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Mercury -- Not Venus -- is the Closest Planet To Earth on Average, New Research Finds (gizmodo.com)
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.
https://physicstoday.scitation...
Interesting work with the best message to get out of this; don't rely on what's obvious, test what you think is true.
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It's all about the delta-v.
I've had people ask me which planet is the closest one to Earth. I now stand corrected. I will now tell them that the order of the is Venus, Mercury, Earth, Mars, etc. and be properly geocentric about it.
So, they pointed out that the current way of calculating is oversimplified and then made some (potentially rather large) assumptions of their own?
Eventually Earth's moon will be a dwarf planet. Then the closest planet will be The Moon.
https://www.universetoday.com/...
Amatuer astronomers love to observe Mars. The problem is Mars is on a close, but outside orbit. Unlike Jupiter and Saturn, which the Earth passes every year in thier orbits, it is a different story with Mars. 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. Even though you can view it through most of its orbit, it is small and normally far away. Venus, even when near the far side of its orbit, it is fairly easy to observe. At least once it rises far enough out of the Sun's glare. Mercury would be even better, but due to the small orbit it doesn't get far from the Sun from our point of view before it dives back down into the glare.
Well, shit, I need to recalculate my horoscope again.
I'd bet that all of the solar system's planets are closer to Sun than they are to any other planet.
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.
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It's not "research". They ran a simulation and reported the results. Which isn't interesting because the simulation was stupid.
p>They assumed a fucking circular orbit (because the extra 1 parameter for an ellipse was too damn much). Which is something that Kepler disproved in the 1600s (and became an immortal name because of it.)
Also, this assumes planets are co-planar (they aren't)
Also, it's meaningless. When people talk about "our closest neighbor", they mean the one easiest to get to. So we want to know the closest point of approach, not "average". Making up a useless measure and publishing it isn't science.
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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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I saw some comments on the Physics Today article about this being pedantic, but astronomy is and always has been about pedantry. It's taking into account tiny details and vanishingly small deviations that allows us to do things like observe the composition of faraway stars or compute the age of the universe.
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.
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 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.
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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 orbit Sun at different rates and I'm not sure the inner planets varying distance will perfectly cancel itself out. They actually simulated this and did a time average.
It's the same phenomenon as the fact that GPS overestimates the distance you've traveled:
It's All About Jensen's Inequality
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.
If something is so important that you feel the need to post it on the internet... It probably isn't that important.
Pro tip: that doesn't significantly change the conclusion that mestar arrived at.
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If we are counting things that aren't planets, the moon is much closer than the sun.
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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.
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 theorum and the average distances between the Sun and each planet). Considering at the two points in the middle of the orbit relative to Earth's position, Mercury is close, you're likely to find that Venus spends more time farther away from the Earth than Mercury.
Of course, what most people consider most interesting is what is the closest approach between any two bodies, and Venus is by far the closest by this measure.
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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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.
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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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.
If the orbits were circular we would be talking about Tycho Brahe instead.
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.
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Why is this news?
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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...
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.
This has always been obvious to anyone who thought about it for a while.
No... Venus might be closer than Mercury at their respective closest, but Venus is also further away from Earth than Mercury at their respective furthest because Venus' orbital radius is more than double that of Mercury. On average, it ends up that Mercury is the closest planet to Earth. It is also, not coincidentally, the closest planet to all the other planets as well... at least on average, over the entire lifetime of their respective orbits.
File under 'M' for 'Manic ranting'
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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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"...!
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% Venus, and 20% mars.
Actually they did calculate average distance as well. 1.05 for mecury, 1.15 venus, 1.65 mars
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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Literally:
https://en.wikipedia.org/wiki/...
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 deployment windows for like the next 100 years, which are the shortest, shortest by planet, when, etc... Now that would be something. Also something useful (which the other is not), where if you see the next best window for a particular planet is coming up, and it won't be that good for another 75 years, you might you know, do something about it and plan ahead or something.
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/...
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Table-ized A.I.
Likely a similar approach will show that, on average, each planet is closer to the sun than to any other planet.
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Squandering taxpayer money on manned missions to uninhabitable waste planets is kinda pointless. You can't terraform MERCURY, VENUS, OR MARS ; on account of fundamental, unchangeable things about their natures. Mercury and Venus are too close to the sun AND too hot, Mars is too far away and insufficiently massive and too small to have enough gravity to hold an atmosphere of the kind that would be necessary for us to be able to BREATHE. Without it, we'd die. If you're going to fly away from Earth and build a colony of humans who have to live cooped up inside and only let out only once in a while in spacesuits, there's no real need to go so far as Mars. The MOON would be close enough. Anyway, just a thought.
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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.
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.
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.
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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
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 the planet's orbit i.e. the sun.
The reason for this difference is that there are two dimensions and the x and y displacements add in quadrature, not linearly. It's a subtle point but, as pedantically stupid as the article is, sadly it is not wrong.
It's pedantically stupid, not interesting. What most people mean by the closest planet is the planet which comes closest to Earth during its orbit not which is closest on average. Indeed the example of Neptune which they give is particularly stupid since its orbit is 165 years long so even if you averaged over an entire human lifespan you would not get that result. What this really boils down to a silly wordplay but I am sure it will be amusing when it turns up on QI!
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.
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.
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 is the normalized inverse of the speed (you're more likely to find the planet at parts of the orbit where it's moving more slowly).
For a perfect circle, which they assume, equal areas in equal time means uniform speed, so uniform distribution.
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 deceleration capabilities, all has much greater meaning and importance.
For most of us planetary travel times all a little arbitrary but in one hundred years, that travel time and arrivals and departures will all become a lot more interesting for everyone.
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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 any so ambitious, calculate the mean distance from Mercury to YourAnus.
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.
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 velocity. Combined with the paper's assumption/approximation that the ellipses are de facto concentric circles, such planets would always maintain a constant distance between them, which can be anywhere between the minimum and the maximum described in this paper and very different from the average of all possible values.
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