## Angular Diameter and the Viral “Moon-Sized Mars” Hoax

Spoilers: BOGUS

Every astro-enthusiast’s “favorite” hoax is making the rounds on social media again. If you haven’t heard already, this is completely untrue. This will not happen. It can not happen. That being said, when I see something like this in my newsfeed, the teacher in me says “This is a really great opportunity to educate people about actual astronomical concepts!” And the non-teacher part of me says, “Puppies! Puppies in my newsfeed! Squeeeeeee!” Well, you’re going to have to deal with the teacher part of me! (Yay?) Also, the really fun thing about this that it is quite easy to verify seemingly-outlandish Facebook posts like this on your own! All you need is:

1. Pretty simple algebra
2. Google-able reference tables (ex: diameters of planets or distances to planets)
3.  Any number of plenty of planetarium apps or software!

To determine the veracity of the Facebook post, let us first discuss Angular DiameterAngular diameter is more or less the measure how big an object appears in the sky. When we look at the sky, it appears to be half of a sphere, so from the horizon to zenith (straight above your head) would be 90 degrees. There are numerous guides on the internet and in books about using your outstretched hand to measure distances in the sky. For example, your fist would be about 10°, your thumb 2°, and your pinky 1°. That is great for measuring distances between objects in the night sky – if you are told that a comet will be 40° above the horizon, you can stack your fists to count up to 40°. However, measuring the size of an object such as a planet can be much more difficult as they appear significantly smaller.

Same Object: Different Relative Distance to Observer; Image: © Justin Starr 2015

Different Objects: Same Distance from Observer; Image: © Justin Starr 2015

We will have to divide the degrees into smaller units: arcminutes (1°=60 arcminutes) and arcseconds (1 arcminute = 60 arcseconds). In the case of determining how large Mars will appear, we will use the small angle-formula:

$a_{arcseconds}= \frac{206265*d}{D}$

• $a_{arcseconds}$ = angular diameter in arcseconds
• 206265 = number of arcseconds in 1 radian
• d = object’s physical diamter
• D = physical distance to the object

Now we should have all of the tools we will need to pick apart the claims of this questionable Facebook post.

1) August 27 00:30 Lift your eyes and look up at the night sky.

OK, for starters they don’t give a location – 12:30am for whom, exactly? Eastern Time? Greenwich time? Let’s pick a location: New York City. Now the post does not actually specifically say that Mars will be next to the Moon. It says it will look “like two of the moon (sic) above the ground,” and the Photoshopped image shows them adjacent to one another. Let’s see what our planetarium software has to say.

Stellarium set to New York City, 15/08/27 00:30 EDT.

Notice anything missing? There’s no Mars! It will not even rise until nearly 4:30am. And just to nitpick, the Moon will not be but rather a waxing gibbous. STRIKE ONE!.

2) “On this night, the planet Mars will pass just 34.65 million miles from the Earth.”

The distance between Mars and Earth is constantly changing. For one thing, Mars orbits further out than Earth and therefore Earth is completing orbits faster than Mars. Sometimes Mars is close in a Sun-Earth-Mars line. This closest approach for a superior planet (further away from the Sun than Earth) is called opposition and gives splendid views with telescopes.  When a superior planet is on the opposite side of the Sun from the Earth, it is called conjunction. Also, the planets don’t have perfectly circular orbits; the slight eccentricity of the elliptical orbits means that Earth and Mars are not always at the same distance during opposition; they can be a little bit closer or a little bit further apart. On August 27, 2003, Mars and Earth were indeed at one of their closest approaches in thousands of years. And, the distance that the post states was the actual distance between the two worlds. A modicum of truth! Nontheless: STRIKE TWO! (But it was once true in 2003) But what does that information mean to us for how the planet would actually appear in the night sky?…

3) To the naked eye it looks like two of the moon above the ground!

The Facebook hoax speaks in terms of miles, but I am going to switch to kilometers here. Using the small angle formula, we can determine how the angular size of Mars on that fateful night back in 2003.

• $d =$ Mars’s diameter is $6792 km$
• $D =$ Mars at opposition in 2003 was $55.8*10^6 km$

$a= \frac{206265*6792km}{55.8*10^6 km}$

$a= 25.1"$

This Wikipedia table lists Mars angular diameter as ranging from 3.5″ – 25.08″, so I think that the small angle approximation was pretty good! The Moon is roughly 30′, or half a degree. That is quite a difference in sizes! But those are just numbers. What does that mean for us in real life? Well, here is a graphic of  that giant  25.1 arcsecond Mars compared to a Moon at perigee (or a “Supermoon”) of 34 acruminutes.

Like spitting images of each other! Image: © Justin Starr 2015

No, it will not look like there are 2 moons above the ground. STRIKE THREE! YOU’RE OUTTA HERE!..

But wait! There’s more!

How close would Mars have to come to Earth for it to appear to be the same size as our Moon? Well, we’ll just use our trusty ol’ small angle formula and plug in some numbers! For the sake of round numbers, I’m going to pick the {impossible) matching angular size of Mars and Moon to be 30′ (remember the Moon can range from ~29.3′-34.1′ due to its elliptical orbit). To plug it into the small angle formula, I first have to convert it to arcseconds (multiply by 60) and get 1800 arcseconds.

Here’s our formula: $a_{arcseconds}= \frac{206265*d}{D}$

I’m going to rearrange it to isolate our variable of Distance because algebra:

$D= \frac{206265*d}{a_{arcseconds}}$

$D = \frac{206265*6792km}{1800arcseconds}$

$D = 778306.6 km$

Remember: The closest approach of Mars was 55.8 MILLION km. In order for Mars to appear as large as our Moon in the night sky, it would have to be 778.3 THOUSAND km. Also, interestingly enough, that would put the Moon nearly half-way between Earth and Mars, as the average distance of the Moon id 384.4 thousand km!

Look guys! Math is fun! I hope you enjoyed learning about angular distances and sizes. And remember: It is always good to be skeptical of anything you read on the Interwebs (including this post; please check my math!) but having the tools to be able to verify outlandish claims will only make you better informed and less likely to fall for such hogwash.  Now go outside and start measuring distances between celestial objects with your hands already!

Posted in Humor, Photoshop Fun, Physics, Public Outreach, Thoughts | | 1 Comment

## Why Don’t Eclipses Happen Every New/Full Moon?

On April 4th, 2015, there will be a Lunar Eclipse for some fortunate parts of the world. I reflect back to when I learned about the Moon, phases, eclipses, and such growing up and how I had trouble grasping some of these concepts. In retrospect, some of the difficulty I had may have been due to the diagrams that often accompanied the written concepts. For example, the image I created below is analogous to some you find in science textbooks and websites. It looks like there should be Lunar and Solar Eclipses in every single cycle.

All Eclipses, All the Time!

The reason that we don’t have eclipses in every lunar cycle is because the plane of the Moon’s orbit around the Earth is actually inclined at an angle with respect to the Ecliptic, or the apparent path the Sun takes during the year. The lunar orbital plane has a slight wobble to it, but the average angle of inclination of Luna’s orbit with respect to the ecliptic is 5.1 degrees. That may sound very small and insignificant. However, the Moon is VERY far away so even at only 5.1 degrees, those approximately 385,000 km can still bring Selene above and below the Earth with respect to the Sun.

We know that eclipses only occur when the objects are aligned in particular configurations.

But that is complicated by the inclination of the lunar orbit. Were the lunar orbit not inclined, there would indeed be eclipses every month. However, the angle of the orbit only allows for eclipses to occur at specific times: eclipses can only occur at nodes – the points at which the lunar orbit crosses the ecliptic – and these nodes must be in line with the Sun.

In order to make the concept easier to grasp, I made an image in Photoshop in which the relative sizes of the Earth and Moon are to scale as well as the relative distance between them. And because of that, it is big. As in, “nearly 6000 pixels wide” kind of big. To borrow from Phil Plait, you seriously need to embiggen this image. Consequence of working to scale, I suppose!

Space is big. Like, really, REALLY big.

Now place the Sun in your mind’s eye anywhere you want. If the Sun is to the left of the image, you can see that the New/Full Moons are below/above the Earth respectively; no one is anyone else’s shadow and no eclipses occur. The nodes are perpendicular to the ecliptic; when the Moon crosses the ecliptic it would be in First or Last Quarter phase. But, ff the Sun is on the other side of the Earth or where we are sitting, you can see the the Moon crosses right behind the Earth (Lunar Eclipse) or in front (Solar Eclipse), causing the objects to cast shadows on one another.

If you were having any trouble visualizing orbits, phases, eclipses, etc, I truly hope this helped. And if it didn’t help, or I only confused you more, let me know why! I’d be more than happy to try and create more visual aids. Clear skies!

## Phases of Venus Resources

Attribution: Statis Kalyvas – VT-2004 programme

On the night of Wednesday, February 11th, I took my new telescope out onto the balcony to get a glimpse of the setting Venus. I had been eager to see her phases with my own eyes for some time. Yes, Venus has phases just like our own natural satellite, the Moon! This is because Venus (and Mercury, for that matter) are inferior planets, meaning they are between us and our star. Sometimes we are looking at Venus when she is near the opposite side of the Sun (Naturally, we cannot see a full Venus because the Sun would be in the way). This placement lights up most of her face. As she swings around, moving closer to being between us the Sun, we begin to see more and more of her back; she increasingly wanes into a crescent while also becoming significantly larger in apparent angular size as well. Consider this: due to the Moon’s eliptical orbit, its distance from the Earth ranges from 225,804 miles (363,396 km) to 251,968 miles (405,504 km). This results in a measly 14% difference in angular diameter from perigee to apogee – a difference that can’t even really be discerned by the unaided eye. Venus, however, is orbiting the Sun, not us. Therefore, her distance from us can range from 24 million miles (38 million km) to 162 million miles (261 million kilometers)! While the range of 9.5 arcseonds – 61 arcseconds will also not be easily noticed by the naked eye, check out the above image for the drastic difference noticed through a telescope!

15-02-11 Sh*tty Venus capture… but it’s definitely not a perfect circle!

Back to that fateful night: I peered through the eyepiece and saw a squished circle. For the first time in my life, I was able to see Venus as more than just a remarkably bright point of light in the early morning or evening sky that was without any type of definite shape. Here she was, in all her glory, with a limb sheared off by shadow. However, the seeing was rather poor that night. The turbulent atmosphere due to weather conditions was compounded by her low placement in the sky. This location brought her closer to the rooftops of the heat sink in which I reside, also known as New York City. The warmth radiating off of these buildings made her very jittery – violent air currents stretched and squeezed her, making her writhe and pulsate. I wanted to know what her actual phase was and how it compared to view I was being provided in these terrible observing conditions. I took to Twitter and asked of anyone who would listen:

Below are some of the useful responses I received. I encourage you to make use of them the next time you go and observe Venus.

The three tweets shown above were my favorites because they included nice visual renderings that were aesthetically pleasing as well as useful. Some of the results below are still quite useful but are more data/word oriented than visual.

## My New Telescope: What and Why

I bought a new telescope. Or a cloud magnet. You say tomato…

What did you DO?!

I will most likely not get to use my new gear for a few days because that’s the unwritten rule of astronomy. I’m not saying new telescopes cause bad skies but… well actually, yes, that is exactly what I am saying. Since I cannot show you what my fancy new optics can do yet, I thought I would at least tell you about the telescope I ultimately decided upon and why I chose it.

This guy right here.

I purchased the Celestron EdgeHD 8 with the CG-5 compatible dovetail rail. I also picked up some accessories to go along with it: a T-adapter for the EdgeHD 8 that threads into the rear cell or into the .7x focal reducer designed specifically for the EdgeHD and for APS-C sensors (like what is in my Canon 1000d DSLR), which I also bought. Why though, with the plethora of telescope choices that are out there, did I choose this particular telescope? I sweat over the decision for a long time – at least a year – but a variety of factors eventually led me to this telescope.

Background

That guy right there.

My first telescope was an Orion ST80. It was cheap and it was small. It had acceptable optics and gave me pleasing views of the Moon, the Sun (with an appropriate solar filter, of course), the Pleiades, Jupiter and the Galileans, and Saturn’s undefined rings. The 4 lb. refractor’s portability made it a cinch to throw over my shoulder with its included carrying case and take it to Central Park or Carl Schurz Park with a tripod. When I eventually upgraded my mount to a computerized goto Celestron CG-5, the f/5 refractor easily captured large objects like the Andromeda Galaxy and the Orion Nebula and could get objects as dim as about magnitude 8.5 like M82, the Cigar Galaxy.

This little guy had some drawbacks, though. Short-tube refractors by nature are more prone to chromatic aberration (CA). This was exacerbated by it being a doublet with relatively cheap glass. I could not get much definition on the planets – no phases of Venus, no Great Red Spot of Jupiter, no Cassini Division in Saturn’s rings. Mars… ugh, I don’t even want to talk about it.

It was time to start researching and saving. But for what?

What Is the Right Telescope For Me?

This can be a trick question. The reason this inquiry is so difficult is because there is no single telescope that is good for everything. Compromises must always be made. I considered high quality refractors – triplets with ED glass which would all but eliminate CA. A widefield triplet could capture massive and faint nebulae easily and with less exposure time because of their “fast” optics (~f/5). But they would be limited in their planetary photography abilities. Refractors also happen to be the most expensive telescope per square inch of aperture. I could spend over $1000 for just 80 millimeters of aperture. It would arguably be the most superior views available, but those views would come at quite a cost. Reflector Light Path ©Justin Starr What about a reflector? I didn’t even want to consider one of these guys just based on their size alone. An 8″ f/5 reflector can be just over 3 ft long, while the optical tube of an f/5.9 Dobsonian reflector can be nearly 4 ft long! I live in a one bedroom apartment in New York City you guys; storage space comes at quite a premium. Further, these things can be unwieldy to move about, which would potentially make it difficult for me to carry one to a park. Schmidt-Cassegrain Light Path ©Justin Starr The idea of a catadioptric telescope, like a Schmidt-Cassegrain (SCT), was quite appealing to me. I could get huge focal lengths in a small amount of physical distance due to the “folded light” design of these telescopes. The EdgeHD 8 has 2032 mm (80″) of focal length in an optical tube assembly that is only 17″ long! However, SCTs have their own drawbacks – namely coma (stretching of stars on the periphery due to the parabolic shape of the primary mirror), mirror shift during astrophotography sessions, and they need time to sit outside and acclimate to the ambient temperature in order to maintain focus. Then Along Came EdgeHD… Celestron: “Cooling vents located on the rear cell allow hot air to be released from behind the primary mirror. Each vent has an integrated 60 micron micro-mesh filter guaranteed to let warm air out without letting dust in.” The EdgeHD design by Celestron had a lot going for it. They advertise coma-free optics, they added a mirror clutch mechanism that locks down the mirror once it is in focus to prevent mirror shift, and there are vents on build into the frame to allow the telescope’s optics to acclimate to the ambient temperature much quicker. Also, it is designed with an easily removable secondary mirror (Fastar compatible) converting the slow optics of an f/10 telescope into to a significantly faster f/2 telescope, which is super cool. (Caveat emptor: this requires buying Starizona’s HyperStar lens and a CCD camera. The use of Fastar with bigger SCTs allows attaching a DSLR to the HyperStar lens, but this feature is not compatible with the 8″ models. Therefore, a CCD camera would be required. A list of compatible cameras with a variety of SCT sizes, as well as additional information regarding HyperStar, can be found on this page.) At 14 lbs it can easily be carried by CG-5 and also be hauled to the park, especially in the swanky padded carry case I purchased along with the new scope. Astrobin.com screen grab with photo by ©Ahmed Jaber I also used a number of fantastic internet resources for researching this particular telescope as well as others. There are a variety of web forums out there will people ask questions, write reviews, and more. These include astronomyforum.net, cloudynights.com, and stargazerslounge.com, to name a few. I asked people on Twitter about the telescopes they were using and how they felt about them. Also, a great resource for astrophotography purposes is astrobin.com. Users fill out tech cards for their photos that indicate all the gear used. All of this data is easily searchable/filtered. As an example, this page shows search results of images shot through the Celestron EdgeHD 8. Astrobin may not be necessary if all you care about is visual observing, but for astrophotography purposes it is an invaluable resource for seeing what other people have been able to do with a given piece of equipment. Sacrifices Must Be Made As previously mentioned, no telescope is good for everything. What did I sacrifice? What corners were cut? And why? For starters, I would have love love loved a bigger telescope. After all, what astronomer/astrophotographer doesn’t get aperture fever? More light, more magnification, more power. But as everyone’s favorite uncle says… “Watch the hair!” No, not that uncle. The other one. Thanks, Uncle Ben. The responsibility of paying for it. The responsibility for having to lug it around. The responsibility of mounting it. The responsibility for storing it, and so on. To illustrate the point, let’s look at the next model up, the EdgeHD 9.25, because I considered it for a bit. This telescope would have provided an extra inch and a quarter of aperture and would have allowed for 2″ eyepieces (the 8″ allows for 1.25″ eyepieces). But that extra 1.25″ of aperture would have cost an extra$1000, weighs 7 lbs more, and would have potentially pushed my CG-5 mount to the limit when the extra astrophotography accessories were added on. I don’t necessarily want to be carrying around a 21 lb OTA when I’m walking to the park. So eventually, you settle. Or make a wise, informed choice. Whatever you want to call it.

Gray Skies Are Gonna Clear Up

I mean, they have to right? It can’t be cloudy forever. It’s not like I live in Syracuse anymore. I can’t wait to get this bad boy outside. In the meantime, I’d like to give a shoutout to the wonderful folks over at Oceanside Photo and Telescope, or OPT (Twitter: @OPT_Telescopes), for helping me out with my purchases. One of their employees advised me against wasting my money on a particular Barlow due to issues of oversampling and explained to me the mathematics to figure out how many pixels per arcsecond I could expect to get. I have ordered from them before and will continue to order from them in the future with their incredible customer service, wonderful and expansive selection of gear, and impeccably shipped parcels. But OPT, if you’re reading this: I only asked for the telescope and accessories. There were no clouds on the invoice. Please, please, please, take them back.

## Measuring the Night Sky: Galilean Moons Vs. The Super Moon

On the night of Saturday, January 10th, 2015, I decided to go downstairs in front of my apartment building to observe and photograph Jupiter and the Galilean Moons. I had not been doing a lot of visual observing as of late, nor have I been taking many pictures through my telescope. My astrophotography habit has been very focused on widefield and landscape astrophotography for basically the last 6 months; I’ve mainly been using my 14mm/2.8 or 50mm/1.8 lenses.

As I processed my images, I grew curious: how much space did Jupiter and the Galileans occupy in the night sky? We often hear that, were it not so faint, we would see the Andromeda galaxy as about 6 times wider than the full Moon. I wanted to continue in the tradition of using Earth’s natural satellite as a standard of measure. How would the angular distance of Jupiter and the orbits of its 4 largest moons compare to the angular diameter of our nearest celestial neighbor?

Super Moon – 34.1 arcminutes of angular awesome!

In order to determine the answer (or an approximation, at least), I could not use any old picture of the Moon. No, it needed to be a portrait of the lovely Selene that I had taken. That way, I would know without a doubt that the Moon and Jupiter were captured through the same telescope (Orion ST80) and with the same size imaging sensor (22.2 mm x 14.8 mm). As luck would have it, I had a photo of the Super Moon from August 10, 2014. This was useful because a little research determined that the angular diameter of the Super Moon is 34.1′ (arcminutes). I could now get a good approximation of the angular distance from the Jovian moon at one extreme (Ganymede) to the moon farthest away (Callisto).

I imported both images, uncropped, into Adobe Photoshop CC. I then aligned the layers so that Jupiter was on top of the Moon and reduced the opacity of the Moon. Jupiter’s orientation was rotated so that the orbits would be parallel to the horizontal axis. I added brackets showing the 34.1 arcminutes of Luna’s angular diameter. Next, I made a box that extended from Calisto to Ganymede and bisected it. Laying the box and subsequent copies along the previously-labeled angular diameter, I found that  in the current orientation of the gas giant’s satellites, it fit almost exactly 2.5 times! That meant that the angular distance from Ganymede to Callisto was roughly 13.64′ (34.1’/2.5).

The angular distance of Ganymede to Callisto compared to the angular diameter of the Super Moon.

## To See the Unseeable Sight, To Hear the Unhearable Sound

“To dream… the impossible dream…
To fight… the unbeatable foe…
To bear… with unbearable sorrow…
To run… where the brave dare not go…”
– The Impossible Dream (The Quest) from Man of La Mancha; Lyrics by Joe Darion

My friend from high school and optical engineer at NASA JPL, Holly Bender, recently shared a post from I Fucking Love Science on the Facebook that began with a simple question: Is your red the same as my red? After a few introductory words by Elise Andrew, we were treated to the following wonderful video from Michael Stevens of Vsauce. Take a few moments to watch it if you can spare a few minutes:

If you chose to not watch the video, here’s a brief description of the first half: Michael discusses how we independently experience vision and touch and other phenomena but we can never know if someone else experiences the same exact sight or sensation. He says philosophers call these indescribable feelings as qualia, and calls the inability to express qualia to others (say, describing color to a person who has been blind their entire life) as the explanatory gap.

The video got me thinking and asking questions. I have found virtually no answers to any of these questions yet, but I will pose them to you and hopefully you will have as much fun (or brain-hurting) thinking about them as I had too. And if you have any insights to anything I say, please share in the comments!

1) As the caption to the IFSL link said, “It’s a question that everyone has pondered at one time or another: does everyone view colors the same way?” Why is it the question is so often applied to color? Why don’t more people ask about, say, sound? Does my perception of 440Hz sound like your perception of 440Hz? What is it about color that makes it a more “intuitive” question to ask and not about other features of our daily existences like sound?

2) Our eyes are attuned to a narrow band of wavelengths that we appropriately call the Visual Spectrum. We construct sensors that allow us to detect wavelengths outside of what we can see, and then create visual representations within our visual spectrum.

JPL’s Art Hammon, seen in infrared and visible light. On the left, he holds a cup of hot coffee, on the right is a glass of ice water. Image credit: NASA/JPL

If you look at the picture to the left, the thermal image is not actually infrared light. Rather, it is a false color image in which lighter colors are hotter (shorter wavelength infrared) and darker colors are colder. Hence the hot coffee cup is bright white and the ice cold water is virtually black. But what would it be like to actually SEE infrared – to see with your own eyes footprints on the floor of where a person just stepped? What would it be like to see microwaves – to look up at the night sky and see the cosmic microwave background radiation, or to actually perceive the signal your cell phone emits?

The cilia deep within our ears give us the ability to hear from approximately 20 Hz to 20,000 Hz (with sensitivity to certain frequencies varying in different parts of the range). Elephants use infrasound in some of their communications – Asian elephants from 14-24Hz and Africans 15-35. (I once saw a 60 Minutes program where the people could not perceive the elephant calls but they were recorded and transposed up into human hearing range).

“Two-Elephants” by Mohan Raj – Own work. Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons

What would it be like to hear that low, or as high as a dog (60kHz), a cat (75kHz), or a bat (some up to 200kHz!). How do these other animals perceive sound in their minds? Is it transposed down? Is it just unfathomable to our limited minds (and visual/auditory receptors) as it is outside of our human experience? As I listen to pitches get higher and higher in frequency, they eventually just fade away as they go above and beyond the threshold of what will cause my insufficient cilia to vibrate.

3) It is interesting that we can simulate an experience of a removed sense but not an enhanced one. You can put special headphones on that will eliminate virtually all sound. You can be put into a pitch black room or where some type of eye covering to inhibit sight. A trichromat can look at picture with a certain color configuration and see what someone considered color-blind might see. But the senses are not able to be built upon. I will never understand the in-between colors that a tetrachromat can percieve (yes, they exist!).

I wish there was some way to experience these things, something that could be plugged into my brain that I could see these wavelengths in my mind’s eye or heard in my mind’s ear. After all, it is my brain that is taking the input from my sensory receptors and converting it into my personal experience. So what if the ears were bypassed and I could just “hear it in my brain? I want to know. I want to experience it. I know it is a fool’s errand, but as Don Quixote sings in”The Impossible Dream” Man of La Mancha:

“This is my quest, to follow that star, no matter how hopeless, no matter how far.”