Image Measurements in pixels using the imageJ program


Stephen McIntyre explored the use of his camera in recording these distances in his Trapezium project: See Stephen J. McIntyre’s Trapezium Project Stephen’s camera for this setup is 0.2663 arc-seconds/pixel. This camera has many pixels and a long focal length so that he is able to see the 4 stars in the trapezium in his images.

Note: Reference chart is upside down because North is down in the telescope. We measure the Arc-Seconds corresponding to the length of the line between the stars.

Calculation of Inter-Star Distance:

Arc Length according to S = R* θ

R the distance to the nebula) 414 parsecs .

θ is the measured length in pixels converted to radians

Let’s take the longest distance BD of 72 pixels. What fraction of a light year is that?

S = R x (72 * 0.2663 )

S = R x (19.2/3600) degrees *(Π /180) radians/degree )

S = 414 x .000093 Radians

S = .038 parsecs (very close indeed!)

How many light years?
Well a parsec is a direct measurement for distance, and it corresponds to 3.2 light years where 1 light year is the distance light travels in 1 year!
Distance BD is .038 x 3.2 = .12 light years
So looking in the eyepiece you are seeing the distance light travelled in 1/10 of a year between stars B and D!
Similar calculations for the other interstellar distances show:
InterStellar Distance (lys) Number of Pixels Arc-Length (parsecs) Distance(AUs) Distance (lys)
AC 49.52 0.03 5342 0.085
AB 37.96 0.02 4125 0.06
BD 72.09 0.04 7947 0.12
CD 51.6 0.03 5688 0.09

Here’s a chart showing astronomical distances courtesy http://en.wikipedia.org/wiki/Parsec