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Mercury is closer to Earth, on average, than Venus (scitation.org)
206 points by briannielson 7 days ago | hide | past | web | favorite | 97 comments

It's hidden in the article but I think this originates from a fascinating episode of the BBC's More or Less: https://www.bbc.co.uk/programmes/m0001y9p

Apologies for blowing my own trumpet, but after I listened to the episode I was so captivated by the idea that I tried my hand at visualising it: https://flother.is/2019/which-planet-is-closest-to-earth/

Oliver Hawkins, the researcher who found the answer for More or Less in the first place, also wrote about it: https://olihawkins.com/2019/02/1

Anyone who produces original/interesting content is welcome to self-promote on HN.

And from an update to that page, (thank you), it's worth picking out his own page and code link: https://olihawkins.com/2019/02/1

As well as the link to his gist "Python module for downloading planetary data for More or Less": https://gist.github.com/olihawkins/90f53659d9a9d22384a3c1dba...

Exceptional write up and mobile presentation. Thanks for posting!

"They’re all wrong. NASA literature even tells us Venus is “our closest planetary neighbor,” which is true if we are talking about which planet has the closest approach to Earth but not if we want to know which planet is closest on average."

Closest approach to Earth is of course what NASA cares about since they plan trips to it. I wonder what future the writer is imagining where average distance matters.

But NASA cares about delta v most. Although that would make Mars closer. So perhaps closest approach is thought to be what laymen mean by closest.

For the fellow curious, here’s a solar system delta-v chart [1].


> Do not use for actual mission planing

Darn it, I have just finished my burns.

Don't leave Jeb stranded on Duna.

Really interesting! The expanded image was 404ing for me, I found this slightly different one for anyone interested:


Is Venus really 27km/s to get to a 400km orbit? I'd have expected a number nearer Earth's

I think that delta v includes an extra allowance for the extremely thick atmosphere as compared to Earth's. The delta-v for Earth is given as 9 km/s, which is actually greater than orbital velocity at 250 km altitude; the difference is the extra delta-v you have to allow for atmospheric drag. Venus' atmosphere would give a lot more drag.

On the other hand, the atmosphere of Venus could also been seen as a help since you could "just" float or fly to a great altitude instead of departing from the ground.

The ground is pretty much impossible to reach anyway, and not as interesting as the atmosphere about 50 km up, where temperature and pressure are about the same as on Earth and where breathable air is buoyant.

> the atmosphere of Venus could also been seen as a help since you could "just" float or fly to a great altitude instead of departing from the ground

Yes, but I don't think the numbers given in the chart consider such possibilities. I think they're for a standard rocket blasting off from the surface and having to account for atmospheric drag when determining how much delta-v is required to reach orbit.

Is that escape velocity or how fast it goes around the sun? I know it's days are exceptionally slow.

Atmospheric density ?

or maybe that the “low orbit” distance given for Venus is 400km vs 250km for Earth.

> maybe that the “low orbit” distance given for Venus is 400km vs 250km for Earth

No, that won't make much of a difference: the gain is basically just the gain in potential energy for the extra 150 km, which is equivalent to only a few tens of meters per second delta-v.

Awesome! Things like that are the reason we can't stop reading HN. There are way too many interesting pieces popping up. I just need to be careful not to spend the entire day here.

That image looks like it would be a great game board for some sort of strategy game.

I have always interpreted "neighbor" in planetary sense as "planet on a neighboring orbit", which is to say, one that's the next closest to / furthest away from the Sun on average. Just like IRL, your nearest neighbor is whoever lives in the house that's closer, not by the average distance between you and them personally.

Now you live in a neighborhood where all the houses, including yours, are constantly wildly moving in all directions. Who's your closest neighbor then?

All directions? No idea.

Each house has a ~circular track and has a different frequency? Then unless you're asking about right this second it's the two houses on the adjacent tracks, or whichever one of those has the closest track to mine.

They live on that ring. It's really easy to figure out neighbors with concentric rings.

> Then unless you're asking about right this second it's the two houses on the adjacent tracks

Yeah, when someone is asking what thing is closest to them they usually mean closest right now, or closest at any random point in time. Not the thing that just so happen to be closest for a very limited amount of time.

Thought experiment: imagine there was a twin Earth on the same orbit but the opposite side of the Sun. According to your metric this is the closest neighbor of Earth.

What's strange is that you still use the average in your metric. You use Venus average distance to the Sun to get its orbital radius and declare it the closest ring track.

Which leads me to a second thought experiment: imagine there was a planet with a very eccentric orbit making it pass very close to Earth at a single point in time, closer to any other body, but its average distance to the Sun is larger than Venus. What is the closest then?

Third thought experiment: imagine we are no longer talking about planet orbits but about a merry-go-round where all rings are moving at a fixed angular speed. You are on a horse on ring 3 and there are other people scattered around. You are asked who is closest to you. Do you still use the ring distance as a metric or the regular euclidean distance to whichever person is closest?

When someone says "closet neighbor", they don't mean the guy from three doors over that's walking down the sidewalk in front of you.

> twin Earth

Yeah, I'd probably say that's a closer neighbor than Venus or Mars. If Venus would stay on the same side of the sun as Earth I would consider it over anti-Earth, but because it goes almost as far away those brief sweeps don't do enough to overcome an orbital match. The delta-v to get to anti-Earth is almost zero.

You might be able to convince me to treat an anti-Earth differently, but that doesn't change my answer on Venus vs. Mercury.

> you still use the average in your metric

No, I use the orbits being concentric near-circles.

> second thought experiment

If it's always between the orbits of Venus and Mars then it easily wins. If it's criss-crossing then the answer gets more complicated. I freely admit this logic doesn't apply when the orbits aren't concentric near-circles. I'm not trying to solve every case ever.

> fixed angular speed

If all the angular speeds are fixed, then you'd use the constant distance. This logic is a fallback for when you don't have a constant distance. Something that takes patterns into account, making it work better than an average.

It gets interesting when the tracks are elliptical, but I assume that is what you mean with "~circular" and "ring".

I think you missed the point of my analogy. Houses aren't planets, they are orbits; humans inside them are the planets. Orbits don't wildly move in all directions.

What is also interesting is that the definition seems to shifts when we talk about star systems. Alpha Centauri might not be the nearest star system if we compared orbits instead of the current distance. Then again, it still might be the nearest... I have no idea.

That's not exactly surprising given that the different configurations caused by planetary orbits recur in a timeframe of years and decades, i.e. within a human lifetime, while stellar orbits are measured in hundreds of millions of years.

> I wonder what future the writer is imagining where average distance matters

Interplanetary communication.

Mercury has less average distance but higher percentage of time blocked by the sun.

then we will communicate in the shade

Needs a metric for maximal distance, not average.

The future where human spaceflight to other worlds is common, and not relegated to a few specific optimal times because it is so costly?

Basically, the future where the distance is a calculation on the cost of the trip like prevailing wind direction and speed is for airlines. We may never get there, but it's a nice thought.

Except in general, cost in space flight scales with delta-v, which is roughly proportional to the distance between the relative orbits, not the average point distance between planets (barring any clever transfer maneuvers).

Unless torch drives are taken into consideration, like a NSWR thruster or black hole engine.


Sci-Fi for now, though.

I love the idea, either as a fusion drive or annihilation drive, but the world had better be damned peaceful before we start making that kind of thing. As Larry Niven explored several times, such a drive is also a weapon of mass destruction on a potentially global scale. It’s the ultimate dual use tech, because it’s effectiveness as a drive is directly proportional to its effectiveness as a weapon. Whether in the form of “The Kzinti Lesson” or a smalle scale like what’s found in The Ethics of Madness we’re talking about something serious. The only difference between peaceful use and militaristic use is just where and how you aim the exhaust.

Thst without worrying about someone turning a ship into an R-Bomb!

We already live in a world where if e.g. North Korea wanted to destroy the huge swaths of our entire species, they probably could. See things such as salted nukes, like a cobalt bomb. [1]. I think there's an even more general lesson there as well. We first utilized nuclear weapons in 1942. Up until that time major developed powers going to war with each other was a relatively normal part of existence. And given that reality, it would not have been unreasonable to predict nuclear weapons resulting in the end of the world. As Einstein witted, "I don't know what world war 3 will be fought with, but world war 4 will be fought with sticks and stones."

But after the realization of nuclear weapons, unrestrained war between developed nations simply ended. And we've entered in what is likely the safest and most peaceful 80 years of human existence ever. I realize how absurd that sounds, but statistically it is almost certainly true. It's hard to even imagine the death toll of previous wars. In World War 2, some 3% of the world's population was killed. Today that would be 231 million people. For some scale imagine a 9/11 type event happening, every single day, for 211 years. If you have kids when you're 30 then your great great great great great grandchildren would be experiencing a daily 9/11 event each and every day of their life. Now take all that death and suffering, and compress it into 6 years. Really puts our modern losses into context.

The point of this is that weapons (or equivalent) capable of immense harm don't necessarily have the impact you might expect. Similarly, get rid of all nukes in the world today while guaranteeing they could not be easily recreated - and you'd likely set in motion a series of actions that would lead to the violent deaths of what could be billions. I find unforeseen consequences endlessly fascinating. Bring on the planet busters. Hope there's nothing we're not foreseeing!

[1] - https://en.wikipedia.org/wiki/Cobalt_bomb

The thing is, there's the time when nobody has nukes, the time when multiple people have nukes and keep each other in check, and the time where one party has nukes. We've got plenty of experience with no nukes and multiple groups with nukes, but had a very short period where one side had nukes. How confident are we that they wouldn't be used much if that period lasted much longer, and the US was less blindsided by the Russian development of nuclear weapons?

I worry less about a future with lots of planet-killer grade weapons than I do about the period where one group has access to them and the others do not. There are any number of ways to justify violence to yourself when you don't have to worry much about the response. For example, preemptively striking before the other side get the same capability because that might lead to another MAD situation which is arguably worse for the species overall...

> Thst without worrying about someone turning a ship into an R-Bomb!

And thus Burnside's Advice - "Friends don't let friends use reactionless drives in their universes."

Semi-related, but Project Rho is awesome. http://www.projectrho.com/public_html/rocket/reactionlessdri...

Also, regarding The Kzinti Lesson ("A reaction drive's efficiency as a weapon is in direct proportion to its efficiency as a drive.") I have to feel like you could drop 'reaction' and maintain accuracy... Given that reactionless drives are planet killers.

Agreed on Project Rho, it mixes entertainment and intellectual stimulation to the point I occasionally find myself giggling. Good point about reactionless drives too!

well when everybody is dead that would be the end of wars

Could you please stop posting unsubstantive comments to Hacker News?

The point I am making is that war has and will always be part of human societies and therefore all technological progress will be applied to warfare. There's no point to complaining about potential use of new tech in war the same way that there's no point in complaining about the laws of physics.

I just thought I didn't need to spell it out.

That's more likely to be a function of: what proportion of the time is the planet within X distance of the earth, though.

Closest approach has less to do with ease of travel than you might think, when it comes to orbital mechanics. Indeed, your basic Hohmann transfer orbit is a half-ellipse and thus intersects the destination orbit at the point farthest from the point of origin!

Closest average orbit radius is what everyone means when they say closest.

The Astronomical Unit is based on the Earth-Sun average distance. It seems a lot of people care about this metric.

These days the Astronomical Unit (AU) is defined exactly (149597870700 m), but historically AU was used to measure relative distances in the solar system because the distance from the Earth to the Sun was unknown.

The transits of Venus in 1761 and 1769 were used to determine the distance to the sun and hence the scale of the solar system in a major scientific endeavor. Several expeditions were shipped around the globe to do simultaneous observations of the beginning and end times of the transit, using the positions of moons of Jupiter as a time reference.

The AU is still in modern use because it can easily communicate distances around the solar system to humans. It is less useful in computation and it's a somewhat arbitrary number given that the orbit of the Earth has minor perturbations.

It used to be that an AU wasn't a constant, and gradually changed over time since the definition depended on things that weren't constants (e.g. mass of the sun). For the last few years, the AU has been hardcoded to a certain number of meters close to its notional value.

The AU is a handy unit when measuring how far things are from the sun, but I think most people's intuition breaks down when using it to measure objects with different orbits and varying angular separations. On top of that I think the argument can be made that just because people care about a particular unit of measure doesn't mean that the definition is particularly meaningful. There's lots of people that care about kilograms and acres, but that doesn't mean they care about a hunk of metal in a French vault or the plowing speeds of European oxen.

Oh, come on. There is a big difference in what "average distance" means when comparing planets (which do not orbit around each other) vs. a planet and the sun (where one body has a nearly circular orbit around the other).

I haven’t done any kind of calculations, but can you say Mercury is closer to points on Earth’s orbit on average than the Earrh is?

My quick testing makes it seem that the center of a circle is closer to the circle "on average" than any point on the circle is.

A quick Python script suggests that a point on the circle is about 1.273 radii away from the other points on the circle on "average", while (by definition) the center is 1 radius away from all points on the circle.

So this fact about orbits seems related: the closest point to your orbit (on average) are things in the middle of it, which are near the center of your "circle".

Further testing supports this -- there's a gradient from the 1.273 at the "edge" to the 1.0 in the "center", as you shrink the radius of the circle you measure from.

So depending on Mercury’s distance from the center of the Earths orbit, it could be closer on average than an average point in the Earth’s orbit.

> So depending on Mercury’s distance from the center of the Earths orbit,

Yep, there's basically there's two groups of things:

1. Those with smaller orbital radii (ie, Mercury which orbits between the Earth and Sun) will always be closer on average -- with a limit of the center point having the minimal average distance of "1 orbital radius".

2. Those with larger orbital radii (ie, Jupiter which always has the Earth between the Sun and itself) will always be further away on average.

This effect happens even when talking about abstract circles and measuring points on them -- not about real orbits.

> I wonder what future the writer is imagining where average distance matters.

Communication time?

A lot of it is arguing semantics, I know, but still pretty fascinating. Even though it makes sense when I think about it, the fact that Mercury is on average the closest planet to every planet in the solar system blows my mind.

Well, in that case the Sun is the closes to everything, since it's center of rotation, but I think that 'average' metric is wrong, no one is going to flight to the Mars when it's opposite to the Earth, it's like average temperature in the hospital.

> That observation results in what we call the whirly-dirly corollary (named after an episode of the cartoon Rick and Morty)

Hoo, boy

Also: If your wonderful new metric gives every planet the SAME closest neighbor, then maybe its not a meaningful metric.

Well, someone making a naive guess at where to put a solar system relay might think to put it in the middle, maybe around Mars or the asteroid belt? This shows that the best place would be around Mercury and maybe 2 more at its Lagrange points to get around the Sun. It certainly made me think about something I hadn't considered before, so I'm glad to have read it

While it's easy to complain that this number is "wrong" in that the radial difference is what we always, or mostly, care about, it's worth pointing out that it does accurately represent radio communication lag times. In other words, messages sent to Mercury will get there, on average, in less time than they would take to get to Venus.

And the sun is even closer on average. It's not a very useful metric.

Although the material is good, I don't see an use of such a metric. Are average metrics like this one used in estimating something?

You don't need any higher math to understand this so I don't know why they don't show kids that (pointing this out did not make me popular in 3rd grade science class).

I used to wonder about the distances if the planetary orbits were not in a plane (which also always seemed weird to me as a kid) and even though I utterly lacked the math to figure it out it was easy to develop an "in principle" qualitative understanding.

School seems to be oriented backwards.

I remember asking science teachers about how it is that trees can grow without depleting soil level around them?

I even had one teacher suggest I was stupid and this question was ridiculous. 'What do you mean?' I insisted there was some discrepancy. 'Trees grow out of the ground, everyone knows that.'

Only later I realized photosynthesis accounts for most of the tree's mass. Later I read in Feynman's Surely you're Joking... and he brought up this question as well. Felt like a vindication.

Just wondering why they needed a new modelling technique with a fancy name, when if you're going to do it numerically anyway (despite the simplifying concentric circles assumption), it's just a double integral:

    import numpy as np
    from scipy.integrate import dblquad
    pi = np.pi

    def av_distance(r1, r2):
        def distance(theta1, theta2):
            z1 = r1 * np.exp(1j * theta1)
            z2 = r2 * np.exp(1j * theta2)
            return abs(z2 - z1)
        integral, err = dblquad(distance, 0, 2*pi, 0, 2*pi)
        return 1 / (4 * pi ** 2) * integral

    print(av_distance(1, 0.723332))
    print(av_distance(1, 0.387098))

Edit: Oh I see - they did it analytically, and reduced it to a 1D integral even by symmetry. That's cool, but I was thrown out when skimming because they said "we devised the point-circle method" instead of "we did the integral".


From the table at the end, it also turns out that the Sun (at ~1AU) is even closer to Earth, on average, than Mercury.

(The Sun is almost certainly average-closest for Mercury itself, but unsure if the Sun would be average-closest for Venus – the table doesn't explicitly include the Sun.)

Having had some coffee since I wrote the above, I realize that under some reasonable assumptions that substantially apply to all our solar system's inner planets, the Sun will always be closer-on-average than any "radial-neighbor", no matter how close the radii are to the sun or each other.

And I had always assumed the ptolemaic model couldn't answer any questions with less work then the heliocentric...

Everything the Magic School Bus taught me was a lie!

Which reminds about the saying "Do not cross a river 4 feet deep on average". And why the average is calculated as an arithmetic mean and not geometric or using any other averages? And consider then that on average Proxima Centauri could be well father away from us then the center of our Galaxy.

What's astonishing is that during its closest approach, Venus is a mere 130 light seconds away from Earth. That's a mere 4⅓ light minutes for a round trip!


           .'   ___    `.
          /   .' __ `.   \
         |   /  /  \  \   |
         E   |  |  M  V   |
         |    \  --  /    |
          \    `.___'    /
           `._        _.'


Suppose there was a bizarro Earth that shared our orbit. Let’s also “ignore” any effect of it on us, gravitationally. I.e. it’s just a point. Now if bizzaro Earth is on the opposite side of the Sun, it’s 2 au’s away. If it’s on top of us, it’s zero. To make things fair, let’s take an ensemble average of bizarro earths over our entire orbit. So Mercury is closer to Earth than Earth is, if you’re gonna be “fair” about it.

TL;DR: assuming circular, coplanar orbits, for any planet A, the sun is on average closer to that planet than any other planet B, because planet B spends a lot of time on the other side of the sun from planet A, and given the way orbital rates work out the closer a planet is to the sun, the lower its average distance is to any planet farther out than it.

In other words, Mercury is on average closer to Neptune than, say, Saturn is, and indeed Mercury is on average closer to every planet than any other planet is.

This is both somewhat surprising (I'd have thought that there would be a symmetry here - that the average distance between Neptune and Saturn would be the same as the average distance between Neptune and the Sun), and also (I think) uninformative.

The way orbital dynamicists think about "close" orbits is in terms of delta-V, which is to say, how big a change in velocity does it take to change one orbit to a different one. Or, in more concrete terms, how much fuel would it take for a spacecraft to travel from a body in one orbit to a body in a different orbit. That's a completely different way to think about closeness than the OP 's metric.

Spaceflight is non-Euclidean like that.

The OP's metric would be helpful for estimating average time-of-flight communications delay, but over distances like this I don't think that averages are that informative. The total variation is quite large; basically it varies as |r1|-|r2| to |r1|+|r2|. For Earth-Mars that's from 4.5 to 20 minutes. Not sure knowing the "average" distance is all that helpful there.

For Mars-Neptune it's 4 hours to 4.4 hours, and for Earth-Neptune it's 4 to 4.3 hours. Even though the distance is much greater, the orbital radius of the outer planets is so large that the variation as the inner planet goes around the sun is almost in the noise.

Takeaway: for comms delay to the the outer planets, just calculate the time-of-flight distance to the sun.

> TL;DR: assuming circular, coplanar orbits, for any planet A, the sun is on average closer to that planet than any other planet B, because planet B spends a lot of time on the other side of the sun from planet A, and given the way orbital rates work out the closer a planet is to the sun, the lower its average distance is to any planet farther out than it.

It doesn't come from orbital rates; it comes from basic geometry.

Imagine that the orbits of Earth and Mercury are perfect circles. Draw them on a piece of paper, and mark the position of Earth.

Now, take a compass, place one leg at Earth, and draw a circle (with the Earth at the center) that passes through the Sun. This is a circle of radius 1AU.

Now note that slightly less than half of Mercury's orbit is inside this circle: Mercury spends more of its time (in this idealized model) more than 1AU away from Earth. That plus an equivalent result for Venus leads to the finding of this link.

This arises because of our old friend, the Pythagorean theorem. When Mercury->the Sun->Earth make a right triangle (that is, when Mercury is neither ahead of nor behind the Sun), the distance between Earth and Mercury is the hypotenuse of that triangle, which has legs of 1 AU and one Mercury-orbit-radius. That's obviously greater than 1AU.

>>Spaceflight is non-Euclidean like that.

Spaceflight maybe, the traveling between objects part, but other space operations are very much euclidean. The folks trying to talk to mars rovers are very aware of exactly how far mars is away from earth, as is anyone trying to image planets using telescopes.

Yes, but I suspect they don't care that much about average distance(1). They care about current distance, and about minimum and maximum distance. Maybe that's being too pedantic though.

(1) I've never driven a Mars rover.

Wow. And the Sun is even closer than Mercury (on average).

Since the sun's orbital radius is close to 0, that makes sense.

It's too bad Mercury isn't tidally locked to the sun; imagine the opportunities for solar collector / manufacturing if that were the case.

Though thinking about it a space station ring or something orbiting around that gravity anchor might be better in some aspects.

> can be useful for quickly estimating satellite communication relays

Wouldn't the communication relay depend on just the farthest distance, rather than the average distance?

I was wondering, does someone know why the planets stay in the orbits they have? Why are they not related to mass or density?

According to the ancient Greeks, "the planets" included the moon. Thus, the moon is actually the closest planet* to the earth, on average.

(Some) Greeks also thought the planets were embedded in "quintessential" spheres and that force was proportional to speed.

Isn't this kind of obvious?

Sure, if you stop to think about it for a minute. Might need to be brought up as something to think about though.

I know, right?

That's just a load of click bate (read: bullshit). That's not what people mean when they ask "What's our closest neighbour" at all... interesting thoughts perhaps, but disingenuous.

But "what people mean", in their over-simplified grade-school understanding, is the actual bullshit.

This is a well-calculated, correct answer from astrophysics experts. If it's 'clickbait', it's not the abusive kind, but the piques-interest-and-teaches-something-new kind. Most readers probably learned something new as well, as the @PhysicsToday Twitter account pre-teased the article with a poll – https://twitter.com/PhysicsToday/status/1105460820148961280 – and fewer than 1-in-5 respondents got the answer right.

I don't know...I think it raises an interesting distinction between "What planet is the closest to us right now?" and "what planet gets the closest to us?" and "what planet is the closest to us most of the time?"

It's cool to be reminded that these are different concepts, even if the actual results should not surprise us too much.

Yes, reminds me of that sf movie/tv show trope where the invaders are coming in from outer space, we see them passing Saturn, then Jupiter, then Mars, then the Moon, on their approach to Earth. As if the planets were all neatly lined up based on their orbits. Because in the minds of most people that's how it "should" look to zoom in from outer space to our planet. Whereas what this is demonstrating is that on average the planet the invaders would be most likely to pass close to on their approach to Earth/Moon system would be Mercury.

This is complete speculation: If you're coming from outside the solar system and want to end up orbiting earth, you probably need to change your delta-v significantly.

Perhaps passing by the gas/ice giants isn't that bad a way of doing that?

It's also a very useful statistical lesson. As averages or nearest is not always representative of the day-to-day reality which decisions and intuitions might be based on.

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