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
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.
Darn it, I have just finished my burns.
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.
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.
or 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.
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.
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?
> 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.
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.
Sci-Fi for now, though.
Thst without worrying about someone turning a ship into an R-Bomb!
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!
 - https://en.wikipedia.org/wiki/Cobalt_bomb
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...
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.
I just thought I didn't need to spell it out.
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.
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.
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.
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.
Also: If your wonderful new metric gives every planet the SAME closest neighbor, then maybe its not a meaningful metric.
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 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.
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
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.)
.' ___ `.
/ .' __ `. \
| / / \ \ |
E | | M V |
| \ -- / |
\ `.___' /
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.
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 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.
(1) I've never driven a Mars rover.
Though thinking about it a space station ring or something orbiting around that gravity anchor might be better in some aspects.
Wouldn't the communication relay depend on just the farthest distance, rather than the average distance?
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.
It's cool to be reminded that these are different concepts, even if the actual results should not surprise us too much.
Perhaps passing by the gas/ice giants isn't that bad a way of doing that?