Episode 118 - The Big Mars Hoax / The Two Moons Hoax
Recap: "Come one, come all! See the never-before-seen and never-to-be-seen again phenomenon of two moons in the sky, when Mars appears as large as the moon! This August 27 ... don't miss it!" So the paraphrased claim goes. And goes around every August. I don't seem to recall seeing Mars as big as the Moon in the sky, so in this episode I explore the origins of the claim and why it can never be true.
Puzzler for Episode 118: There was no Puzzler in this episode.
Q&A: There was no Q&A in this episode.
- Logical Fallacies / Critical Thinking Terms addressed in this episode: Basic math
- Relevant Posts on my "Exposing PseudoAstronomy" Blog
Claim: This claim makes the rounds almost every August. It used to be a chain rumor passed through e-mail and on various IRC chats, newsgroups, and dubious websites, and more recently it has taken to Facebook. One of the more recent versions from August of 2014, reads, "SEE MARS AS LARGE AS THE FULL MOON ON 27TH AUGUST 2014. Should be spectacular! Truly a once in a lifetime experience!"
The versions of this claim collected by Snopes seem to be getting shorter as the claim ages. Back in 2007, the claim was longer:
*Two moons on 27 August*
27th Aug the Whole World is waiting for...*
Planet Mars will be the brightest in the night sky starting August.
It will look as large as the full moon to the naked eye. This will cultivate on Aug. 27 when Mars comes within 34.65M miles of earth. Be sure to watch the sky on Aug. 27 12:30 am. It will look like the earth has 2 moons. The next time Mars may come this close is in 2287.
Share this with your friends as NO ONE ALIVE TODAY will ever see it again.
Chances are, most of you listening to my docile tones or reading the transcript have seen or heard this claim. Maybe a friend sent it to you. Maybe a relative. In 2009, my Great Aunt Ester sent it to me in an e-mail blast that included other family members and friends of hers. I had to let her down easy because, as I'll explain over the next 10-20 minutes or so, this has been a hoax since 2003.
To understand what's going on and the origins of this claim, we need two pieces of background information. The first is planetary orbits. In the spirit of my return to podcasting and a return to some of my roots, this part relies on one of the main sponsors of this podcast, Johannes Kepler. Kepler, in the early 1600s, using data very carefully gathered by Tycho Brahe, derived his Three Laws of Planetary Motion.
Kepler's First Law, or "K1" as we often abbr. it in introductory astronomy, simply states that the orbit of a planet is an ellipse with the sun at one of the two foci. Revolutionary for its time, it's generally taken for granted that "everyone" knows this today. Except for the geocentrists.
What this simply means is that the sun is near the center of a planet's orbit, and a planet's orbit can be any form of ellipse. If the closest distance the planet gets to the sun is the same as its farthest distance, then the planet is on a special form of elliptical orbit: a circle. All circles are ellipses, not all ellipses are circles.
The closest a planet gets to the sun is called "perihelion" where you can think of "peri" for proximity, and "helion" means Sun. The farthest a planet gets from the sun is aphelion. You can remember this by thinking of the "a" as "away" and again "helion" meaning Sun. I'm going to use these terms a lot more in a few minutes.
Kepler's Second Law, or "K2," states that a planet sweeps out an equal area in equal time along its orbit. This equal area refers to a triangle with one point where the planet starts, one point on the sun, and one point where the planet ends in its orbit after a period of time. If the planet is closer to the sun, then it has to move faster to sweep out an equal area than when it's farther away from the sun. That's why comets spend most of their time way far away from the sun.
Kepler's Third Law, or "K3," states that the square of the planet's year is proportional to the cube of the semi-major axis of its orbit, where the major axis is the long axis of the ellipse. Put more simply for our purposes with this episode, a planet has a longer year - it takes more time to go around the sun - the farther from the sun it is. This is not only because it has a bigger distance to travel in its orbit, but it moves more slowly.
To recap, we have three laws: Planets travel in ellipses which could include a circle, planets move faster the closer to the sun they are in their orbit, and planets have a longer year the farther they are from the sun.
Putting these together, consider Earth and Mars. Mars is farther away from the sun than Earth, so it moves more slowly in its orbit and it takes longer to go around the sun, making one year in about 1.9 Earth years.
If Mars and Earth were on perfectly circular orbits, then the closest and farthest distance they get from each other would not vary from year-to-year. The closest would be when they are aligned such as Sun-Earth-Mars - so they're on the same side of the sun - and the farthest would be when one is on the opposite side of the sun, such that looking down on the solar system you could draw a line from Earth through the Sun to Mars. This is somewhat basic stuff, but I want to slowly build this case, and some people have trouble understanding that even if Earth and Mars were on perfect circles about the sun, the distance between them would still change significantly.
With that in mind, we can introduce the fact that they are NOT on perfect circles around the sun. And, the long axes of their elliptical orbits are not pointing in the same direction, and they move over time because of the influence of other planets' gravity, especially Jupiter's gravity on Mars. And Jupiter's gravity will change the ellipticity of Mars' orbit over periods of 10s of thousands of years, but we'll ignore that for this discussion.
What does this mean for their closeness? It still means that the CLOSEST they could possibly ever get is when it JUST SO HAPPENS that Earth's aphelion corresponds with when Mars is at perihelion, AND that you can draw a straight line from the sun out through Earth all the way to Mars. So Mars would appear opposite the sun in Earth's sky, so you'd see Mars best at midnight. Conveniently, this is called Mars being at opposition.
But, as you might expect from how I've been building this up, this phenomenon very rarely happens. You have to get the elliptical orbits - which precess - to be properly aligned. You have to have Earth at its farthest point happen at the same time Mars is at its closest point. And Mars is going to move more quickly at that point, giving you a smaller window of time.
With that in mind, let's tuck that information away and get to the next piece of background information ...
Background: Apparent Size and the Small Angle Approximation
... the apparent sizes of objects in the sky. In every day life, assuming you have two well functioning eyes, you have a general sense of how big common things are, even if they are not the same distance away from you. For example, I live in the mountains of Colorado, and when I go outside and see my car, it looks bigger than my neighbor's house a mile away. But I know that my car isn't REALLY bigger, it just looks that way because it's closer. It has a larger apparent size.
We measure apparent size in angles. The car fills more of my field of view - a larger angle - than the house. It's only by knowing or approximating the distance to the car and the house that I can convert that angular size to real, physical size. My brain does that for me because of parallax between my two eyes and because of prior experience. It can practically instantly realize that the distance to the car is much less than the distance to the house, and also use prior experience that cars are rarely larger than houses, to inform me that the car is closer and not as big as the distant house.
This is not the case for objects in the sky, and this was the entire subject of Episode 2 of the podcast. For purposes of this episode, what's important is how big objects appear in the sky given their distance.
Normally, you have to use trigonometry to figure out how big an object is, or how distant it is, or how big it will appear given any two of those pieces of information. For example, if I tell you how far away the moon is and its diameter, then you can use trigonometry to figure out how big it will appear in the sky.
We can simplify that using something called the Small Angle approximation. This means that for small angles - like how big astronomical objects appear in the sky - you can actually drop the trigonometry part of the problem. So the size the object appears is linearly related to how big it is and how far away it is.
I've probably lost a lot of you just now, so let me explain by way of example. I have an apple. I tell you it is 10 m away and 10 cm in diameter. You do some math and come up with an angular size - how big it will appear. The actual number isn't important because I want you to compare it to a watermelon. I hold the watermelon 50 m away and tell you it's 50 cm in diameter. How big is the watermelon going to APPEAR to you RELATIVE TO the apple?
If you want an exact solution, you'd need to do trigonometry. But because of the small angle approximation, you can use simple ratios: The watermelon is 5x farther away, but it's 5x bigger, so the 5 cancels out the 5 and it will appear the same size. Yes, that's why I just went through the last two minutes droning about math, to explain how simple this ends up getting.
Another example: I have a building that's 100 m high and 1 km away. Another building is 300 m high and 0.5 km away. So you have a ratio of 1/3 for size and 1/2 for distance, multiply them together and the second building will appear 6x larger to you.
Can Mars Appear as Large as the Moon?
This brings us back to whether Mars can ever appear as large as the Moon in the sky. To quote Phil Plait, "No. Just, no."
Let's assume perfect conditions: Earth is at aphelion when Mars is at perihelion and this happens when Earth is directly between Mars and the Sun. Ideal conditions, and this is going to be the biggest Mars can ever appear, at least given its current orbital parameters.
Distance to Mars in this case is 54.6 million km (33.9 million miles). Mars is 6792 km (4220 miles) in diameter.
Meanwhile, the average distance between the Moon and Earth is about 384 thousand km (239 thousand miles). The Moon's diameter is 3474 km (2159 miles).
Simplifying the numbers a bit, Mars' closest approach takes it about 140x farther away from Earth than the Moon. The Moon is about 1/2 the diameter of Mars. Multiplying these together, the LARGEST that Mars could ever appear in Earth's sky is about 1/70th the diameter of the Moon. You just take the 140x farther away and divide by 2 - the ratio of the diameters - to get that 1/70th number.
That's it. That's using basic math, the basic sizes of these objects, and basic principles of orbit figured out over the last 400 years. For Mars to appear as large as the Moon in Earth's sky, it would need to be either 70x larger than it currently is - and note that Jupiter is about 20x the diameter of Mars, so Mars would need to be 3.5x larger across than Jupiter - or Mars would somehow need to come as close to Earth as just twice the Earth-Moon distance.
Origins of the Claim
And so, how did this claim even get started? Well, it did have a legitimate past. Back in August of 2003, Earth and Mars were VERY close to those ideal circumstances where Earth was at its aphelion, Mars at its perihelion, and this happened when Mars was at opposition. Almost. Very close.
The distance between them on August 27/28, 2003, was "only" 55.8 million km (34.6 million miles), just 1.2 million km (0.7 million miles) shy of the closest they can ever get. This was the closest they had gotten in 59,619 years, and it was widely touted in the media. I used to work at a grocery store in high school, and I actually remember going back while on summer break during college that year and explaining to some of my former co-workers who were friends, late at night when there weren't any customers other than myself, what was going on and why this was a big deal. I used rubber bands to explain the orbits, because they were asking me about it.
That completely superfluous anecdote aside, the point is that this was very widely spread, and most people knew about it, people who had no real prior interest in astronomy.
Never mind that two years earlier, they had been separated by only 7.2 million km more when at their closest. And on July 31, 2018, they'll be 57.7 million km (35.8 million miles) apart, so just 1.9 million km (1.2 million miles) farther apart than they were in 2003. And again on September 11, 2035, it'll be 1.3 million km (0.8 million miles) farther apart than in 2003. But I digress, and these dates will be linked in the shownotes.
The point is that the ORIGINAL e-mail going around at the time was even longer than its 2007 variant:
The Red Planet is about to be spectacular! This month and next, Earth is catching up with Mars in an encounter that will culminate in the closest approach between the two planets in recorded history. The next time Mars may come this close is in 2287. Due to the way Jupiter's gravity tugs on Mars and perturbs its orbit, astronomers can only be certain that Mars has not come this close to Earth in the Last 5,000 years, but it may be as long as 60,000 years before it happens again.
The encounter will culminate on August 27th when Mars comes to within 34,649,589 miles of Earth and will be (next to the moon) the brightest object in the night sky. It will attain a magnitude of -2.9 and will appear 25.11 arc seconds wide. At a modest 75-power magnification Mars will look as large as the full moon to the naked eye. Mars will be easy to spot. At the beginning of August it will rise in the east at 10 p.m. and reach its azimuth at about 3 a.m.
By the end of August when the two planets are closest, Mars will rise at nightfall and reach its highest point in the sky at 12:30 a.m. That's pretty convenient to see something that no human being has seen in recorded history. So, mark your calendar at the beginning of August to see Mars grow progressively brighter and brighter throughout the month. Share this with your children and grandchildren. NO ONE ALIVE TODAY WILL EVER SEE THIS AGAIN
Some of this message is true. Some of it is false. Some of it is true but highly misleading.
The most false part is the whole thing about astronomers not knowing if or when this will happen again or have happened before due to Jupiter's gravitational perturbations on Mars' orbit. It's true that over the very long term, as in 10s to hundreds of millions of years, our computer models become chaotic and we can't predict things at that fine a resolution. But 10s of thousands? No problem.
The misleading part, and the part that was almost immediately dropped from this e-mail or that people ignored, is the line, "At a modest 75-power magnification Mars will look as large as the full moon to the naked eye."
Remember the math we did earlier, or "maths" if you're British? Mars at 140x farther away but 2x the diameter of the Moon will be 1/70th the size. So, if you're using a telescope that magnifies things by about 70, and you look at Mars, Mars will appear to be the same size to your eye as the Moon would appear without the telescope. But, this is a nonsensical comparison, unless you have one eye peering through the telescope at Mars and the other eye aimed in a different direction looking to the Moon.
And perhaps because of that very confusing sentence, which even for me - and I know what it means - is difficult to understand, the whole "Big Mars" hoax was born.
And, ever since then, every late July to August, the Big Mars hoax gets sent around the internet.
By this point, more than 11 years later, it's as predictable - if not more-so - than a meteor shower and met with an eye-roll by skeptics and astronomers. I think people tend to be well-meaning by sending it along, and I know for certain that my Great Aunt was embarrassed but thankful that I had corrected her, and it gave her a chance to show off her great-nephew's smarts to her friends.
I certainly don't attribute malice or willful deceit on the part of people who spread this these days, unlike many of the topics I discuss on this podcast. But by this point, most people do know it's a hoax, or at best a gross misunderstanding of what's going on. Phil Plait's covered it. NASA's covered it, Wikipedia's covered it, Space.com's covered it, Universe Today's covered it, IFL Science's covered it, The Reality Check has covered it, and now I've covered it.
I hope the real explanation is reaching critical mass.
But, I worry: In just 4 short years, Mars and Earth will be very close together again, and while you might call me a pessimist, I have a hunch that we might see a surge in these chain e-mails come the lead-up to July 31, 2018.
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