# Geometry and The Moon

Please do not run away. We are about to use adult language here. For example we will be using the word trigonometry. Still here? Good.  Here is a very pedestrian looking lunar eclipse photo taken with a 280mm lens*, cropped.

Very Ordinary Photo of the Lunar Eclipse with the planet Uranus in the lower left.

This past lunar eclipse several of us put our heads together to try to come up with a more creative photo than the one above. We had a trigonometry problem, however. On the West Coast the last moment of totality occurred at 4:24 AM PDT. We were brave enough to be out at any time of night – even if it meant extreme sleepiness in our day jobs but our problem was that the lowest the moon would be in the sky at the last bit of totality was 32.6 degrees above the horizon. We determined that angle using Stellarium, by the way. Unfortunately there is pretty much nowhere to go to get a nice large moon near an interesting object when the moon is almost 33 degrees high.

Wait: Why do we want the moon and the object to be similarly sized? Here is why… we want the moon to be noticeable like the Fantasy version below, not merely “present” like the real photo on the right. Even bigger would be better, right!?

Notice above right (Reality) and below how tiny the moon is compared to the building in the foreground?  Indeed, if you see a photo taken from anywhere on the West Coast where the eclipsed moon is significantly lower in the sky or larger than shown against foreground, you know it has been “photoshopped“.

Plan C: San Jose City Hall Eclipse Sequence

In short, it is nigh impossible to get the large moon effect with an altitude (angle) of 32 degrees here is why:

Calculating the Angles

Just how far away do we need to be in order to get the moon the same size as an object of interest:

114.6 x object size

In other words, an object that is one foot tall, requires us to stand 114.6 feet away to make the 1/2 a degree angular size of the moon the same angular size as that 1 foot tall object.  The number “114.6” is from this calculation:

1 / TAN (0.5 degrees)

Yeah, that is trigonometry. Using still more trigonometry it is possible to calculate how high above the horizon a 9 inch tall object has to be so that it is “moon sized”.  We did that for you in the “Calculating the Angles” diagram above. Once you calculate the distance from the camera of 85.9, you can multiply that by the sine of the angle to calculate a height of about 46 feet! Here is the trigonometry:

Height = 85.9′ * SIN (32 deg)

You can go one step farther and calculate the distance from the object with ‘distance = 85.9 * COS(32 deg)’.

Of course after all that calculating you will still need to find a location, have contingency plans for weather and so on. At StarCircleAcademy we have built some tools and put together materials to help in all these endeavors.  We teach these things in our NP111 Catching the Moon Webinar.

# The Road To The Temple

Below is where we ended up. This image is from our friend and co-conspirator Andy Morris.

Lunar Eclipse over Temple by Andy Morris of PhotoshopScaresMe

Four of us plotted and schemed to get an interesting shot. Above is Andy Morris’ result.  Click the image and you can read a great article about how he created the shot using Photoshop Skills at his site: PhotoshopScaresMe.com. In fact, it’s a great article which we strongly encourage you to read. You’ll learn how he composited the images together in Photoshop as layers.

### The Long Conversation to Pick a Location

Andy has more details including how alcohol played a part in the process. Mostly I, Steven, was the wet blanket explaining why the geometry was all wrong.

• The Stanford (Hoover) Tower looks like it is shrouded in trees from the needed angle
• Bank of Italy (formerly BofA) in SJC doesn’t work
• The main problem with the wind turbines is that the angle to the top of them is something around 12 degrees above the horizon which is 40 moon diameters below the eclipse.
• Here is why the GG Bridge doesn’t work…
• This seems to be the best solution I could find: the Coit Tower…
• Darn. It would appear the coast is out. Forecast calls for Fog from SF to HMB
• This might make an interesting foreground (see below)… Somebody want to check if they will mind us being on their property in the wee hours?

*Ok, we lied, it was actually a 70-200mm lens with a 1.4 TC on a full frame camera, but the net is the same: 280 effective mm focal length.

Where did you go and what did you get in your planning efforts?  Post a comment and link below… we’d love to see what you came up with!

# Astrophotography – The Polarie

```Published: November 1, 2012
Last Revised: December 16, 2018```

We have a once-in-a-while webinar on beginning Astrophotography. The purpose of the webinar is to get people acquainted with the tools and techniques required to delve into this interesting genre of night photography.  As we teach in that webinar the single most important piece of equipment you can buy is an Equatorial Mount.  An Equatorial mount is an apparatus that counteracts the rotation of the earth so that your camera can peer at the same place in the sky for long enough to capture an image without streaks. There are many equatorial mounts that range in price from almost nothing (and not even worth nothing) to more expensive than logic would dictate.  For more background please see our survey of Astrophotography Gear.

One of the newer pieces of equipment in the arsenal is a less-than three pound piece of gear called a Polarie.  Here is what it looks like with a ball head attached to its face.

Polarie – Close Up

## What Polarie Can Do

As noted earlier, the primary purpose of Polarie is to counteract the effect of the earth’s rotation so that objects in the night sky can be exposed longer without getting streaking. Below are examples of 42 second exposures using an effective focal length of 215 mm. The image at the left is with the Polarie turned on in normal mode, the middle image is the same length exposure but in 1/2 speed mode, and the right is what you get if you use no tracking at all.

Tracking is less critical when shooting with wider angle lenses. I ran a test with a 200mm telephoto lens because it is a more difficult scenario. For example when shooting the Milky Way, an effective focal length of 10 to 50mm makes more sense.

## A Critical Look At Polarie

I purchased only the Polarie unit (about \$400 USD) not any of the accessories. The unit is deceptively heavy at almost 3 pounds but at that weight it is still – and by far – the lightest equatorial mount you can find. The only other device in its weight class at present is the Astrotrac with a starting price about twice as much. The Astrotrac does come with a better tripod mount, however at a total cost of around \$1300 USD.  I paired up the Polarie with my Canon 50D and the 70-200 f/4 lens.  The addition of a Giottos ball head brings the total weight of the equipment attached to Polarie to about 6 pounds.

### The Positives

• Inexpensive
• Good instruction manual
• Mostly easy to set up and to use
• Suitable for a beginner
• Good power for the price.
• Can be powered with mini USB (or two AA batteries). Claimed life is 4 hours on AA batteries but mine lasted at least 6 hours using rechargeable batteries.
• Compact and MUCH lighter than almost everything else.
• Can be used in Northern or Southern latitudes.
• Tracks at star, solar or lunar rates (and yes, they are all different) as well as a 1/2 speed rate which should be good for Landscape Astrophotography.

### The Negatives

• The back plate can be unscrewed to peer through the axis of the motor and also houses a built-in magnetic compass but the plate is almost flush to the Polarie body and it is quite hard to grip.
• The inclinometer (angle measurement device on the side) seems like a good idea except that the markings are so small and coarse that to my eyes it is illegible.  The lighted inclinometer *might* help if the North Star is obscured by trees or such.
• The front plate has a 1/4″ retractable bolt and attaches awkwardly to the motor plate with two thumbscrews that are hard to reach once a head is on the motor plate. I would have preferred that Polarie supply a 1/4 to 3/8″ adapter since most good heads attach via 3/8″ bolts.
• The battery compartment door is a nail buster to open.
• Since Polarie will certainly be used with a DSLR camera, Vixen really missed an opportunity to add a remote release cord – I see no jack for one.
• Not sure what the point of the flash shoe is. I do see the Vixen has another (much larger) inclinometer that can be attached there, but you may be able to do better using an application on your smart phone.
• The optional polar alignment scope is expensive, and bulky. It’s also complicated to operate because you must remove the ball head and camera from the device. BUT the weight of the camera and ball head is likely to create enough “sag” that the careful measurements will be wasted.  We like the SkyTracker much better in this regard.

There is a sight hole to line up Polaris – the North star. I used only that method to align Polarie and got fair results. To get really long exposures one of two methods will need to be undertaken to increase the alignment accuracy: either invest in a Polarie polar alignment scope at almost double the cost or do drift alignment. Drift alignment is not simple and probably would frustrate the aspiring astrophotographer. The Polarie can be purchased with an optional ratcheting tripod base which might be a good idea, however the stated load capacity of the bundled tripod seems too low to use with a heavy camera.

### Noteworthy

Remember that you will need at least two heads and you’ll want them both to be ball heads for optimum configurability. The head on the tripod should be sturdy – see below for why.  Below I refer to tripod head – the apparatus that joins the tripod to the Polarie, and to the Polarie head – which is the hardware used to attach a camera to the Polarie.

Problem Areas

In addition to the negatives listed above, there are several other sources of problems including every point where one element attaches to another. For example: the Polarie base if not attached securely to the tripod head can rotate.  If using quick release plates the attachment point creates another source of rotation. If the camera is not securely attached to the Polarie head rotation can occur there, too. All the pieces together may severely tax a cheap tripod head making it difficult to hold up or adjust the load.  In my configuration I found I had to allow some slouching – meaning I had to adjust the camera so it was pointing slightly above my target and then tighten the head so that it would settle to the right place.

## What Can You Do With A Polarie?

Maybe we should have put this section first! Some of these things can only be done with a Polarie are highlighted in RED.

• Point the Polarie straight up and use it as an automatic panning motor for a time-lapse.
• Align Polarie and take a series of shots of the night sky – the sky will stay in the same place in every shot – and any minor movement can be compensated for using Astrophotography procedures.
• Outfit your lens with a solar filter and track the sun (e.g. for photographing eclipses or solar activity)
• Track the moon e.g. to catch the space station flying across its face, the slow creep of the terminator, or just to get a time-lapse as the moon sets or rises.
• Double your exposure on a landscape astrophotography shot by using 1/2 speed mode.

For more hints tips and examples on how to use Polarie, stay tuned to this channel!

My first test of the Polarie was to track the radiant point of the Orionid Meteor shower. My attempt was mostly a bust due to clouds, however note how stable the time-lapse is – and remember this spans almost 14 minutes of real-time.

Here are two more ways I’ve used the Polarie – as a horizontal panning device

As a sky tracking device

# Zoom Zoom

Last Updated: May 2, 2021

Phil McGrew had an out of this world idea. Capture the International Space Station as it hurtled across the face of the pre-dawn moon.  Great Idea – because it worked! How we figured out when and where to be to make this happen is described in the references below.

We agreed to meet at a spot that fell near the “blue line” (centerline) of the event: Muir Beach Overlook.  I woke up at 3:00 AM and arrived there at 4:45 AM. Everyone showed up on time at 5:00 am and we lugged our equipment into the conveniently located World War Two era machine gun bunkers which kept us out of the wind. There were 3 such bunkers and I took up residence in the closest one since I had the most gear to haul (and am the most lazy).

Bunkered Down for the Morning…

My companions picked two other bunkers, while Rick headed further North along the coast highway.  Note: Don’t let the term Highway confuse you it is a tortuous winding road hanging on sheer cliffs above the Pacific Ocean.

## Resources and References

Before we left we had some discussions about whether the ISS would be visible and how to prevent it from “streaking” and smearing. The ISS is moving at  17,800 miles per hour. At its altitude from our location, that means it crosses the ½ a degree wide moon in under two seconds! At minimum I needed to select an fast enough shutter speed to max out the camera’s frames per second (more chances to get at least ONE hit) which on the Canon 50D is about 5.3 fps.  However we weren’t sure about the comparative brightness of the ISS compared to the moon.  If it were sufficiently dimmer then the moon brightness would overwhelm the ISS.

It’s interesting to try to get the ISS against both the lit and unlit portion of the moon – and we indeed got both.  The ISS trajectory and where you choose to go affects what you will see.  One of our group went farther north and got the ISS brushing the lit edge of the moon, though not crossing it.  This proved to be a quite interesting shot as it is definitely true that the ISS does not stand out well against the moon.

I went with about f/9. This is a rough calculation factoring the f/7.5 refractor  [80mm aperture with 600mm focal length], and a 1.4 teleconverter.  I had to tape over the pins on the camera-teleconverter or it would not let me take the shot “cannot communicate with lens” well – duh, the lens in this case is a TELESCOPE.  ISO 800, speed 1/500th of a second and the camera in BURST (continuous high speed exposure) mode.

We were not expecting a whole lot but were all high fives and thumbs up afterward.  Now that I’m groggy from sleep deprivation I’m wondering if driving about 4 hours round trip was worth 3 seconds of glory.  Yeah, I think so.

If you’re interested in catching the moon near your favorite STATIONARY object, I’ve got a well reviewed, well attended webinar on that.  Want to try some Astrophotography? I’ve got webinars and field shoots for that, too.  Join me and let’s do something unusual with night and low light shots.

For the latest predictions for the San Francisco Bay Area, Yosemite National Park, and Research Triangle North Carolina see this page.