Planetary Orbits and Terms, 101

Introduction

I’ve been made aware lately that some people who profess certain types of pseudoscientific beliefs, such as Mars’ orbit being ridiculously eccentric (highly elliptical), do not understand basic orbital terminology and geometry.

With that in mind, I thought this would be a good post not only because of that, but also towards a general explanation of terms for people who hear them from time-to-time who may not have known what they meant. I should also probably mention (normally goes without saying) that these are basic terms and definitions and are not unique to me and are not unique to any given field.

Terms! (Vocab Words!!)

Some geometry terms, parts of an ellipse:

• Major Axis: The longest axis of an ellipse (goes through the center).
• Minor Axis: The shortest axis of an ellipse (goes through the center).
• Foci/Focus(es): All ellipses have two foci, or two “focuses.” The foci have the property (or ellipses have the property) such that if you add the distance between the point and each focus, every point along the ellipse will have the same distance. This leads to the “pins and string” method of drawing an ellipse. In a circle – a special form of an ellipse, the two foci are in the same location, the center.
• Center: The point exactly between the two foci. And the intersection of both the major and minor axes.
• Eccentricity of Ellipse: Always between 0 (a perfect circle) and 1 (a line). It is defined as the SQRT(1-(minor/major)^2).

Some astronomy terms, parts of an ellipse:

• Semi-Major Axis: Half the longest axis of an ellipse (starts from the center or edge, goes to the edge or center).
• Semi-Minor Axis: Half the shortest axis of an ellipse (starts from the center or edge, goes to the edge or center).
• (Primary) Focus: In the solar system, the sun is at one focus of the ellipse for all planetary orbits, and there is nothing physical in the second focus. For moons orbiting planets, the “primary” focus is the planet, there is nothing physical at the other focus.
• Eccentricity of Orbit: Eccentricity of an orbit is typically defined as: (apoapsis – periapsis) / (apoapsis + periapsis).
• Ellipticity: Rarely used, sometimes confused with eccentricity. Ellipticity is just major/minor axis and is always a value greater than 1 (1 = circle). A value of 2 would mean the major axis is twice as long as the major axis, though in this case the eccentricity would be 0.87.

Some astronomy terms, other parts of an orbit:

• Peri-: Prefix meaning “closest.” If you’re a planet on an orbit around the sun, your perihelion is the closest approach to the sun. If you’re around Earth, it’s perigee, moon is perilune, Jupiter is perijov, and I’m sure there are others. Generic term for any body is “periapsis.” Periapsis can be calculated as the semi-major axis multiplied by (1-eccentricity).
• Apo-/Ap-: Prefix meaning “farthest.” If you’re a planet on an orbit around the sun, your aphelion is the farthest approach from the sun. If you’re around Earth, it’s apogee, moon is apolune, Jupiter is apojov, and I’m sure there are others. Generic term for any body is “apoapsis.” Apoapsis can be calculated as the semi-major axis multiplied by (1+eccentricity).

Some perspective terms. These are visual things, as viewed from one object relative to another. Formally as parts of an orbit, for orbital mechanics, they are irrelevant.

• Conjunction: When one object appears at the same location in space as another object, as seen from a third object. For example, when viewed from Mars, if the moon Phobos appears in front of the sun (so you get an eclipse), then this is a conjunction.
• Inferior Conjunction: When the conjunction happens such that the object conjuncting is physically “in front of” the other object as seen from the third. In the previous example, a moon creating a solar eclipse (blocking part of the sun) is always in an inferior conjunction with the sun.
• Superior Conjunction: When the conjunction happens such that the object conjuncting is physically “behind” the other object as seen from the third. In the previous example, when the moon creates a solar eclipse (blocks part of the sun), the sun is in superior conjunction. As another example, when Mars appears to go behind the sun as seen from Earth, and so we can’t get any data back from spacecraft, Mars is in superior conjunction.
• Opposition: When one object appears in the opposite location in space as another object, as seen from a third object. For example, when viewed from Earth, a full moon is in opposition to the sun, because as the sun sets, the full moon rises, so they are directly opposite each other in the sky.

As a matter of orbital mechanics, an inferior planet (one inside Earth’s orbit) can never be in opposition with the sun. And, as a matter of orbital mechanics, a superior planet (one outside Earth’s orbit) can never be at an inferior conjunction with the sun (appear between Earth and the Sun).

Applying These Terms

Let’s look at Earth’s orbit. Earth’s perihelion is 147 million km, the aphelion is 152 million km. The eccentricity is therefore 0.017 ((152-147)/(152+147) = 0.017). The major axis is aphelion+perihelion = 299 million km. The semi-major axis (what’s often quoted as Earth’s “average distance” from the Sun) is 299/2 ≈150 million km.

Notice that these have nothing to do with conjunction or opposition — by definition, and in practicality, they cannot, because opposition and conjunction requires three objects, not two. Earth and the sun could be in conjunction or opposition from a given third object / vantage point at any time regardless of where Earth is in its orbit.

Applying These Terms to Mars

We have a bit more we can do here if we consider Earth’s vantage point when looking at Mars and the Sun.

As before, we can look at its orbit in isolation, independent of Earth, because looking at it in some other way does not make any sense. Mars’ perihelion is about 207 million km. Mars’ aphelion is about 249 million km. (By the way, these two bits of data are available pretty much anywhere online, but I tend to use the very basic table at NASA’s Planetary Fact Sheet.) With those two numbers, we can calculate others. For example, Mars’ eccentricity is easily calculated to be 0.094: (249-207)/(249+207)=0.09. Much larger than Earth’s, but not as large as Mercury’s (0.21) or Pluto (0.24) or most comets and even Earth-crossing asteroids. We can also calculate its semi-major axis: (249+207)/2 ≈ 228 million km, which is what NASA lists as the distance from the Sun of Mars.

We can also look at the terms opposition and conjunction. Opposition is when Mars appears opposite in the sky relative to the sun. Physically, this happens with Sun-Earth-Mars would appear in a line to someone looking down/across/up towards the solar system. This means Earth can be any distance from the sun (between its perihelion and aphelion) and Mars can be any distance from the sun (between its perihelion and aphelion). It doesn’t matter. However, Earth and Mars, along their orbits, are the closest they will ever get. This means that Mars opposition means Mars will be anywhere from 102 million km from Earth to 55 million km from Earth (a factor of nearly 2 difference!). This is calculated simply by taking Mars’ aphelion minus Earth’s perihelion (249-147=102) and Mars’ perihelion minus Earth’s aphelion (207-152=55). As in, the closest, physically, that Mars can be to Earth is when opposition just happens to coincide with when Mars is at its perihelion and Earth is at its aphelion. The farthest, physically, that Mars can be from Earth during opposition is when opposition happens to coincide with when Earth is at aphelion and Mars is at aphelion.

Conjunction is when Mars appears at the same spot in the sky relative to the sun. Because it’s a superior planet (outside Earth’s orbit), it can only be in superior conjunction (on the opposite side of the sun as from Earth). This means that, during opposition, Mars can be anywhere from 354 million km to 401 million km from Earth. This closest would be when conjunction just happens to coincide with when both Earth and Mars are at perihelion; the farthest is when conjunction happens when both are at aphelion.

With all that in mind, practically speaking, the distance between Earth and Mars during conjunction and opposition varies from event to event. Because each have different years, while perihelion and aphelion tend to happen at the same longitude in their orbit (time of year — as in perihelion for Earth is in January every year, so aphelion is in July every year), the time of year that opposition and conjunction occur vary from event to event.

Earth and Mars orbiting the sun.

This is shown to some extent in this animation from Wikipedia. You can see how oppositions and conjunctions will vary from year-to-year and that the distance will, as well, given Mars’ orbital distance changing much more than Earth’s.

Some may remember back in July 2003 when opposition happened almost exactly when Earth was at aphelion and Mars at perihelion. It was widely reported, such as in this NASA press release, and it’s been widely hoaxed since then. Opposition since 2003 has not been as bright because Mars has not been as close to its perihelion and Earth has not been as close to its aphelion. They won’t line up again like that for roughly 60,000 years.

Application

This has been a lengthy explanation, but I hope that I’ve explained everything clearly by this point. Importantly, one should not confuse opposition with perihelion, and one should not confuse conjunction with aphelion. After all, Mercury and Venus cannot be in in opposition, ever, and yet both have perihelion and aphelion points, by definition.

For those wondering where this is coming from, well, back in 2011, I wrote a lengthy post about some of Mike Bara’s claims, and the last one was his definition of an ellipse. He claimed that Mars has an orbital eccentricity that is very high. Specifically, he wrote, “In fact, Mars’s orbit is so eccentric that its distance from Earth goes from 34 million miles at its closest to 249 million miles at its greatest.” Mike uses this as evidence to support his idea that planets are birthed in pairs, flung off via fission from the sun.

What he was referring to was the average distance between the two during opposition and conjunction. Which, as I’ve just explained (and explained with diagrams in that post), has nothing to do with perihelion and aphelion, which are how you get eccentricity. Opposition and conjunction have nothing to do with aphelion and perihelion. More recently on his blog, he has attacked me while defending his claim that Mars is on a highly eccentric orbit. Note that I never said Mars’ orbit is not eccentric (see 3 paragraphs below: “Except …”). It has the second-highest eccentricity of any planet (since Pluto is not a planet). It’s half as eccentric as Mercury yet around 6 times as eccentric as Earth’s. But, it’s 0.09 because of its min and max distances from the Sun, not its min and max distances from Earth.

Venus has the lowest eccentricity of any planet (0.007), and yet its minimum distance from Earth (its aphelion, our perihelion) is a mere 38 million km, and its farthest distance from Earth (both aphelion) is 261 million km, a factor of almost 7 difference.

But, getting back to what Mike versus I wrote, Mike wrote: “Now, let’s examine your statement that “It’s really simply incredibly stupid of Mike to claim that Mars’ orbit is highly eccentric.” Oh really?” Mike then goes on to point out that its orbit is the second-highest eccentricity-wise. And then wrote: “Excluding Pluto, which is no longer considered a planet, Mars orbit is the 2nd most elliptical of all the “planets.” You can see from the graph that it is far more eccentric than Earth’s, exactly as I characterized it. Put another way, Earth’s relative distance to the Sun varies by only about 3.1 million miles in the course of one orbit (year). Mars’ orbit, by contrast, varies by as much as 26.5 million miles over the course of a Martian year. Obviously, Mars’ orbit is more eccentric by an order of magnitude. How Stuart fails to grasp this I do not know. Maybe he’s just stupid.”

Except, what I wrote is quote-mined in that context. What I wrote, if you go to my original post, was this: “It’s really simply incredibly stupid of Mike to claim that Mars’ orbit is highly eccentric because it comes as close as about 0.38 A.U. (“astronomical unit” is the distance between the sun and Earth) but goes as far as 2.67 A.U.” Given the diagram that accompanied that text, it was clear those numbers are relative to Earth. I stand by that statement when it’s read in full context. It’s not eccentric because of its distance from Earth during opposition versus conjunction, it’s eccentric because of its distance from the sun during aphelion and perihelion. In fact, when calling me stupid for not grasping Mars’ eccentric orbit, Mike directly quotes the numbers that support what I stated and not what he did.

Final Thoughts

I suspect that if Mike reads this, he will still claim that I am mistaken somehow. It’s odd that he would fight so much over something so trivial instead of just admitting he made a mistake and moving on. After all, he claimed later in his attack that it’s not even important to his overall point.

Why then am I devoting time to pointing out and not moving on from something so trivial? Because I consider this to be the heart of this blog and what I do as education and public outreach: Using a real-life example of where someone goes wrong in their thinking to teach something. In this case, I had the context to get into some basics of orbits and definitions that people don’t often learn or remember if they had learned it. And, with the idea of how NOT to apply these terms, I find that people usually better remember how to use them correctly.

But, I don’t expect Mike to agree. Why? Well, his latest is that he’s promoting his new book, “Ancient Aliens on Mars” (there, Mike, I gave you a plug). He has put up a Picasa album with, I presume, images from the book (considering that’s the title of the album). In the second set of five images, he goes over ellipses. With specific notes to me. And, makes the same, fundamental mistakes. Including one figure labeled “”Perihelion” or Opposition” with the caption “Explanation of Mars Opposition, for Stuart Robbins.” And, there is another image showing “Aphelion” which just shows conjunction, and it has been captioned “Pay attention Stuart.”

Yup, I paid attention, and Mike, you’re still wrong in your terms and definitions. And I have been much more polite about it than you.

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Podcast Episode 90: Investigation into Billy Meier’s Alleged Foreknowledge About Stuff About Jupiter and Saturn

Investigating
When people knew what about
Jup’ter and Saturn.

I’ve been doing some research on and off for this episode for quite awhile and finally had enough to post it: Episode 90: “Investigation into Billy Meier’s Alleged Foreknowledge About Stuff About Jupiter and Saturn.” The shownotes for this episode are extensive with lots of references. It’s been scheduled as Episode 90 for about two months. I decided to do it because I found it an interesting scavenger hunt, despite the fact that UFO-related posts are among my least-read blog posts.

The blog entry I reference towards the end of the episode is from January: “How Astronomers Are, According to Popular Press, Constantly Discovering the Same Thing.” I recommend looking through it because it’s a good example that has nothing to do with the Meier case where even peer-reviewed, professional science papers will sometimes ignore work that has shown the same “new” thing before, and it’s a good example of how press releases can play up various “discoveries” … even if they’ve been made before.

The podcast episode also has a few notes at the end, and there’s some feedback clarifying the discussion about why oxygen isotopes are important for understanding where objects formed in the solar system.

 

Given what’s happened in the past when I’ve talked about Meier’s material, I’m going to reiterate my comments policy: Comments need to be on-topic, and I make the final decision of what comes through; I do not owe you an explanation if your comment is not posted, my comments policy is pretty clear. Any comment to this post needs to be specifically about this podcast episode.

If you’re going to dispute material in it, you need to provide specific references and be specific about what you are disputing. You need to be succinct. That means no lengthy essays. That means no posts with numerous links to random stuff. That means no links to videos about trees — no embedded videos period, I will remove them and I will remove posts that are simply a bunch of random links to Meier material, especially if they do not support the specific thing you are refuting / referencing. That means not debating whether trees in a video are real or models.

This episode is specifically about certain claims about Jupiter and Saturn, whether those claims/statements were true, and whether it was known or openly speculated before Meier’s writing that they were true or existed, which is what the claim is for Meier’s prophecy: “… with literally dozens of other such documented examples of Meier’s having published specific, accurate information years, and even decades, before terrestrial scientists, the case must be recognized as being authentic based on these irrefutable facts alone.” It is not the claim that this stuff was known on Earth but Meier didn’t have access to that information so he still got it from ETs — and if that’s what is going to be claimed now, then that is an unfalsifiable and unverifiable claim and is moving the goalpost.

A New Revelation on UFOs and More Evidence They Aren’t Aliens

Introduction

I tend not to write that much on UFOs = aliens. Of the now 25 posts (including this) that are tagged “UFO” on this blog, very few actually deal directly with the issue. The reason is fairly simple: There’s no new evidence, and what evidence there is, leaves much to be desired.

Let me be very specific about my terms here: When I say “UFO,” I mean an “unidentified flying object.” As in an object, in the sky, that appears to be flying, that is unidentified. When I say “UFOs = aliens,” I mean the belief that about half Americans share that UFOs are alien craft. Obviously the former is real. The latter is what people argue about.

Primary Evidence

The vast majority of UFOs = aliens “evidence” is in the form of eyewitness reports. UFOs = aliens researchers often tout these from “highly credible” witness despite those witness accounts claiming things that are impossible for them to know: Height, speed, and size of the “craft.” For details on why that is impossible, I will direct you to my Podcast Episode 2.

But, briefly, all you can do is measure the angular speed and size of the object, but without knowing the physical speed or size or distance, you cannot convert the angular measurement into a physical measurement. Ergo, anyone who states they saw a craft that was, for example, a mile wide, 100 miles up, and traveling at 5000 miles per hour is wrong (intentionally or not). They have no way of knowing if it was that far away or just something that was 100 ft up, 1 ft wide, and traveling at 50 ft per hour instead. (This is, again, unless they have an independent way of measuring the actual value for one of those or have a solid frame of reference, such as if it went behind a tree, then you know it was at least as far away as that tree.)

The primary other evidence for a UFO = alien craft typically is in the eyewitness stating they saw the craft do something that is impossible for terrestrial aircraft (which hopefully readers recognize as a classic argument from ignorance (you don’t know something, therefore you assume it’s something by default)). For example, the object would be seen to stop, or hover, or dart in various directions much faster than an airplane could.

Another common claim is that the craft is silent. Therefore, it’s either very far away, or it’s some sort of anti-gravity non-engine propulsion (usually one or the other is claimed by the witness, not either-or).

Very often, no physical craft is ever seen. It’s just lights in the dark night sky. And the lights are constant, not blinking like an airplane.

I’m Building a Toy

A few months ago, I saw some amazing video done by a guy who put a camera on a quadcopter and flew it over Niagra Falls. Since I do a lot of landscape photography, this seemed like a very neat new/different approach that I could get into: Fly the camera over the landscape and take shots from vantage points I couldn’t possibly get to. (Note that quadcopters have been around for nearly 100 years.)

I’m opting for a build-your-own approach and the parts are finally shipping (except for the flight control board, which is still on back-order). In the meantime, I’ve been learning how to fly on a mini version, the Blade mQX. With the Blade, I’ve been able to fly several hundred feet up, and my starting point is 6000 ft above sea level.

I’ve also been able to dart all over the place. For photography – and especially videography – you don’t want to do that, but it’s a good way to learn how to really control the craft, to do crazy things with it. And with something cheap like the Blade with several spare parts on-hand, it’s okay if I crash (and you will crash if you haven’t flown one before). Here’s just one of many videos on YouTube showing the kind of flying you can do with a quadcopter.

One issue with quadcopters – or at least something that I’m mildly worried about – is what happens if I don’t know which way is forward anymore? I’m getting bright orange propellers for the back and bright green for the front, but 500ft up, will I see that? So, I got running lights to put along the arms. Again, green and orange. That way, hopefully I’ll be able to see which way is forward and which is backward. That way, when I push the controller for it to go left, it goes left instead of right or away from me or towards me or in some other direction. Other people just put one light at the end of each arm, under the motors.

Put These Together: UFOs = Quadcopters

Take a look at this video of a quadcopter with a few lights flying at night. He went a bit out there in terms of lighting, but the effect is fairly clear: This is the kind of behavior described by many UFOs = aliens eyewitnesses:

• The craft is silent (if you’re more than 100 ft away, you can’t hear a quadcopter).
• The craft is lit.
• It performs aerobatics.

You can also cut the power for the lights. You can zoom it up. You can bring it down. You can also build a hexcopter (6 arms) instead and light only three legs, giving you three lights for the typical “triangular craft.”

Final Thoughts

I’m not saying that aliens / ETs do not exist.

I’m not saying that some UFOs could be alien / ET craft.

I’m not saying that all UFOs are actually hobbyist heli/quad/hex/octo/etc. copters.

What I am saying is that there is an extraordinary claim (those lights in the sky that I don’t know what they are are actually extraterrestrial craft) that lacks ANY extraordinary evidence (eyewitness arguments from ignorance). That argument from ignorance is commonly of the form, “No terrestrial aircraft could possibly do what I saw that UFO do!” That argument from ignorance also frequently contains meaningless conjecture on the size, distance, and speed of a few lights in the sky.

What I am saying is that quadcopters and similar toys that a lot of people build and fly for fun are out there (for some reason my brother is now getting into it, and my dad’s been thinking about it for awhile, and now I’m building one), but many people have never heard of them (I hadn’t until a few months ago). And, if you put lights on them (which many do) and fly them at night for fun (which many do), they behave exactly the way that these eyewitnesses say their UFO did in those kinds of UFO = aliens cases.

What I am saying is that I would not be surprised if many UFO reports are actually hobbyist aircraft like these.

Podcast Episode 89: Remaining Issues with Lunar Formation, Interview with Robin Canup

What are the problems
With current models of the
Earth’s Moon’s formation?

Another slightly late one, this is the long-anticipated “what’s left in lunar formation?” episode, a follow-on to Episode 53: Lunar Formation and Origins, put up almost exactly one year ago. The episode is an interview with a leading researcher in the field, Dr. Robin Canup, and it’s about a half hour long.

The next episode is still slated to be about the claim that alleged UFO-contactee Billy Meier knew about Jupiter’s rings before scientists did. I expect the comments on that post might fill up, but I’ll note now that no comments to THIS blog post will be allowed on IF they are about Billy Meier material UNLESS they are a suggestion for a puzzler. Generic Meier conversations will be allowed on the next post about Episode 90.

Also, I’m starting to roughly plan out Episode 100. If you have Skype and are good at making stuff up for a few minutes that’s related to anything discussed so far on the podcast, please let me know and you might get on the first three-digit episode.

Podcast Episode 88: Is Phobos Hollow?

Mars’ odd moon Phobos:
Is it hollow? Is it not?
Hoagland thinks he knows.

It’s a bit late (but back-dated), but as I ‘splained, I was co-leading a field trip to Yellowstone National Park. And then the government shut down. This episode is near the classic style with a basic dissection of the claim and the claimed evidence for Phobos being hollow.

The episode also has Q&A and feedback. The next episode has already been recorded and is an interview with Robin Canup about lunar formation models (she even has her own Wikipedia page!!!)

The episode after that is slated to be about the claim that alleged UFO-contactee Billy Meier knew about Jupiter’s rings before scientists did. I expect the comments on that post might fill up, but I’ll note now that NONE will be allowed through on this post unless someone has a suggestion for a puzzler on it.