Exposing PseudoAstronomy

February 4, 2015

New Horizon’s First Images of Pluto from Its Approach Phase – What’s Going On?


New Horizons is a spacecraft headed to Pluto. It launched nearly a decade ago, but it will arrive in July of this year and do a fly through the system. Doing lots of amazing science.

One of the instruments is LORRI, a long-focal-length camera that will be the prime imager for much of the mission because it will be able to take the highest spatial resolution images. It will also be used (was being used and is being used, too) for optical navigation — make sure we’re headed in the right direction.

Just a few minutes ago, on the anniversary of Clyde Tombaugh’s birth (the guy who discovered Pluto), NASA released the first image from LORRI of Pluto and its main satellite, Charon, taken during the Approach Phase. There’s a lot going on here – one point in particular that I just know is prone to misunderstanding later on – so I want to talk a bit about this image.


I am involved with the New Horizons mission. I am not a NASA employee. This is my personal blog and everything on it is my opinion, are my words, and is done completely independently (time-wise, resource-wise, person-wise) from my work on New Horizons. In fact, it is on record that this blog is legally distinct from my professional work. Nothing I say here should be taken as an official statement by NASA or the New Horizons team.

Resolution / Pixel Scale

That out of the way, let’s get to the meat of this post. Also, I’m going to use “resolution” and “pixel scale” a bit loosely here, so pedants need to forgive me right away.

LORRI is an amazing camera. It is a 1024×1024 pixel detector, and each pixel has an effective angular size of 4.95 µrad (micro radians, or about 1.02 arcsec). 1 arcsec is about the width of a human hair from 10 meters (33ft) away. (source)

At the moment, New Horizons is around 200,000,000 km away from Pluto. That’s okay, it still has 5.5 months to get there. Pluto is approximately 1180 km in radius. That means, from some simple trigonometry (remember SOHCAHTOA?), Pluto is about 1.2 arcsec in radius, or 2.4 arcsec in diameter. Charon is very roughly half Pluto’s diameter, so it’s around 1.2 arcsec in diameter. Charon and Pluto orbit on opposite sides of their center of mass, which means they are around 8.6 Plutos away from each other, or around 9.1 arcsec separated.

Okay, lots of numbers there. Basically, that means that right now, if we had perfect optics, Pluto is about 2 pixels across, Charon 1, and they’d be around 8 pixels away from each other, max (since their orientation on the plane of the sky is not perpendicular to the spacecraft right now).

(No) Perfect Optics

No such thing exists. Given the best, most perfect optics ever, you can never get infinitely fine details. This is because light will behave as a wave, and give rise to Airy disks and patterns meaning that the light will spread out as it travels through the optics. Unless you had an infinitely wide optical system.

When you factor everything together about the optics and system and detector and other things, from a point source of light, you get a point-spread function (PSF). This is the practical, measured spreading out of the light. In astronomy, we often measure the PSF based on fitting a Gaussian distribution to a star, since a star should be a point source and just cover one, single pixel.

With a telescope aperture of 208mm for LORRI, and a passband of light centered around 0.6 µm (red light), the Airy disk should be around 1.22*0.0006/208 = 6.8 µrad. That’s around 1.4 LORRI pixels. Amazing coincidence!

Actually, not. When designing an instrument, you typically want to just about over-sample the Airy disk. You don’t want to under-sample because then you’re losing valuable resolution and information. You don’t want to over-sample because then you’re just wasting money on a detector that is too “good” for your optics, and other issues that come about when you have small pixels. So, designing a system that’s around 1-3 pixels per Airy disk is good.

When you go to a practical PSF, it’s going to be a bit bigger just because no system is perfect.

What’s the Point?

Oh yeah, back to Pluto.

First New Horizons Image of Pluto and Charon from Approach Phase

First New Horizons Image of Pluto and Charon from Approach Phase (©NASA/APL/SwRI)

Let’s put these parts together: Right now, Pluto should be around 2 pixels across, Charon 1, and a separation of around 7-8 pixels. But, add in the PSFs due to the laws of optics. That means that the light should now be spread out a bit more.

And that is why this image looks like it does. It’s also been enlarged by 4x, such that each original LORRI pixel has now been resampled. So, if you look at the image NASA released, and you blow it up a lot, Pluto looks like it’s around ten pixels across, and Charon around five.

To repeat: The released image shows Pluto to be around 10 pixels wide, and Charon around 5. Despite the theoretical values now (2 pixels and 1 pixel, respectively). That’s because (1) the PSF spreads the light out because we live in a world with real and not ideal optics, and (2) the released image was enlarged by a factor of 4.

Moving Forward

New Horizons is zipping quickly along. In May, it will surpass all previous images taken and we will truly be in new territory and a new era of discovery (so far as imaging the Pluto system — note that the other instruments have already taken a lot of data and are learning new things). That best image that exists so far of Pluto shows Pluto to be approximately 8 pixels across.

And that’s why I started this post out by stating, “one point in particular that I just know is prone to misunderstanding later on.” So, today, NASA released an image that shows Pluto with as many pixels across as what it will take in late May, when it will have that number of pixels across.

See why I wanted to bring this up now? I can just hear the pseudoscientists claiming that NASA is lying about the power of the New Horizons telescopes, they’re deliberately down-sizing images (later, based on images released now), and various other things. While they’ll still almost certainly say that, at least you know now why that’s not the case, and what’s really going on now versus then.

There are only 2 (well, about 4, since it’s 2×2) “real” pixels in the Pluto disk right now, the others are interpolated based on expanding the size to make the image look nice for this release, celebrating the image and Clyde Tombaugh’s birthday. In four months, we’ll have all these pixels, but they won’t be based on a computer algorithm, they’ll be “real” pixels across Pluto taken by LORRI. Convolved (“smeared”) with a PSF that’s about 1.5-2 pixels.

June 28, 2011

The Magical Hyperbolic Tetrahedral Geometry of 19.5° Latitude


Hyperbolic Tetrahedral Geometry

"Hyperbolic Tetrahedral Geometry"

Take a tetrahedron (4-sided solid made of four equilateral triangles) and put it in a sphere such that each point of the pyramid touches the inside surface of the sphere. Draw a straight line through the center of the sphere such that one end of the line intersects a point of the pyramid; think of this line as the polar axis, and now orient it in your mind so that the line that goes through the pyramid point is down. Now draw a line around the circle’s equator. Now, if you take the angle between the equator, the center of the sphere, and one of the three non-pole points of the pyramid, you get 19.5°.

That’s the magic of Richard C. Hoagland’s hyperbolic geometry and all the claims of importance for the 19.5° latitude that I’m going to explore in this post.

Richard C. Hoagland’s Magical Thinking

Richard C. Hoagland says a lot of stuff. Almost everything he says sounds crazy. Over the decades, he has built up a vast conspiracy-laden mythology about the universe, how it supposedly works, and why things are the way they are.

To go into every single one of his claims, as I’ve said before in other posts about Hoagland (like here, here, or here), would be next to impossible. As in previous posts, the point in this is to go over a very specific claim.

The “19.5° is an important number” stems from his whole “hyperdimensional physics” mythos. Again, something I’m not going to go into. Partly because it’s incomprehensible, nonsensical, and made up. Suffice to say, “A tenet of these views holds that vast amounts of energy originating from dimensions we cannot perceive are available at latitudes 19.5° both south and north on the Sun and every planet in the solar system” (quote source).

In other words, Hoagland and fellow believers claim that it is at 19.5° latitude on every body in the solar system that we have the biggest/bestest/scarriest/craziest/powerfulest/whateverest feature. Let’s take a look, shall we?

What’s at 19.5° Latitude?

Taken from Hoagland’s own website, we have a short list proving that everything of importance in the solar system is at 19.5° latitude.  Note that everything in this table is directly copied from his website except for the comments, which I have simplified/shortened/clarified.

Object Feature Latitude Importance
Venus Alta Regio 19.5° N A Volcanic Region
Beta Regio 25.0° S A Volcanic Region
Earth Hawaiian Caldera 19.6° N Largest Shield Volcano (on Earth)
Moon Tsiolkovskii 19.6° S Unique Farside “mare-like” Lava
Mars Olympus Mons 19.3° N Largest Shield Volcano (on Mars)
Jupiter Great Red Spot 22.0° S Vast Atmospheric “Vorticular Upwelling”
Saturn North/South Equatorial Belts ±20.0° N/S Region of “Storms” Observed from Earth
Uranus Northern/Southern IR 1-2 K “Dip” ±20.0° N/S “Upwelling” Created by High-Altitude Clouds
Neptune Great Dark Spot 20.0° S Presumably Same as Jovian Counterpart*

*Hoagland calls this “Neptune Great Red Spot” but it has, since it was observed by Voyager 2 in 1989, disappeared.

Since Hoagland posted this (his page is ©1989), many other people have found other things on other planets that they claim enhances this idea. One such site, for example, indicates that the Pyramid of the Sun is at 19.6° N (on Earth). Other people claim, such as Will Hart, that all solar storms and susnspots originate from 19.5° latitude on the sun; another twist from this site about the sun is “sunspot activity and the region of peak temperatures is limited to 19.5 degreees north and south.” Others remark simply, “It is interesting how most planets in our solar system display phenomena at this latitude.” The list of claims goes on.

Dissecting the List, and Are These Features Important?

One of the first things you should notice from Hoagland’s list is that only one of the 9 things I pulled (the ones I didn’t are on Jupiter’s moon Io) is at 19.5°. Two more are within 0.1° of it. For a precise geometric phenomenon where huge amounts of energy are released, this isn’t very precise.

On Earth, Mauna Loa, Hawai’i, with a summit at 19.48° is a correct claim of the largest shield volcano presently on the planet. However, it’s really not that spectacular a volcano in terms of energetic potential. The Yellowstone caldera is about 34×45 miles (55×72 km) across. That’s just the caldera. It is at a latitude 44.4° N. The most recent known supervolcano eruption on Earth was in Lake Taupo, about 26,500 years ago, and its latitude is 38.82° S.

Additionally, the largest earthquakes – more releases of energy – since 1900 haven’t been anywhere near 19.5°. None of them.

As for structures on the Earth to harness this energy, one might consider the Pyramid of the Sun and say, “wow, that’s pretty neat that it’s at 19.5°.” But what about Egypt’s pyramids? Or South America’s? What about other architecture, say, Stonehenge? None of these are near 19.5°. This is what we call “cherry picking” to an extreme.

If we want to expand the notion of cherry picking, let’s go to the moon. Hoagland has found some random feature at 19.5° … err, 19.6° … latitude on the far side that has something to do with a volcanic feature. Except that the moon is covered in volcanic features. When you look at the moon, all those dark splotches on the near side are vast volcanic areas where ancient impacts allowed magma from deep below the crust to breach the surface and fill them. And these seas of volcanic material — maria (plural) — are not in any way centered around 19.5°. Nor are the smaller volcanic features that we observe today still strewn throughout them.

Or there’s Mars. Hoagland and his ilk claim that the vast Olympus Mons volcano – the tallest volcano in the solar system – is centered at 19.3° on Mars and is perfect evidence for this hyperbolic geometry. Except that it’s not. The caldera complex of Olympus Mons (there are at least 6 distinct calderas at the summit) range between latitudes 17.8° and 18.8° North. In addition to that, Olympus Mons is so vast with a diameter of around 650 km that the northern scarps start at around 23.5° N while the southern margin is around 13.5° N latitude. So with it spanning over 10°, it’s not that hard to hit it. Besides, Mars has 23 other major volcanoes, and Alba Patera, which is actually the most voluminous volcano in the solar system (as Mauna Loa is the most voluminous volcano on Earth), has a caldera centered at 40.3° N.

The claim of the sun having sunspots centered at 19.5° is also wrong, as can be seen on any given day.

We can also look at other features of interest. I’ll name only one for brevity since I think I’ve made my point by now. Saturn’s moon Enceladus was, in the last few years, shown to have active geysers spewing material from the interior of the moon. What’s their latitude? About 90° S — that’s right, the south pole. Not anywhere near 19.5° North nor South latitude.

Final Thoughts

This particular magical belief is only supported by very very careful cherry-picking. As clearly shown above, even in the features that these people claim shows 19.5° is special, more than half the time they’re just wrong, off the mark, or are being very generous with reporting their numbers. And still the features that are “correct” are not especially unique.

I don’t really think much else needs to be said on this topic. It’s just made up and features are found to fit it while ignoring everything else.

April 11, 2010

What Happens When All the Planets Line Up Against Us?


This is a claim that has persisted for a long time, and though people who believe in the 2012 stuff have propagated it, it is not specifically a Planet X / 2012 claim: If all the planets (plus our moon) lined up opposite the sun, they would pull us out of orbit. As the “lolcatz” say, “Oh noez!”


The force felt by an object due to gravity is a very simple mathematical function, codified by Newton’s Universal Law of Gravity:

In this equation, F is the force felt, G is the Gravitational Constant, M m are masses of the two objects in question, and r is the distance that separates them.

To figure out how much more or less two different objects will pull on the same object, we can simply remove one of the two masses, so the equation simplifies to F = G * m / r2.

The Math

To determine the relative forces, one simply needs to know the mass of the planets and sun, and the distances between Earth and those objects. This can be found in any basic astronomy textbook or online source. One then can simply plug in the numbers and figure out the forces.

For the sake of argument, let’s say the sun is on one side of this tug-of-war, and the moon, Mars, Ceres, Jupiter, Saturn, Uranus, Neptune, and even Pluto are all on the other (Venus and the sun don’t count ’cause they would have to be on the sun’s side). Let’s calculate the force first due to the sun:

Mass (1024 kg)
Distance from Sun (106 km)
Distance from Earth (106 km)
Relative Force
Sun 1,989,100 149.6 0.0059

Alright, now let’s do all the rest, remembering that for the planets, we’ll need to subtract out the distance between Earth and the sun from what are commonly quoted as the planets’ distances:

Mass (1024 kg)
Distance from Sun (106 km)
Distance from Earth (106 km)
Relative Force
Moon 0.07349 0.3844 3.32·10-5
Mars 0.6419 227.9 78.32 6.98·10-9
Jupiter 1,899 778.6 629.0 3.20·10-7
Saturn 568.5 1434 1284 2.30·10-8
Uranus 86.83 2872 2723 7.82·10-10
Neptune 102.4 4495 4345 3.62·10-10
Pluto 0.00125 5906 5756 2.52·10-14
Ceres 0.00095 415 265.4 9.00·10-13

Final Thoughts

This is a really short post because it doesn’t need to be long. To be perfectly honest, I was actually surprised at how small the force of Jupiter actually is on Earth relative to the sun. If we add up the force from all of the other objects, we only get a force that is 0.566% as strong as the sun’s. And then if we take the moon out of the equation because that would be the first to move out of the alignment, then we have a force of only 0.000592% as strong as the sun’s.

If we look at Venus if it were also lined up, helping the sun, its force is 1.90·10-7, or about half as much as all the other planets (again, leaving out the moon), so it would cancel 54% of the effect of all those other objects (again leaving out the moon). The force from Mercury is only about 1/3 that of Mars.

So really, if anyone who makes this claim were to bother to spend about 10 minutes looking up the numbers and plugging them into an Excel equation (what I did), they would quickly see that this claim is simply and utterly nonsense. And this is besides the fact that the planets aren’t lining up any time soon on the other side of Earth to try to pull us out of orbit.

January 25, 2009

Planet X and 2012: The Real and Historical Story of Planet X


This is the first post in what will become a series of posts over the next few days/weeks about the oft-portrayed mysterious, dangerous, possibly alien-harboring, Earth-destroying object touted as “Planet X.”

This being a blog about pseudo-astronomy, you should not be surprised to learn by reading it that there is no dangerous Planet X out there that’s going to cause a pole shift as Earth goes through the “dark rift” of our galaxy in 2012. However, in this first post, I’m going to describe what the real Planet X was in astronomy, a mystery that was created with the discovery of the planet Uranus in 1781, and didn’t end until we precisely calculated the mass of Neptune in 1993.

All posts in this series:

Finding Uranus

Until 1781, the solar system was known to consist of Earth, Venus, Mercury, Sun, Mars, Jupiter, and Saturn, along with the moon, some other moons, and some unexplainable and unpredictable comets. That was it, and it wasn’t until William Herschel observed a ball-like object (not star-like) moving among the fixed background stars.

It took two years for Herschel to admit that he had really discovered the first planet in recorded history. But since it was discovered after Newton created Calculus and Kepler the Laws of Planetary Motion, various astronomers and mathematicians were able to observe it and predict its orbit based on its distance from the sun and the gravitational interactions with other planets.

The First Planet X

One of these people was Alexis Bouvard, who published tables of dates and coordinates that predicted where Uranus should be at a given time. These were based on the known laws of physics. But, Uranus refused to follow Bouvard’s tables.

In 1843, John Couch Adams (from Britain) calculated the orbit of a hypothesized eighth planet that could account for Uranus’ odd orbit. But no one really seemed to care about this undiscovered Planet X.

Two years later, a Frenchman by the name of Urbain Le Verrier did the same thing, but more precisely. Again, no one seemed to care. That was until Le Verrier sent his calculations to the Berlin Observatory’s astronomer Johann Gottfried Galle. A then-student at the observatory, Heinrich d’Arrest, convinced Galle to look for it.

That evening, September 23, 1846, Galle looked for this mysterious planet, responsible for Uranus’ weird orbit, and he found the planet within 1° of where Le Verrier thought it would be (for reference, the moon on the sky is 0.5°). This was within 12° of where Adams thought it should be.

At the time, there was no real debate that this object was a “planet,” as they had been looking for it and thought it was massive enough to account for Uranus’ orbit.

The Second Planet X

However, there were still some unexplained perturbations of Uranus’ orbit. These persisted for 70 years, to the time that Percival Lowell became interested in the problem and wanted to search for a now possible ninth planet at his observatory in New Mexico. I think that he was the one who really first coined the term, “Planet X.” Lowell searched for 12 years, 1905-1916, until he died, without finding it.

The search resumed in 1929 when the then-director of the observatory assigned the task to a young, 23-year-old Clyde Tombaugh. After a year of fruitless searching, Toubaugh found an object moving against the background of stars from two photographs he had taken in January of 1930. Pluto was discovered, Planet X, that was supposed to solve all the orbital problems.

A Third Planet X? — Nope, Just Fixing Neptune’s Mass

When Pluto was initially discovered, it was assumed to weigh in at several times Earth’s mass. However, estimates over subsequent decades were refined down, not up, and it was realized that Pluto could not account for Uranus’ orbit. The present-day mass estimate is about 20% Earth’s.

The search half-heartedly didn’t really continue for a mystery object that could explain planets’ orbits.

In 1989, the space probe Voyager 2 flew by Neptune. Calculations based on the orbital changes from that gravitational interaction were published in 1993 by Myles Standish, and they revised Neptune’s mass downward by 0.5%. This revised mass, when put into the calculations for the orbits of the outer planets, was then able to precisely account for Uranus’ orbit. No mystery object was needed, nor found, and as a result, nearly all astronomers today discount its existence.

Modern-Day “Planet Xs” (The Real Ones)

To be sure, I do not mean to imply that there are no more large objects out in the solar system. But “large” is always a relative term that needs to be qualified. The proton is gigantic relative to an electron. A sequoia tree is large relative to an oak. And Neptune is large relative to Pluto.

What I mean by “large” in this context is 100s to possibly 1000s of kilometers in diameter, icy bodies much like Pluto. These are the Kuiper Belt Objects, or at least the large members of the Kuiper Belt Objects. To-date, (January 2009), 4 are large enough such that the International Astronomical Union has termed them “Dwarf Planets” (Pluto, Eris, Makemake, Haumeamea). These objects are “large,” but they are smaller than our moon (our moon is 3,474 km in diameter). And, since density is related to volume which is the cube of a linear measurement, the actual mass of these objects is much smaller than that of a planet.

But, But, But … There Could Still Be Giant Things Out There!

Maybe. But they would have to be very far away from the 8 planets and inner Kuiper Belt Objects. Remember, even with the technology over 160 years ago, astronomers were able to calculate that Uranus, an object 19x farther away from the sun than Earth was being very slightly perturbed by an object 30x farther away from the sun than Earth. And these were both objects that weigh about a dozen times more than Earth – fairly small compared with what modern-day Planet Xers are claiming (that will be addressed in future posts).

Nothing in science is locked in stone, so-to-speak, and it’s impossible to prove a negative. However, keep in mind now that we can explain all the orbits of the planets with known, observed solar system objects. For there to be another object out there, it either has to be very small, or it has to be very far away. And when things are very far away, they take a very long time to move. Even a comet out by Jupiter heading towards us would take at least a year to get to Earth. And we could see it. The idea that there is a massive, planet-sized object that will hit or pass by Earth in just 4 years is ridiculous, unless you invoke the supernatural or physics that we don’t know about that can somehow shield even gravity.

Final Thoughts

Now that you have a historic basis for the present-day Planet X claims, as well as some preliminary information on why we “know” (as far as science can know anything) that there is no doomsday planet headed for us in 4 years, I will actually address the various fear-mongering premises that have been posited about Planet X, and how it is supposed to destroy Earth (or not?!), land ETs on Earth that want all our gold, or will cause a pole shift (another ridiculous idea that has its own problems), or whatever else people have invented throughout the past few decades.

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