Mercury -- Not Venus -- is the Closest Planet To Earth on Average, New Research Finds (gizmodo.com) 177
That's the finding presented by a team of scientists who have published their results this week in an article in the magazine Physics Today. From a report: They explain that our methods of calculating which planet is "the closest" oversimplifies the matter. But that's not all. "Further, Mercury is the closest neighbor, on average, to each of the other seven planets in the solar system," they write. Wait -- what?
Our misconceptions about how close the planets are to one another comes from the way we usually estimate the distances to other planets. Normally, we calculate the average distance from the planet to the Sun. The Earth's average distance is 1 astronomical unit (AU), while Venus' is around 0.72 AU. If you subtract one from the other, you calculate the average distance from Earth to Venus as 0.28 AU, the smallest distance for any pair of planets. But a trio of researchers realized that this isn't an accurate way to calculate the distances to planets. After all, Earth spends just as much time on the opposite side of its orbit from Venus, placing it 1.72 AU away.
One must instead average the distance between every point along one planet's orbit and every point along the other planet's orbit. The researchers ran a simulation based on two assumptions: that the planets' orbits were approximately circular, and that their orbits weren't at an angle relative to one another.
Our misconceptions about how close the planets are to one another comes from the way we usually estimate the distances to other planets. Normally, we calculate the average distance from the planet to the Sun. The Earth's average distance is 1 astronomical unit (AU), while Venus' is around 0.72 AU. If you subtract one from the other, you calculate the average distance from Earth to Venus as 0.28 AU, the smallest distance for any pair of planets. But a trio of researchers realized that this isn't an accurate way to calculate the distances to planets. After all, Earth spends just as much time on the opposite side of its orbit from Venus, placing it 1.72 AU away.
One must instead average the distance between every point along one planet's orbit and every point along the other planet's orbit. The researchers ran a simulation based on two assumptions: that the planets' orbits were approximately circular, and that their orbits weren't at an angle relative to one another.
Link to the Physics Today Article (Score:5, Interesting)
https://physicstoday.scitation... [scitation.org]
Interesting work with the best message to get out of this; don't rely on what's obvious, test what you think is true.
Re:Link to the Physics Today Article (Score:5, Interesting)
Anybody that understands that all the planets aren't always in a single synchronized line could have inferred this - all the planets do not have the same orbital period, so there will always be a distribution around the Sun. This means that some of them may be on the opposite side of the Sun from us, and even though their average distance from the Sun is close to Earth's average distance from the Sun, they are not close to each other at that point in time.
I didn't know there was opportunity for publishing papers that spell out common sense and grade school two-dimensional geometry, though.
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Pedantically Stupid, destined for QI (Score:2)
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Interesting work with the best message to get out of this; don't rely on what's obvious, test what you think is true.
Yes, testing common sense systematically is a valuable undertaking that will always get blow-hards here opining that "so what, it is obvious/unimportant/blah-blah".
But my intuition for this question would have been Mercury since it is so close to the Sun, on the far side of its orbit it would never get as far away as Venus would, even if it never gets as close on its closest approach.
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Let me repeat myself for the retarded folks:
Science: You have studies to figure out how something works or what outcome you get from a hypothesis
Liberal pseudo-science: You rig studies in favor of coming out with your chosen outcome. If it doesn't you simply do not publish that study.
Liberalism isn't a conspiracy, it's just fucking stupidity incarnate.
So next time don't try to apply conspiracy theories to where there are none you hack.
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Liberal pseudo-science: You rig studies in favor of coming out with your chosen outcome. If it doesn't you simply do not publish that study.
No, sorry, you need to explain again why this isn't a paranoid conspiracy theory.
Distance doesn't matter (Score:3)
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Time doesn't matter?
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Say one mission takes 5 years while the other takes 1000 years.
That might matter to the astronauts on board, the people funding the trip, etc.
You've minimized the energy involved, but that's not the only consideration.
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What planet is easiest to send a spacecraft to? Is not exactly the same question as "What planet is at this moment closest to us?"
That's no moon (Score:2)
Eventually Earth's moon will be a dwarf planet. Then the closest planet will be The Moon.
https://www.universetoday.com/... [universetoday.com]
Obvious to anyone who observes them (Score:5, Interesting)
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It is only really close for two months every 2 years. It spends most of its time on the far side of its orbit until the Earth can chase it down again, and then quickly races away.
It's because of this that make some interesting "artifacts" show up when plotting the path of Mars from the point of view on Earth when doing so on a 2d "map" of the night sky.
On such a map, one sees Mars following a line as one would expect, then that path curves back around and it looks as if Mars is orbiting in the opposite direction for a time (roughly those two months), before it loops back around to continue in the original direction but along a path slightly offset from the original "tail" for the re
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Presuming as an armature you are not going around Earth to chase this ideal view and instead are waiting for it to happen overhead where you are at, you have to not only wait for the right two month period it is close, but also the right two year period it is closest to where you are looking from.
You'd think if we had armatures for the Earth we would have figured out how to rotate it so everyone can get a look during those two months by now...
My prediction (Score:4, Funny)
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Mars is closer to the earth than you thought, and you will still die alone surrounded by cats.
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By the same argument ... (Score:2)
I'd bet that all of the solar system's planets are closer to Sun than they are to any other planet.
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Order of Orbits vs Distance (Score:2)
The order of the planets people think of is based on their orbiting distance from the sun.
We resolved the whole geocentric vs heliocentric model of the solar system long ago.
Figuring out the actual distance between the planets is useful information if you want to figure out the shortest distance to get from one planet to another.
If Mercury is close to the other planets, it may be beneficial to get to there rather than to Mars.
Re: Order of Orbits vs Distance (Score:2)
If Mercury is close to the other planets, it may be beneficial to get to there rather than to Mars.
Not really. The only reason that the average distance between Mercury and the other planets is shortest is because the distance is shorter when Mercury is on the far side of the sun so you would need to travel thru the center of the sun to traverse this path. It would still technically be the shortest also by going around the sun but I canâ(TM)t think of a scenerio where stopping at Mercury first on the way to a planet on the far side really makes sense unless it was to take advantage of a free rid
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If Mercury is close to the other planets, it may be beneficial to get to there rather than to Mars.
If you could travel to planets as the light flies, perhaps. What matters when traveling is not the straight line distance, it's the delta-v. Mars is much closer in delta-v to earth, thus is it easier to get to. Venus is the closest planet in delta-v, so it's the easiest to travel to.
https://external-preview.redd.... [external-preview.redd.it]
The sun is the center of all planetary orbits (Score:2)
The average location should always be the center of the orbit.
The planets orbit the sun, so that should be their average location.
QED, shouldn't all planets be be equally close?
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Think about two planets on the same solar orbit but opposite one another. They will always be the diameter of their orbit apart from one another. Not whatever distance you are referencing here (zero?).
I think there is something to the idea that the orbit of the inner planet's varying distance might "cancel itself out" and could be modeled as sitting at the center of Sun. Even then though, the distance between Jupiter and Earth will be smaller than the distance between Neptune and Earth.
But I'm not even s
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You're disagreeing with Kepler's first law? Do tell...
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You are very confused, the center of mass of the earth-moon system moves in an elliptical orbit, because orbits are elliptical. to the stool in the corner with the pointy hat, dunce.
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No if parallax shift between the bodies is significant, than you can't base average distance off of average location, as trig functions aren't linear.
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Of course it's pedantic (Score:5, Insightful)
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It's not pedantry, it's changing the understood definition of "closest".
This is taking the average distance between the celestial bodies themselves over a long period of time, instead of the common definition, the distance between the rings describing their orbits.
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In astronomy? In astronomy the answer how far away something is might depend on how long it takes light to get there, but for most things astronomy the answer to how long it will take you (or any physical object we could launch) to get there is "you won't."
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Jensen's Inequality Strikes Again (Score:2)
It's the same phenomenon as the fact that GPS overestimates the distance you've traveled:
It's All About Jensen's Inequality [bayesium.com]
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That is completely and entirely irrelevant. All that matters is that there is unbiased measurement error.
Enh. Ok. A curiosity. (Score:2)
Shit thinking (Score:2)
There is no 'misconception.' By 'closest' people have the orbits in mind, not the average vector distance. There is a clear rank of orbits from inner to outer and that's all that's meant be 'closest,' this stupid pedantry aside.
One must instead average the distance between every point
No one must not. One must stop publishing click-bait tripe like this.
Uhm.... on average, mercury is the closest.... (Score:2)
Why is this news?
Not research (Score:2)
This has always been obvious to anyone who thought about it for a while.
And the Sun (Score:2)
Is even closer than Mercury, on average...
"On average" can sometimes be a terrible way to measure anything, though. Many times it tells you absolutely nothing.
A man can drown swimming in a lake with an average depth of 1"...!
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True. That is why so many don't grasp global warming ... average temperature increase of 1C or 2C has complete different meanings for every location.
Swimming in a lake with average depth of 1 inch (Score:2)
A man can drown swimming in a lake with an average depth of 1"...!
Let me simplify that to a man can drown in 1 inch of water - no swimming required. Average (is that mean or median?) is almost always useless without standard deviation or chi squared.
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True for two-parameter distributions. Shocking, you need to know both parameters.
It's not true for one parameter distributions.
Research is a joke (Score:2)
Literally:
https://en.wikipedia.org/wiki/... [wikipedia.org]
So for the sake of this research lets assume that all planets are on the same plane (they are not). Lets also assume perfectly circular orbits (they are not).
Any other assumptions they want to make? They pretty much took all the realism out of it already.
What would be a really interesting question (and likely take a lot of computational power), is to look at the criteria for launching spacecraft using gravitational techniques, and calculate all of the optimized dep
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Any other assumptions they want to make?
Spherical cow in a vacuum.
not another one (Score:2)
Blasphemy! Lockem up with that Galileo bloke.
The sun (Score:2)
Likely a similar approach will show that, on average, each planet is closer to the sun than to any other planet.
trivial mathematical facts (Score:2)
why
Physicists discover geometry? (Score:2)
I mean, yes? But doesn't this fall out of the geometry of Kepler's laws of planetary motion? I guess I'm confused how this isn't an April 1st article.
One can't ignore velocity (Score:2)
The authors completely ignore the velocities at which the planets move. Their results may be kinda accurate for our solar system as it happens to be (but this should be checked properly), but they will still be "wrong" and surely are not as universal as their mathematical derivation/description suggests.
By omitting the velocities, the authors ignore the fact that the distribution of the various distance values over time is not uniform. In the most extreme case, two planets might have the same angular vel
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They didn't ignore the different orbital periods. That's why they used a uniform random distribution of all the planets on their orbits. The idea being that if you sample the planets all being randomly placed on their orbits enough times, then you approach looking at the planets over all time.
Yes, this assumption and randomized analysis doesn't work if two or more planets are on the same orbit or have "locked" periodic orbits with one another.
Re:I call bullsht (Score:4, Interesting)
If perfectly circular, average distance from any planet to any planet should be equal to the center of their path circle, which is, drum roll please, the center of the sun.
No? Planet A at 1AU orbit and Planet B at 2AU orbit have distance between 1AU and 3AU. Planet C at 1000AU has distance to planet A between 999AU and 1001AU. Whatever are their periods, some average of 1-3 won't get anywhere close to average of 999-1001.
So, Earth-Mercury average distance shares the first place with any other of 45 planet pair combinations.
Not sure how you came up with number 45. 8 planets give 28 combinations, so it should be 'any other of 27 combinations'. Even if you didn't get memo from 2006 about Pluto, it would be 36-1=35 combinations.
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Right. You might be able to argue that the inner planet's orbit cancels itself out and can be modeled as sitting at center of Sun. I'm not sure that's true, but the OP's argument that all planets are on average right on top of each other is obviously wrong.
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If perfectly circular, average distance from any planet to any planet should be equal to the center of their path circle, which is, drum roll please, the center of the sun.
So, Earth-Mercury average distance shares the first place with any other of 45 planet pair combinations.
Reading through the article, they're doing something where they are considering the position of a planet to be "a uniform probabilistic distribution around a circle defined by the average orbital radius". It's not clear exactly how that distribution is defined, but depending on how that was done, it seems possible that the distance calculated could be different than the distance from the Earth to the sun.
There's no explanation that I can see on why they would believe that assumption of distribution to be a
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There's no explanation that I can see on why they would believe that assumption of distribution to be a good one in the first place, though; if they did some research that led them to that assumption, that is probably more interesting than their "closest planet" result.
They did. To quote:
The PCM treats the orbits of two objects as circular, concentric, and coplanar. For our solar system, that’s a pretty reasonable assumption: The eight planets have an average orbital inclination of 2.6 ± 2.2, and the average eccentricity is 0.06 ± 0.06. An object in a circular orbit maintains constant velocity, which means that over a sufficiently long period, it is equally likely to be in any position in that orbit.
Then, they pull out an ephemeris and actually integrate the distances from time point to time point, and that answer is within 1% of their "circles" estimate.
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You quoted the sentence that tells you precisely how the distribution is defined: it's a uniform distribution (same value everywhere) over the perfect circle that is their approximation of the planet's orbit.
The distribution of a planet's location is not uniform for elliptical orbits. Copernicus's second law is more or less a statement of the actual relation: an orbit sweeps out equal areas in equal time. You can convert that into a speed at each point in the orbit, and the actual probability distribution i
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Are you trying to say that the average distance between two planets should be whatever the distance is of the further planet to the center of Sun? That the circular orbit of the inner planet effectively cancels itself out in terms of varying distance and can be modeled as sitting at the center of Sun with no passage of time?
That might be true, but then the average distance between Jupiter and Earth versus Saturn and Earth would still be quite different, with Saturn being further.
Beyond that, the planets or
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As human social development proceeds and we slowly but surely leave the mud monkey (earth primate) transitional stage, a lot of this persnickety astronomical stuff takes greater precedence. So the definition between the closest planet at any one time and the closest planet on average and the closest orbiting planet and as such the fastest planetary trip at any specific time and whether you travel in the direction of orbit or the opposite direction, to arrive there, taking into account acceleration and decel
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But we can also compare to the average distances of all of Earth's which is also the center of the Sun and find the distance is 0.
Or you can realize that given one point of Earth's orbit, compared to all of Venu's v Mercury's locations will usually results in Mercury for two reasons. Consider when both Mercury and Venus are both perpenducilar to the line between the Earth and Sun. The distance between Earth and Mercury is approximately 160,465,000 and Earth and Venus is 184,835,000. (Using the pathagorian t
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Thank you for that insight! I was wondering if the average distance between, say, Neptune and all the inner planets would all be the same / similar (i.e. - if an inner planet's orbit effectively cancelled out it's varying distance and could be modeled as sitting at center of Sun). Your point is, no -- it wouldn't, even without bringing time varying orbit distortions into the picture.
Re:I call bullsht (Score:5, Insightful)
No. Distance is a scalar, not a vector. So the average distance doesn't work out to the center of the sun. It works out to the the sum of all points along the circular orbit. For Venus' case, since its orbit is bigger, the scalar distance to each equivalent point in Mercury's orbit is on average bigger because it's at a greater angle from the Earth (with Earth-to-sun line being the shortest distance).
e.g. Pretend Mercury is located in the sun, and Venus has the same orbit as Earth. Consider four points on each orbit spaced 90 degrees apart.
Average these four points. The first two cancel out (both average a distance R). The second two result in Mercury being at distance R, Venus at 1.414R. And hence Mercury is on average closer than Venus, even though we're pretending Venus has the same orbit as the Earth.
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You're wrong, because we're looking at average distance between Earth and another planet, NOT the distance between the average positions of Earth and another planet. You need to learn about Jensen's Inequality:
http://bayesium.com/its-all-ab... [bayesium.com]
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Not true, as trigonometric functions aren't linear. Do the math. Take venus at a right angle orbit to earth. sqrt(1+0.728^2)= 1.234 AU. Then Take Mercury at the same right angle, sqrt(1+0.39^2) = 1.073 AU. Mecury is closer for at least half of it's orbit.
But a weird thing is that by average closest planet, they don't mean average distance is the least, they mean if you pick a random time, it's most likely that at that moment, mercury will be closer than mars or Venus. The result was about 45% Mercury, 35%
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Actually they did calculate average distance as well. 1.05 for mecury, 1.15 venus, 1.65 mars
Sadly it is Right (Score:2)
If perfectly circular, average distance from any planet to any planet should be equal to the center of their path circle
Sorry but that is wrong. If we assume that the Earth is fixed and we then look at the path of a purely circular orbit around the Sun we can draw a circle centred on the Earth with a radius equal to the Earth-Sun distance. Now if you look at the length of the orbit that is inside the circular you will see that this is less than half the orbit and slightly more than half the orbit is outside. Hence the average distance to the planet from Earth is going to be slightly more than the distance to the centre of t
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If the orbits were circular we would be talking about Tycho Brahe instead.
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The issue is one of scale.
We are often shown our Solar System, with an inaccurate scale. Mostly so we can see the order from the sun.
This article, is kinda of an Oh-Yea that makes sense to me, but I never really though about the average closest planet, I always think in terms of closest possible.
Re:You are technically correct. (Score:4, Funny)
The best kind of Correct.
You're obviously not married.
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No you can be far more annoying, and ask them?
On Average? Or when the orbits reach their closest points? Or When orbits reach the furthest points?
For some reason I have hard time making friends.
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When you ask whether object x is closer than object y, you obviously want to know which is closer right now, not on average. If you haven't memorized the current orbital positions of the planets, just be honest and tell them you don't know.
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It's not meaningless. Look, in absolute terms, yes, Venus gets closest to us. But, if you're planning a permanent settlement that is going to need to be resupplied several times a year, it might be more useful to put that settlement someplace that gets close *several times a year*, even if that isn't as close as Venus gets once in a while.
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Mars is too small to maintain a breathable atmosphere on a scale of millions of years, but it is large enough to hold a breathable atmosphere for tens of thousands of years, which is "good enough" for most human purposes. Nor is it "too far away"; it is very much close enough to the Sun that an atmosphere with sufficient greenhouse gasses could make the temperature comfortable, and the light intensity is sufficient to power photosynthesis.
Now, whether terraforming an appropriate atmosphere is practical is
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Yes, but in terms of being a settlement, only Mars makes sense as Venus and Mercury are both way too hot to be anywhere close to hospitable. Mars, despite being further away has many qualities that make a good candidate for a permanent settlement.
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Possibly. My point wasn't that it would be a *decisive* factor to consider, only that is IS a factor to consider, and that's why it isn't "meaningless" as was asserted. And there may be other mission profiles aside from colonization where it *would* be decisive.
As an aside, personally, I'd prefer to see us colonize a station or stations at Lagrange points, and then the Asteroid Belt, if at all possible - why put yourself back into another gravity well when you've already paid the heavy (literally) cost to g
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Mars is a dustball that looks to have little to no natural resources making it attractive. It's only advantage is that it has an appreciable gravity, which is actually a double edged sword. I'd think colonies on Moon, in the belt, and other moons would make more sense. Also, the shaded zone of Mercury could be quite nice. You'd have a huge amount of solar power easily available.
The vast, vast, vast majority of humanity will remain on Earth until if/when we can leave the solar system and seed the galaxy.
Re:So, pre-Kepler? (Score:5, Informative)
Actually, they did pure math with those simplifying assumptions first. Then they ran a simulation using the actual orbital characteristics (PyEphem uses the real orbits) to check.
That simulation then demonstrated that the assumptions in the pure math produced an error of under 1% for relations among the major planets.
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And running a sim would just asymptotically approach the actual average distance. But doing the math to calculate that value is much cooler.
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That and relativistic precession.
To the moon Alice! (Score:2)
Re:Potato, Potaato (Score:4, Funny)
Seriously, there are more important problems to solve. How about something that's actually useful?
Hey, now, this research evelated pedantry to a whole new level! If ever there was a story that belonged on Slashdot...
But I don't get why they "simulated" this. Isn't this just an integral?
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Not really - the equation to reasonably accurately describe a planet's position in space is actually a pretty ugly kludge of approximations of the various perturbations it's subjected to, even in polar coordinates. Combine that with the math for finding the vector difference between two points as expressed in polar coordinates... the math is going to get ugly.
A skilled mathematician would probably have no great trouble performing the integration, but very few scientists are skilled mathematicians.
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Not when you make their simplifying assumptions: perfectly circular orbits with zero inclination. As stated in the summary. It's not even an integral. It's the circumference of a circle.
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If you want to track the planet to cm precision and account for every N-body chaotic perturbation, sure, what you said. But dude, it's an ellipse for all practical purposes. That's why we can have a calendar or farmer's almanac. Hell, you don't even need an integral. It's algebra. The position of Mercury or Earth can be plotted parametrically as x(t) and y(t), and then for any t you can solve sqrt (delta x^2 + delta y^2), (and indeed, you can integrate and divide by t to get the average). Next, for an
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So no, it's not the complicated proper math. They really should have been able to find the closed form solution. However, the lead author is a grad student who is apparently Python happy, so...
That explains it then. Heck, you don't even have to be able to solve the integral, that's what Wolfram Alpha is for.
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If we are really going to get picky and bring gravity into this, then there is no known closed form solution for any of this.
https://en.wikipedia.org/wiki/... [wikipedia.org]
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True, but we don't need one - we're not trying to solve for the motion of an N-body system, we're trying to find the average distance between two bodies whose motion has already been well-characterized by observation.
Our current approximations aren't perfect, but I believe they're generally accepted as accurate enough to project planetary positions for several centuries in either direction of the epoch.
useless solution too (Score:2)
What does distance matter? If you are traveling to the planet you care about paths that don't clip the sun. Likewise if you are communicating with the planet you care about the average time it has line of sight to earth. And if you are launching a probe you care about closest approach to earth and relative velocity.
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Actually, the closest approach doesn't necessarily matter, especially for the inner planets as the traveled path usually uses gravity assists. Here is an example of Parker's path to get close to the sun:
https://directory.eoportal.org... [eoportal.org]
And one for Messenger going to Mercury:
http://messenger.jhuapl.edu/Ab... [jhuapl.edu]
It's not like you can take a direct route without using a shitload of fuel.
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Relative velocity is the big one for probes. It's actually easier to fly by Pluto then Mercury.
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You're on the right track, but you didn't go far enough.
If you're travelling to a planet, launching a probe, whatever, you don't give a crap about distance, paths that don't clip the sun, or closest approaches. You can about delta-v. And delta-v, particularly with their simplifying assumptions, is proportional to the difference between the two planets' orbital radii.
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More importantly it's still a shit way to measure distance since if you wanted to travel to the planets in question you would have to match orbit and velocity of the celestial body in question.
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I think the point the OP was trying to make is that Venus "lingers" at its closest distance to Earth longer than it does at its furthest distance due to their relative motion around the Sun. That is, from the perspective of Earth, Venus moves relatively fastest when it is at its furthest distance, while it moves relatively slowest at its closest distance.