
Mercury is closer to Earth, on average, than Venus - briannielson
https://physicstoday.scitation.org/do/10.1063/PT.6.3.20190312a/full/
======
flother
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](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/](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](https://olihawkins.com/2019/02/1)

~~~
richardhod
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](https://olihawkins.com/2019/02/1)

~~~
jdnier
As well as the link to his gist "Python module for downloading planetary data
for More or Less":
[https://gist.github.com/olihawkins/90f53659d9a9d22384a3c1dba...](https://gist.github.com/olihawkins/90f53659d9a9d22384a3c1dba05d5cf3)

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brlewis
"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.

~~~
JumpCrisscross
> _I wonder what future the writer is imagining where average distance
> matters_

Interplanetary communication.

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

~~~
Pristina
then we will communicate in the shade

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paxy
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.

~~~
varelaz
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.

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nategri
> 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_.

~~~
skolsuper
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

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theothermkn
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.

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

~~~
fourier_mode
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?

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doubleunplussed
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))
    

...

    
    
        1.063544409973366
        1.0156870128527526
    

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".

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gumby
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.

~~~
wallace_f
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.

------
gojomo
Interesting!

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.)

~~~
gojomo
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.

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

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lostgame
Everything the Magic School Bus taught me was a lie!

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fpoling
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.

------
waynecochran
TLDR

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

~~~
henryscala
Smart

------
GlenTheMachine
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.

~~~
sandworm101
>>Spaceflight is non-Euclidean like that.

Space _flight_ 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.

~~~
GlenTheMachine
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.

------
Tepix
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!

------
aj7
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.

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

~~~
empath75
Since the sun's orbital radius is close to 0, that makes sense.

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mjevans
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.

------
fourier_mode
> 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?

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

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mattnewport
Isn't this kind of obvious?

~~~
gojomo
Clearly not:
[https://twitter.com/PhysicsToday/status/1105460820148961280](https://twitter.com/PhysicsToday/status/1105460820148961280)

~~~
ummonk
This reply wins the thread:
[https://twitter.com/Jozzzzef/status/1105479189334032389](https://twitter.com/Jozzzzef/status/1105479189334032389)

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

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

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xemoka
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.

~~~
abakker
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.

~~~
zuminator
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.

~~~
Beldin
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?

