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Cosmic perspectives: how to grasp the true grandeur of deep-sky splendors.

"KEEP YOUR PERSPECTIVE!" Most of us have heard this advice in a social context. But in the telescope eyepiece --where we observe objects that are unimaginably distant, large, and old--it's a formidable challenge to see things for what they really are.

In an attempt to gain some kind of cosmic perspective, I've found it helpful to visualize the scale of what I see through my telescope. Let me give you some examples.

For starters, you can use your eyepiece to measure the physical sizes of your deep-sky targets. Suppose you're looking at Messier 13, the Hercules Cluster, and it stretches 40% of the way across your eyepiece's field of view. How many light-years wide is this star ball? To answer that, you need two pieces of information: the distance to M13 and your eyepiece's angular field of view.

M13 is 25,000 light-years from Earth, give or take 10%. Deep-sky distances are hard to measure and constantly being revised, so it's usually best to get them from an up-to-date, authoritative website. Most of the distances in this article come from objects.html, which has a wealth of good information about each Messier object. There's a link near the bottom of the page for signi. cant non-Messiers.

A standard Plossl eyepiece has an apparent field of view 50[degrees] wide. At a magni. cation of 100x, that gives a true field of view of 50[degrees] / 100 = 1/2[degrees], or 30 arcminutes. Or you can measure the true field directly using the star-drift method described above. If M13 stretches 40% of the way across a 30' field, its apparent diameter is 12', or 1/5[degrees].


Observing guides list a larger size for M13--somewhere between 16' and 20'. It's not surprising that visual observers can't see the cluster's full extent, given the limitations of our telescopes, observing sites, and eyes. In fact, I've grown to enjoy comparing my own estimates of objects' sizes against the "official" estimates.

Now, if your eyepiece had a 1[degrees] field of view, it would just fit an object 1 light-year across at a distance of 60 light-years. (The actual factor is 57.3, the number of degrees in a radian, but 60 is close enough and a lot easier to work with.) So at a distance of 25,000 light-years, a 1[degrees] eyepiece spans approximately 25,000 / 60 [approximately equal to] 420 light-years. Since M13 appears to be 1/5[degrees] wide, the part you can see must be about 420 / 5 = 84 light-years across. Or if you prefer to use its "official" size of 1/3[degrees], M13 is about 420 / 3 = 140 light-years across.

How Big Is 140 Light-Years?

To get some perspective on that figure, try visualizing the cluster's diameter in terms of the 4.4 light-years separating the Sun from its nearest stellar neighbor, the triple star Alpha Centauri. The Hercules Cluster is 32 times that wide, and there are upwards of a million stars packed into it!

Another example: how would the separation of the Sun from Alpha Centauri project onto the Crab Nebula, Messier 1 in Taurus?

I can fit M1 about 8 times across an eyepiece with a 0.5[degrees] field of view. At the Crab's distance of 6,300 light-years, that eyepiece spans about 0.5 x 6,300 / 60 [approximately equal to] 52 light-years. So the visible part of M1 is 52 / 8 = 6.5 light-years long. That's almost 50% bigger than the distance from the Sun to Alpha Centauri. At our current space-probe velocities of 40,000 kilometers (25,000 miles) per hour, it would take 115,000 years to travel to Alpha Centauri and 170,000 years to traverse the Crab Nebula. Cosmic perspective!

How Bright Are Those Stars?

Now that we've used our imagination to place the Sun and Alpha Centauri in the Crab Nebula, the obvious next question is, how bright would they look at that distance? More realistically, what would they look like in the company of some stars that you're used to viewing--like the ones in M11, the Wild Duck Cluster in Scutum, which at 6,000 light-years is nearly as far away as the Crab? The answer's not hard to compute.


The Sun's absolute magnitude is 4.8--that's how bright it would look from a standard distance of 10 parsecs, or 32.6 light-years. The Wild Duck is 184 times farther than that, so if the Sun were there (or in M1), it would appear a factor of 1842 fainter than magnitude 4.8. Checking the graph below, you'll find that this works out to magnitude 16.1--too faint to see in any but the very largest backyard telescopes. This lets you know that the members of the Wild Duck Cluster visible in your eyepiece are intrinsically much brighter than the Sun.

The Pleiades Poster

Because it's so close to Earth, the Pleiades cluster (Messier 45) is particularly enlightening when visualizing the 4.4-light-year separation between the Sun and Alpha Centauri. With good sky conditions, most people can see at least the six stars of the Pleiades' dipper asterism, which is almost exactly 1[degrees] across. At the cluster's distance of 440 light-years, this equates to a diameter of 7.5 light-years.

If the Sun were in the Pleiades, it would appear magnitude 10.5--easy to see through a telescope, and detectable with good binoculars under a dark sky. The Alpha Centauri system would be a little brighter, magnitude 9.7. And the 4.4-light-year separation between them would span 34' in the sky. (This is viewing the Pleiades as a flat, two-dimensional map. In reality, two stars could be quite far apart in space but still appear side by side from our earthly perspective.)

On the photograph at left I've marked two stars whose brightnesses and separation almost precisely match what the Sun and Alpha Centauri would have if they were placed in the Pleiades. Once you've located these through a telescope, it's hard to look at the Pleiades without seeing this amazing model of our two closest stars!

Now replace light-years by miles, and imagine the Pleiades on a poster so huge that the dipper asterism is 7.5 miles wide. If you were to place this poster 440 miles away and view it through your telescope, it would look just like the real thing. By a wonderful coincidence, there are 63,360 inches in a mile and 63,240 astronomical units (a.u.) in a light-year. (An a.u. is the average distance from Earth to the Sun, about 93 million miles, or 150 million kilometers.) Picture yourself driving 440 miles to this poster, placing a microscopic dot 1 inch from the star representing our Sun, and driving back home to your telescope. Two points 1 inch apart wouldn't stand out on this poster, but that's how big a properly scaled model of the Sun and Earth would be. We live in a truly huge universe!

Bringing Faraway Things Near

The last perspective deals with the relative sizes of star clusters and nebulae. The Wild Duck Cluster appears to be much smaller than the Pleiades, but is that just because it's farther away, or is the Wild Duck really smaller?

To answer that, turn to the photomontage on page 83, where I've shown a selection of deep-sky showpieces as they would appear if they were all at the same distance as the Pleiades.

The tables below show statistics for a wider selection of objects, and more data are available on the Web as an Excel spreadsheet at cosmic_perspectives.

If you compare the true sizes of open clusters, you'll see that they range from relatively modest ones like the Pleiades to whopping NGC 869 and 884, the members of the Double Cluster in Perseus, each of which would be 8[degrees] across--nearly the size of the Big Dipper's bowl. What a sight they would make side by side! Globular clusters are generally larger than open clusters. But Messier 28, the smallest listed, isn't quite as large as the members of the Double Cluster.

Planetary nebulae and supernova remnants vary greatly in size, depending on how long they've been expanding from the star that spawned them. The Ring Nebula is relatively young and small. If it were in the Pleiades it would be just 7' across --barely nonstellar to the unaided eye.

Diffuse nebulae show an even larger range of sizes. The Orion Nebula, which appears so big and bright to us, is actually much smaller than M8, the Lagoon Nebula. But that in turn is dwarfed by two easily observed nebulae in other galaxies: the Large Magellanic Cloud's Tarantula Nebula, and NGC 604 in M33, the Triangulum Galaxy. Both of these are too large to include in our list. If they were centered on the Pleiades just 440 light-years away, we'd be well inside them!

Visualizing the true scale of your targets brings a novel perspective to telescopic observing. If you'd like to pursue it further, measure the fields of view of your favorite eyepieces, fire up your spreadsheet, and bring your favorite deep-sky wonders close to home.

GAINING PERSPECTIVE The slanted lines tell how bright various stars would appear at different distances. Each star other than the Sun (the lowest line) is marked at its actual distance and brightness. You can use this diagram to find out how bright a deep-sky object's stars really are. For instance, all the stars that most telescopes show in M13 are more luminous than Vega but less luminous than Polaris.


COMPUTE IT YOURSELF Here are the formulas to find any object's actual size, and the apparent magnitude of any star, at any distance. Let d = distance to object in light-years, and a = angular size of object in degrees.

Then s, the width of the object in light-years, is given by

s = [pi]da / 180

In addition, let

[M.sub.V] = star's absolute magnitude (4.8 for the Sun). Then V, the star's apparent magnitude at distance d, is given by

V = [Ms.sub.V] + 5 [log.sub.10](d) - 7.6

For example, to find the apparent magnitude of the Sun, use

V = 4.8 + 5 [log.sub.10](d) - 7.6 = 5 [log.sub.10](d) - 2.8

PHILLIP KANE observes with a 6-inch refractor from a ranch in northeastern California. He occasionally retreats from his observing field when he hears the scream of a nearby mountain lion.

These tables show various objects' apparent magnitudes and sizes both
at the objects' actual distances and as they would appear if the
objects were brought alongside the Pleiades at 440 light-years. The
Sun's magnitude is given as it would appear at the object's actual
distance. The photographs at right show M78, M8, and M42 in
true relative scale, as they would appear if they were all at
the same distance. The Deep Sky in the Mind's Eye

Visualizing Nebulae and Supernova Remnants

                                  Distance    Size
Nebula            Type            (l-y)       (l-y)

Dumbbell (M27)    Planetary          1,250    2.9 x 2.1
Messier 78        Refl ection        1,600    3.7 x 2.8
Orion (M42)       Emission           1,600     40 x 30
Ring (M57)        Planetary          2,300    1.0 x 0.7
Veil              SNR                2,500       130
Lagoon (M8)       Emission           5,200     140 x 60
Crab (M1)         SNR                6,300      11 x 7

                             Apparent Mag.
Nebula                  Actual     At 440 l-y

Dumbbell (M27)             7.4         5.1
Messier 78                 8.3         5.5
Orion (M42)                4.0         1.2
Ring (M57)                 8.8         5.2
Veil                       7           3
Lagoon (M8)                6.0         0.6
Crab (M1)                  8.4         2.6

                            Apparent Size
Nebula            Actual                      At 440 l-y

Dumbbell (M27)    8.0' x 5.7'                 23' x 16'
Messier 78          8' x 6'                     29' x
Orion (M42)        85' x 60'                  5[degrees] x 4[degrees]
Ring (M57)        1.4' x 1.0'                  7' x 5'
Veil               3[degrees]                 17[degrees]
Lagoon (M8)        90' x 40'                  18[degrees] x 8[degrees]
Crab (M1)           6' x 4'                   1.5[degrees] x 1[degrees]

Distances to planetary nebulae and supernova remnants (SNRs) are not
known very accurately.

Visualizing Star Clusters

                                 Distance    Size
Cluster             Type        (l-y)       (l-y)

Pleiades (M45)      Open           440          14
Wild Duck (M11)     Open         6,000          24
NGC 869             Open         7,100          62
NGC 884             Open         7,400          65
Messier 28        Globular      18,300          59
Hercules (M13)    Globular      25,100         146
Messier 3         Globular      33,900         177

                          Apparent Mag.
Cluster               Actual   At 440 l-y

Pleiades (M45)         1.6         1.6
Wild Duck (M11)        6.3         0.6
NGC 869                4.3        -1.7
NGC 884                4.4        -1.7
Messier 28             6.8        -1.3
Hercules (M13)         5.8        -3.0
Messier 3              6.2        -3.2

                           Apparent Size
Cluster              Actual           At 440 l-y        Sun's mag.

Pleiades (M45)       110'                    110'           10.4
Wild Duck (M11)       14'                 3.2[degrees]      16.1
NGC 869               30'                 8.1[degrees]      16.5
NGC 884               30'                 8.4[degrees]      16.5
Messier 28            11'                 7.6[degrees]      18.5
Hercules (M13)        20'                 19.0[degrees      19.2
Messier 3             18'                 23.1[degrees      19.9

NGC 869 and NGC 884 together constitute the Double Cluster in Perseus.
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Title Annotation:backyard basics
Author:Kane, Phillip
Publication:Sky & Telescope
Article Type:Table
Geographic Code:1USA
Date:Sep 1, 2007
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