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.
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.
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.
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.