Which planet happens to be the closest to us right now is the metric most congruent to people's notion of closest and is often important for things like time delays in radio communication. By that metric it's currently Mercury, closely followed by Venus[1]. But it will change and keep changing.
In terms of how hard it is to get places you really want a delt-v map[2]. By that metric Venus is the closest at 640 m/s from Earth intercept to Venus intercept.
It's sort of interesting that, over an indefinite period of time, Mercury is closest on average but that doesn't really correspond to our intuitive notion of "closest" nor is it a particularly useful metric for anything that comes to mind. So the whole gotcha here is really pretty silly.
Basically, the average distance between one planet and another will always be greater than the distance between the respective planet and the sun. (Note that in the table on the last page, all average planet distances for earth are > 1 AU.) Thus whichever planet is closest to the sun will always be the closest on average to any other planet.
Did you read to the end? The point of the paper is not the gotcha about which planet is really closest. Their point is that their PCM method allows you to quickly estimate distances between groups of planetary bodies in a novel way. They aren't trying to be "gotcha" about it, they're introducing a new model for estimating solar distances.
This exact reasoning is why I've always been kind of annoyed by the song Bitch Don't Kill My Vibe by Kendrick Lamar.
In the chorus he goes "I can feel your energy from two planets away" and even though I know art doesn't have to conform to scientific reality, poetry and music almost especially, it ALWAYS bugged me from the first time I heard it til today.
Like what does 2 planets away even mean? that's a hugely variable distance.
> In terms of how hard it is to get places you really want a delt-v map[2]. By that metric Venus is the closest at 640 m/s from Earth intercept to Venus intercept.
Well, that's also a minimum that changes over time. It might be closest at a particular moment but still not "on average"
> By that metric Venus is the closest at 640 m/s from Earth intercept to Venus intercept
By the way, I think there is a typo on that delta-v map. I doubt low Venus orbit to Venus is 27km/s, vs 9.4 for the earth, when Venus gravity is just 90% that of Earth.
I don’t understand. Two objects are on average closest, but that’s unintuitive because another object is closer based on some astronomical measurement which isn’t distance, which is more intuitive how?
it is interesting that earth spends more time with mercury closer than venus due to orbital mechanics, but the entire premise of the article is just an annoying "gotcha" twist of language.
the planet earth is ever nearest to is Venus, which is what people will mean by "closest neighbor". if you work from home and your next door neighbor works at the office, it doesn't make the retired lady in the next house over your closest neighbor, regardless of spending more time in closer relative proximity to her.
Taking your argument to the extreme, if there was a planet that somehow brushed by extremely closely to Earth every thousand years, that planet would be the closest neighbor? I would argue not. I think the average is more meaningful.
I don't think that way. It's more like this: your two blocks down the street neighbor drives by you every morning, would you classify it being closer to you? Because that's how we look at the Venus at the moment. Mercury should be the real neighbor.
I had never heard of the concept of closest average neigbor before. When I read it, I assumed it meant: draw a straight line between the two bodies, that is the current distance between the two bodies, now average it over a couple of years of motion of these two bodies in space.
I appreciated having this pointed out to me - it's fairly clear once the point is made, but I'd never really thought about it. Of course most of the time other planets are over on the other side of the sun and very far away, but it's easy to just picture the school-style orbital map where everything is in a line together and closest approach = closest, period.
I dunno, I thought it was neat! A slight paradigm shift in how I think about the solar system.
Distance: a straight line (i.e. shortest line in Euclidean geometry) between two points - is a one dimensional object/projection.
On Earth crust where we evolved as 1 m long objects immersed in 1 atm of mostly nitrogen at around 290 K and at a constant pull at 1 g on a spinning ball at 11.5 µHz ... you get the idea ... a very straightforward concept.
Applying it to dust and gas particles (massive enough for gravity to shape it into a spinning sphere) in a vacuum falling towards (on a stable enough orbit) a gas ball with 99.8% of the total mass in the system, itself in hydrostatic equilibrium with its own gravity pull through nuclear fusion of hydrogen into helium ... Well, we are not used to that kind of motion i.e. geometry on astronomical scales. But once you see what dictates the (near) stable motions of all those tiny particles the solution is simple: in the solar system the sun is nearest to all objects in the system, on average. Whatever is nearest to the Sun is the closest on average to all other elliptical moving objects. From Neptune's perspective Mercury is barely moving and oscillating so fast as to standing still.
So, in the case of planets the underlying geometry is moving along (stable) elliptical (i.e. closed path) orbits (approx. Newtonian mechanics), applying our "straight" lines for "distance" is amiss here and can lead to confusion. I personally like to see it more - inspired through e.g. Kepler's imagination[0] - as a geometrical-dynamic system (Kepler orbits) more akin to music.
This question came up when I was studying for my PhD, and had access to software with built in solar-centric planetary locations. From what I recall, across the full-range of time available in the software (which was something like 300 years) it did apply that the Mercury-[PLANET] distance was minimal, although possibly not for Pluto since 300 years is only like one-and-a-quarter orbits.
Yes, play of words. And with a choosen weight function.
If, e.g., the weight function would not be ‘sum over all distances in a given timeframe with the same weight’ but for instance ‘… with weight 1/(distance^2), the results would be different (mercury would not win for each planet).
I guess if someone asks, ‘which neighbour’ is closest, I would say the neighbour living literally next door, even though on workdays our distance is much larger (as we work in different cities) then that other neighbour three blocks down who works in the same city as myself.
Similarly, Mount Everest is the highest mountain (above MSL), however Mauna Kea is higher if measured by prominance (starting from its base which is under water).
When saying Mauna Kea starts at the base, why not claim that with Everest?
Of course in reality neither are the highest mountain, that honour goes to Chimborazo, a good 2.1km higher than Everest (when measured from the Earth's centre)
But under what definition of "closet" would it be Venus?
According to CGP Grey's video linked in the comments, not only Mercury has lowest average distance to Earth, it's also spend the most time being the closest planet to Earth, so it already met two definitions I can think of.
I think you can replace the whole analysis with a single diagram. You don't actually need to find the closed-form solution in terms of elliptic integrals; the only part we use is whether the integrals have a certain monotonicity property (smaller radius => smaller mean distance). And you can rearrange the "mean distance" integrals in way that the rearranged integrands are pointwise monotonic; and the proof that they're monotonic is an elementary geometric one.
The integral over the circle can be rewritten as an integral of a sum of two terms over a semicircle – the term for the local point, plus the term for the mirrored point on the other semicircle. This sum-term is an everywhere-monotonic function of the radius of the circle (in the proof diagram: XA + XB > XC + XD).
(XAQB, XCRD, and XC¹QD¹ are constructed as parallelograms. XC¹RD¹ doesn't mean anything; it's just a construction whose perimeter compares easily against the other two).
Kinda weird argument. The average actual distance of two planets on some orbits can be expected to be roughly equal to the distance of the farther planet from the sun (because the max. distance is r2+r1 and the min. distance is r2-r1, so this type of 'average distance' is ((r2+r1)+(r2-r1))/2 = r2), of course with some variation because the orbits are not truely uniform nor truely random.
The usual notion of comparing the orbit radii is way more intuitive, I think.
> The PCM treats the orbits of two objects as circular, concentric, and coplanar.
Keeping the coplanar assumption, in common with previous estimates, may be a problem. Mercury happens to have an orbital inclination of 7°, second only to Pluto's at 1x7°. Mercury also orbits in an ellipse with an eccentricity of 0.21. Again, this is second only to Pluto, with an orbital eccentricity of 0.25.
I'd like to see a model that takes into account inclination and eccentricity. For the most accurate model, the concentric assumption also fails. Strictly speaking, none of the planets orbit the sun. Rather, the sun and the planet both orbit the barycenter of the sun-planet system, and that will be different for each planet. While the difference is negligible for most planets, for Jupiter the barycenter is quite a distance from the center of the sun: at 1.07 times the diameter of the sun. That's just shy of 100,000km above the surface of the sun.
Let's say my friend was born on January 2, 1900, and I was born on January 1, 1900. Who has the closer birthday to someone born on January 1, 2000?
If you say it's me, well guess what, you're wrong! My birthday is 1 day farther away, just count the days.
If you say it's my friend, well guess what, you're wrong! January 1 == January 1. It's the same birthday, obviously.
Incidentally this is why I think LLMs are a lot more impressive than many here give them credit for. Language is ambiguous and being able to create something novel & coherent using an algorithm is an amazing achievement. Embedded in our use of words is a lot of information that is often incongruent with the understood meaning of the word, as this example shows. Apparently humanity itself has two divergent "hallucinations" of what the word "closest" means in this context. We really can't blame the AI for imitating us when that's what we ask it to do.
Mercury by average. I've wondered in the past it we could land people on Mercury... at the right distance from the sunset terminator where the surroundings had cooled to, say 21 degrees C, (70F). With a 1408 (Earth) hour day, the landing party could stay for quite a while before needing to relocate again towards the terminator, or leave.
[+] [-] Symmetry|2 years ago|reply
In terms of how hard it is to get places you really want a delt-v map[2]. By that metric Venus is the closest at 640 m/s from Earth intercept to Venus intercept.
It's sort of interesting that, over an indefinite period of time, Mercury is closest on average but that doesn't really correspond to our intuitive notion of "closest" nor is it a particularly useful metric for anything that comes to mind. So the whole gotcha here is really pretty silly.
[1]https://www.theplanetstoday.com/
[2]https://i.imgur.com/AAGJvD1.png
[+] [-] akolbe|2 years ago|reply
[+] [-] dr_dshiv|2 years ago|reply
[+] [-] distortionfield|2 years ago|reply
[+] [-] BurningFrog|2 years ago|reply
Over an indefinite period of time, I'd expect that all planets are on average placed in the center of the Sun, and equally far away.
Now:
Oh, right. It's not the distance to the average, it's the average of the distance.
[+] [-] ryanmcbride|2 years ago|reply
[+] [-] nuncanada|2 years ago|reply
[+] [-] adql|2 years ago|reply
Well, that's also a minimum that changes over time. It might be closest at a particular moment but still not "on average"
[+] [-] MayeulC|2 years ago|reply
By the way, I think there is a typo on that delta-v map. I doubt low Venus orbit to Venus is 27km/s, vs 9.4 for the earth, when Venus gravity is just 90% that of Earth.
[+] [-] eyelidlessness|2 years ago|reply
[+] [-] knome|2 years ago|reply
the planet earth is ever nearest to is Venus, which is what people will mean by "closest neighbor". if you work from home and your next door neighbor works at the office, it doesn't make the retired lady in the next house over your closest neighbor, regardless of spending more time in closer relative proximity to her.
[+] [-] 0xFF0123|2 years ago|reply
[+] [-] mercuryftw123|2 years ago|reply
[+] [-] manojlds|2 years ago|reply
If Mercury and Venus had people, which of those people is our closest neighbour?
[+] [-] davidgrenier|2 years ago|reply
[+] [-] dreamcompiler|2 years ago|reply
It does matter a lot if you're trying to send a rocket to a particular one of those neighbors at a particular time.
[+] [-] hpaavola|2 years ago|reply
[+] [-] Blammar|2 years ago|reply
[+] [-] m348e912|2 years ago|reply
[+] [-] 8note|2 years ago|reply
[+] [-] BlackLotus89|2 years ago|reply
Oh and don't forget the followup https://www.youtube.com/watch?v=LIS0IFmbZaI :)
Edit just saw that someone already commented this ^^
[+] [-] lc9er|2 years ago|reply
[+] [-] rini17|2 years ago|reply
[+] [-] Ekaros|2 years ago|reply
[+] [-] ta1243|2 years ago|reply
As a photon flies? Mercury.
In terms of energy required to get there? Venus.
In fact Mercury is the furthest planet in terms of energy required -- it's easier to get to Neptune than Mercury.
In time to get there assuming minimum energy and no gravity assists from other planets? Venus I think, but maybe Mars.
[+] [-] friend_and_foe|2 years ago|reply
All they're finding is "on average each planet is closer to the sun than any other planet" which isn't saying anything.
[+] [-] magneticnorth|2 years ago|reply
I dunno, I thought it was neat! A slight paradigm shift in how I think about the solar system.
[+] [-] anton-107|2 years ago|reply
[+] [-] dav_Oz|2 years ago|reply
Applying it to dust and gas particles (massive enough for gravity to shape it into a spinning sphere) in a vacuum falling towards (on a stable enough orbit) a gas ball with 99.8% of the total mass in the system, itself in hydrostatic equilibrium with its own gravity pull through nuclear fusion of hydrogen into helium ... Well, we are not used to that kind of motion i.e. geometry on astronomical scales. But once you see what dictates the (near) stable motions of all those tiny particles the solution is simple: in the solar system the sun is nearest to all objects in the system, on average. Whatever is nearest to the Sun is the closest on average to all other elliptical moving objects. From Neptune's perspective Mercury is barely moving and oscillating so fast as to standing still. So, in the case of planets the underlying geometry is moving along (stable) elliptical (i.e. closed path) orbits (approx. Newtonian mechanics), applying our "straight" lines for "distance" is amiss here and can lead to confusion. I personally like to see it more - inspired through e.g. Kepler's imagination[0] - as a geometrical-dynamic system (Kepler orbits) more akin to music.
[0]https://en.m.wikipedia.org/wiki/Harmonices_Mundi
[+] [-] NeoTar|2 years ago|reply
[+] [-] ilyt|2 years ago|reply
Technically correct but not exactly first thing you think about.
[+] [-] rdlw|2 years ago|reply
[+] [-] plank|2 years ago|reply
If, e.g., the weight function would not be ‘sum over all distances in a given timeframe with the same weight’ but for instance ‘… with weight 1/(distance^2), the results would be different (mercury would not win for each planet).
I guess if someone asks, ‘which neighbour’ is closest, I would say the neighbour living literally next door, even though on workdays our distance is much larger (as we work in different cities) then that other neighbour three blocks down who works in the same city as myself.
[+] [-] fisian|2 years ago|reply
Similarly, Mount Everest is the highest mountain (above MSL), however Mauna Kea is higher if measured by prominance (starting from its base which is under water).
[+] [-] ta1243|2 years ago|reply
Of course in reality neither are the highest mountain, that honour goes to Chimborazo, a good 2.1km higher than Everest (when measured from the Earth's centre)
[+] [-] thrdbndndn|2 years ago|reply
According to CGP Grey's video linked in the comments, not only Mercury has lowest average distance to Earth, it's also spend the most time being the closest planet to Earth, so it already met two definitions I can think of.
[+] [-] perihelions|2 years ago|reply
[+] [-] perihelions|2 years ago|reply
https://i.ibb.co/kxjDbWP/a.png
Pure classical geometry (I think?)
The integral over the circle can be rewritten as an integral of a sum of two terms over a semicircle – the term for the local point, plus the term for the mirrored point on the other semicircle. This sum-term is an everywhere-monotonic function of the radius of the circle (in the proof diagram: XA + XB > XC + XD).
(XAQB, XCRD, and XC¹QD¹ are constructed as parallelograms. XC¹RD¹ doesn't mean anything; it's just a construction whose perimeter compares easily against the other two).
[+] [-] belter|2 years ago|reply
https://spaceplace.nasa.gov/barycenter/en/
https://space.stackexchange.com/questions/9365/do-the-planet...
[+] [-] ta1243|2 years ago|reply
However the Earth-Sun barycentre is always inside the Sun.
[+] [-] beeforpork|2 years ago|reply
The usual notion of comparing the orbit radii is way more intuitive, I think.
[+] [-] cratermoon|2 years ago|reply
Keeping the coplanar assumption, in common with previous estimates, may be a problem. Mercury happens to have an orbital inclination of 7°, second only to Pluto's at 1x7°. Mercury also orbits in an ellipse with an eccentricity of 0.21. Again, this is second only to Pluto, with an orbital eccentricity of 0.25.
I'd like to see a model that takes into account inclination and eccentricity. For the most accurate model, the concentric assumption also fails. Strictly speaking, none of the planets orbit the sun. Rather, the sun and the planet both orbit the barycenter of the sun-planet system, and that will be different for each planet. While the difference is negligible for most planets, for Jupiter the barycenter is quite a distance from the center of the sun: at 1.07 times the diameter of the sun. That's just shy of 100,000km above the surface of the sun.
[+] [-] fnovd|2 years ago|reply
Let's say my friend was born on January 2, 1900, and I was born on January 1, 1900. Who has the closer birthday to someone born on January 1, 2000?
If you say it's me, well guess what, you're wrong! My birthday is 1 day farther away, just count the days.
If you say it's my friend, well guess what, you're wrong! January 1 == January 1. It's the same birthday, obviously.
Incidentally this is why I think LLMs are a lot more impressive than many here give them credit for. Language is ambiguous and being able to create something novel & coherent using an algorithm is an amazing achievement. Embedded in our use of words is a lot of information that is often incongruent with the understood meaning of the word, as this example shows. Apparently humanity itself has two divergent "hallucinations" of what the word "closest" means in this context. We really can't blame the AI for imitating us when that's what we ask it to do.
[+] [-] curiousObject|2 years ago|reply
Would it be correct to say that, on average, that statement is false for more than half of each Earth year?
[+] [-] manojlds|2 years ago|reply
[+] [-] mikeInAlaska|2 years ago|reply
[+] [-] unknown|2 years ago|reply
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