The story of how they actually first measured the distance to the Sun is quite fascinating. They timed the transit Venus and used Kepler's laws to figure out the rest.
This is a great introduction into how real astrophysics is done. We don't know how far away things are until we measure, but our measurements are never precise, and we don't have very many 'calibrated' distances to compare to. Little by little it's possible to exclude possibilities and narrow down on the likely true value.
Indeed, this might be good methodology background for the current "crisis in cosmology" where new JWST observations "close the gap" so that it no longer includes some previous upper/lower bounds at all ( https://www.youtube.com/watch?v=-kTe0xRAU1w for a scicomm explainer with more detail )
Well, and the crisis! The allowed regions from different methodologies don't overlap, pointing to one of the pillars of cosmology potentially being wrong.
I almost got my degree on astrophysics. Yes, I read a lot of bad and good textbooks. This one is rather brilliant, lucid, and well done.
But I have to follow up with:
"Well, but... how do we really know?"
A: We have followed up well worn paths of scientific inquiry, and looked at our assumptions, in designing an experiment that, we assume to fail. When it does not follow our assumption, then we can only rule out failure, and call it a success. This follows centuries of this type of exacting and painstaking scientific work. Although I would normally have 10 ~ 12 citations of very diverse work, that exercise is left to the reader.
This is way outside my area of expertise (if I have one at all), but assuming we know the diameters of the sun, Earth, and our moon, as well as the distance between Earth and our moon, could we not determine the distance between Earth and the sun based on the scale of the shadow Earth projects onto the moon during a partial lunar eclipse?
If you know the diameter of the sun you should be able to measure the distance by just measuring the size of the sun in the sky and using some simple geometry. I.e. if the sun takes up x degrees of space in the sky then tan(x) = (radius of sun / distance to sun).
But... how do you measure the diameter of the sun?
If you sent out probes to calculate the travel time of beams of light between two points, but at Lagrange points from one another, and then had them simultaneously slow their orbits to fall into the sun, and considered the "edge" of the sun the point at which it destroyed the probes...
How do you measure the diameter of the sun when your most advanced technology does not include a telescope. And even when it does, but just a telescope about 8x power (approx Gallileo’s first one)
I feel like shadows are the "simple tech" path. It was known since ancient times you can get the circumference of the Earth (remarkably accurately) by doing some calculations based on the angles of shadows from the mid-day sun at two points sufficiently north/south from each other (a fantastic application of trig). Knowing the circumference of the Earth and these angles lets you know the diameter/radius as well which lets you create a "straight line" distance (i.e. not the over the surface distance) between those two points. Using those two points and known angles to construct a triangle with the Sun should let you see it is at least extraordinarily far away, even if your measurements are relatively innacurate.
By looking at it through a tinted glass, and noting down the apparent size of the core disk, then assume its a sphere, and calculate the diameter from that?
How to measure the distance? Easy, compare the apparent size to the actual size and calculate the distance from that. Then how do you measure the actual size? Easy, multiply the apparent size by the distance!
In the context of having just explained "this is how you get the distance from the diameter" in the broader context of "from first principles and simple technology"...
Why did those silly 18th century physicists even bother with those sextants and complicated mathematics when they just could have looked up the answer on Wikipedia?
The article has a whole section about how there's no way to know the distance to the sun in light-minutes to use as an input to figuring out how big it is
Do you think you could have deduced that stars are distant suns if you'd lived in the ancient world?
Apparently the only pre-modern people (i.e. pre-Giordano Bruno) recorded as making the claim were Anaxagoras and Aristarchus of Samos, but their ideas were completely rejected by contemporaries:
In retrospect, it just seems so blindingly obvious that I'm tempted to believe that I too would have seen through the Aristotelean BS.
But surely there must be aspects of reality that will seem similarly obvious to future generations, and yet I don't feel any insights coming on.
I should say, Aristarchus is the ideal of maximizing information from minimal data:
"Aristarchus of Samos (Samos is a Greek island in the Aegean Sea) lived from about 310 to 230 BC, about 2250 years ago. He measured the size and distance of the Sun and, though his observations were inaccurate, found that the Sun is much larger than the Earth. Aristarchus then suggested that the small Earth orbits around the big Sun rather than the other way around, and he also suspected that stars were nothing but distant suns, but his ideas were rejected and later forgotten, and he, too, was threatened for suggesting such things."
The ancients were misled by apparent size of stars, not realizing they were point sources spread out by atmospheric diffraction. Placed far enough away, they would have to be implausably big by that measurement.
So people promoting distant stars had a glaring contradiction they had to ignore. Lesson for modern theorizing.
One sees signal beacons (a bonfire on a hill, used to send a simple warning message) both up close, and from a distance of many miles. Thus one sees with the naked eye that a great fire looks like a mere candle from far enough away. Then one boldly extrapolates: perhaps it is the same with the sun and the stars.
I definitely wouldn't have reached that conclusion.
Evidence in favour: The sun is a light source, they are much dimmer light sources with much smaller radii, consistent with the hypothesis.
Evidence against: There are none at intermediate distance, they're either the sun or so far away to practically be a point light [1]. The sun is yellow, they are not [2]. The sun has a partner in size (measured in portion of the sky it takes up) with the moon, which I presumably know is relatively close by, suggesting some form of relation between them [3].
Ultimately I know that there are lots of ways to give off light. Fire, fireflys, lightning, the sun (if it isn't fire), hot metal, sparks from static electricity, ... There just isn't enough evidence to believe that it's more likely that the stars are the same source as the sun than yet another source.
[1] As it turns out "so far away to be a point light" is the intermediate distance, but that result requires an amount of empty space that I would find unlikely. I haven't checked this but I suspect a statistical analysis would also find it unlikely. Assuming all stars are the same size as our sun, and that they're distributed uniformly in space. Given that I count the stars and come up with a reasonable minimum and maximum distance bound from their brightness, I suspect it is extremely unlikely that there are as many as there are but none close enough to be noticeably brighter. This result (assuming it is true) is of course the result of the fact that many stars are far larger/brighter than the sun, so we're actually sampling from a much larger volume than my naive estimate suggests.
[2] I'm not sure I fully understand this one... the sun appears yellow because of some quirk to do with the light the atmosphere lets in, but why doesn't that make the other stars yellow too?
> why doesn't that make the other stars yellow too?
Most stars appear white/bluish because they are too dim for our colour receptors to perceive. The spectra arriving at our eyeballs is consistent with what you would expect given the type of star, redshift, and atmospheric conditions, but the perceived colour is not.
Re [1] The situation is even worse, when telescopes became available it was discovered that the stars are specifically not point sources. It's just an optical phenomenon, but this was another serious obstacle.
By watching solar mass ejections you can see how fast they leave those in transverse directions, and assuming those directed at us (whose speed we can't track by watching) go the same speed, we can measure how long they take to generate an aurora.
One thing he sort of implies but doesn't directly state -- which I think a lot of people don't know -- is that it's impossible to measure the "one way" speed of light. We can only measure the speed it takes for light to go "there and back". It's possible (but not likely), that light goes faster in one direction than in another direction, and AFAIK, there's no possible way to measure it. You'd think you could do it based on clock synchronization, but clock synchronization itself depends on the assumption that the speed of light is equal both directions.
Isn't this essentially essentially the ether theory of light? You can measure the round trip of light along two different axis. If the speed of light was dependent on direction, you would expect these results to differ.
It is possible that physics conspires such that the speed of light is direction dependent, but that it averages out if half your path is the exact opposite direction from the other. I think this can be excluded by comparing more complicated paths; although the nessesity for it to form a closed loop might be give physics an unavoidable out if it really wanted to mess with us.
There are also theories where the speed of light differs based on direction; but space itself differs in the same way, canceling the effect. These are fundamentally equivelent to a theory where both are constant.
No, it is not the ether theory of light, and that is a magnificent question: This idea was settled by Mickelson/Morley, who not only measured the round trip in one direction, but measured it in several directions, and found the speed of light to be invariant. For which Albert Einstein received the Nobel Prize for his theory of light.
Later, Richard Feynman used first principals to both confirm this for Enistienien physics, and break it for quantum physics.
The best reference for this work is not the classic experiment, but on Henry Cavindish's balance, which led to the calculation of G, the gravitation constant to 7 digits of accuracy, based upon the speed of light calculated to 9+ digits of accuracy.
The speed of light is invariant: What you the observer actually see, is a frame of reference in space-time, which transforms the space, so that light still travels as fast as it always does, but the space around it is transformed.
There have been a few theories of exceptional note: Sir Fred Hoyle solved Einsteins equations for an invariant size of the universe based on a shrinking frame of reference, and found no contradictions. Hence the wimper theory of cosmogony. I count myself as pretty bright, on this subject, able to argue the point rather succinctly, but I never claim to hold a candle and a mirror ( Cavendish ) to Henry Cavendish, nor Sir Fredric Hoyle: You want to get the real brilliance of this total failure:
"The Michelson-Morley Experiment (MMX) tried to prove the existence of ether, but they did not observe the movement of interference fringes, which led to the assumption that the speed of light is constant in the inertial reference frame, which is also the theoretical basis of Einstein's special relativity (SR)."
It failed to prove the existence of ether. Failed. Richard Feynman also found that for Eisensteinian physics, this was also true from first principals. This is really one of the most brilliant failures in the history of Physics.
“Success is the ability to go from failure to failure without losing your enthusiasm”
― Winston Churchill
It's impossible to measure because it has no real existence. The one-way speed of light is as metaphysical of a quantity as the British pound. Numerical speeds can be whatever you want them to be in an arbitrarily curved coordinate system - and the speed of light is defined in the "flattest" one of them.
Or 1.27 USD. Today. According to Google. Which is pegged to some market rate at some time. Which may differ based on your exact location and the conditions in the area. And is expected to be different a short time from now.
I think we need an investigation into why the British Pound isn't allowed to float.
The fixed exchange rate between pounds and kg is obsolete and inappropriate for a modern economy and is the kind of thing BREXIT was supposed to free us from.
Thats, you, what? The british pound is a currency, it is fiat, its exchange value freely floats against other world currencies, it has no objective measure in mass of anything.
Oh, how exciting: there are special units of measure for currants, as there are for wood, paper, gold, and so on? Is the the same in all regions where currants are cultivated?
It's wonderful that we have different miles and feet for different purposes, and even different exchange rates between them.
Let the Europeans suffer under the yoke of the rigid and procrustean french measurement system. Let freedom of expression flourish!
Not sure if this is a joke about weights changing over time or in different places due to gravitational differences - but if you mean mass that was true until fairly recently, the kg is no longer defined by the mass of a specific physical item.
A gram is the division of a standard Kilogram (Kg ) into 1000 divisions. It's a poor description to both be circular about it, but the Kg is the standard measure of mass. Look to The definition of the standard kilogram.
"Since the revision of the SI on 20 May 2019, we can now compare the gravitational force on an object with an electromagnetic force using a Kibble balance. This allows the kilogram to be defined in term of a fixed numerical value of the Planck constant, a constant which will not change over time."
"A Kibble balance is an electromechanical measuring instrument that measures the weight of a test object very precisely by the electric current and voltage needed to produce a compensating force. It is a metrological instrument that can realize the definition of the kilogram unit of mass based on fundamental constants."
"One important reason for the change is that Big K is not constant. It has lost around 50 micrograms (about the mass of an eyelash) since it was created. But, frustratingly, when Big K loses mass, it's still exactly one kilogram, per the current definition. When Big K changes, everything else has to adjust."
Speed has no existance in space, it requires the passage of time. The one way speed of light can be measured, and is very important to the design of curcits. Anytime you wish to argue this point, take it up with RtAdrm Grace Hopper. I count myself as very very bright, but I do not hold a burning punch card to Hopper.
"Since 1 July 1959, the international avoirdupois pound (symbol lb) has been defined as exactly 0.45359237 kg. In the United Kingdom, the use of the international pound was implemented in the Weights and Measures Act 1963. (a) the yard shall be 0.9144 metre exactly; (b) the pound shall be 0.45359237 kilogram exactly."
"The kilogram is defined by taking the fixed numerical value of the Planck constant, ℎ, to be 6.626 070 15 × 10-34 when expressed in the unit J s, which is equal to kg m2 s−1, where the metre and the second are defined in terms of the speed of light, , and the hyperfine transition frequency of the caesium-133 atom..."
Nothing new. Rando hacker news poster, vs say... the International Standards Organization on Weights and measures. Hmm... I am going to place my faith in say... a group of people who's degrees far outnumber most of the colleges I studied at.
No, the speed of light is not defied in the "flattest" one of them. Please do your homework. "The speed of light is a universal constant denoted by c."
In my second college physics class, the final exam was one single question: "Derive the speed of light." I got a grade of 4/10, which put me at the top two students in the class. The class was a 5 1/2 month exercise in brutality of math. I would suggest you get a few college physics classes under your belt.
Well, how about this: I have a central facility. In that, I synchronize several clocks. I then slowly move them to satellite facilities in opposite directions. I don't move all the clocks by the same path - some go via triangular routes rather than directly.
If all the clocks agree at the satellite facilities, then I have established that space is isotropic for the slow transport of clocks (or at least, it is isotropic for the paths chosen - a skeptic can always device a "sufficiently smart anisotropy" that would appear to be isotropic for the paths chosen). Per the article, that was one of the assumptions that couldn't be trusted, but if we can experimentally establish it, we can trust it.
We now have synchronized clocks at the two satellite facilities. (We know they're synchronized because we established that space is anisotropic to the slow transport of clocks, and also because at least some of the clocks were transported with identical profiles in opposite directions.) We can now use time of receipt minus time of transmit to establish the one-way speed of light.
> If all the clocks agree at the satellite facilities
The idea is that you can't know this. You're somewhere in the middle receiving messages from all the clocks, and you can't tell if they're synchronized unless you've already defined the speed of light between you and each clock.
Perhaps I said that badly. "If all the clocks agree at satellite facility A, and all the clocks agree at satellite facility B". I'm not comparing clocks at A with clocks at B.
Second, I was thinking of labs perhaps tens of km apart. You can have people at the center, and at satellite facility A, and at satellite facility B.
Here's the problem: you can only observe a remote clock, or any remote object that light from your source reached, at the speed of the light that traveled back from it.
Put another way: the speed of any signal or causality coming back from your measuring device is always a factor with no way around that.
He is just logging timestamps of when the signal arrived. It shouldn't matter if the timestamp gets back to the central location by carrier pigeon. But maybe the catch is that it doesn't matter how slowly he moves the clocks into position, they'll always be skewed by time dilation.
> But maybe the catch is that it doesn't matter how slowly he moves the clocks into position, they'll always be skewed by time dilation.
I dealt with that by moving the clocks with identical velocity profiles, so time dilation should be the same...
Unless time dilation is anisotropic. I dealt with that by sending multiple clocks, with some sent on triangular routes and some direct. In more detail:
C
A B
D
If I send a clock from A to C to B, and a clock from A to D to B, and the two clocks arrive with the same time, then I have evidence that time dilation is anisotropic (for at least those two routes). I don't necessarily expect that they have the same time as a clock sent direct from A to B - they have an additional acceleration, from the change of direction at C or D, and they have more time at velocity, because of traveling the longer distance. I think I said that very badly in my first post.
But the point is, if I can show that time dilation is anisotropic, then the clocks that went direct from A to B, and the clocks that went the same distance in exactly the opposite direction, should have the same time on them.
> If I send a clock from A to C to B, and a clock from A to D to B, and the two clocks arrive with the same time, then I have evidence that time dilation is anisotropic (for at least those two routes).
You mean isotropic, and you don't really. D->B is the same as A->C and C->B is the same as A->D; whatever clever path you come up with, a clock going from A to B will end up having had vertical movements that sum up to 0. If moving up induces some extra time dilation and moving down reduces it, or vice versa, you'll never be able to detect it; ultimately you can only ever make measurements when you and your clocks (and/or signals) have moved in closed loops, however squiggly.
OK, so that diagram was intended to be horizontal, not vertical. Obviously you want to minimize vertical movement as much as possible.
But I see what you mean about the sides (as drawn) being parallel.
And, yes, I meant isotropic, not anisotropic. Embarrassing.
OK, how about this: I have an equilateral triangle, with vertices A, B, and C. I synchronize clocks four clocks at A. I send one clock to B directly, and one to C and then B. I send one clock to C directly, and one to B and then C. I do the same from points B and C. Then, I can look at the difference between clocks that came direct and clocks that came the long way. If all the differences are the same, then I can say that going A-to-B-to-C has the same effect as going A-to-C-to-B or B-to-A-to-C or any other route. Doesn't that show isotropy?
> Then, I can look at the difference between clocks that came direct and clocks that came the long way. If all the differences are the same, then I can say that going A-to-B-to-C has the same effect as going A-to-C-to-B or B-to-A-to-C or any other route. Doesn't that show isotropy?
Again, no, because you can only measure around the full loop. Any clock you can compare has gone just as far east as it has gone west, just as far north as south, and just as far up as down. You can rule out some particular kinds of anisotropy, but there are possible patterns that just wouldn't show up.
How do you measure if the clocks agree or not after you move them? You can try and synchronize all the moved ones at point B, but how do you measure their relative timing to A clocks without relying on the speed of light between A and B.
Synchronize A & B in one location. Move A & B apart in a careful manner. Send light pulse from A and record time-stamp on A's clock when pulse sent. When pulse is received at B, record time stamp on B's clock. Return clocks A & B together (in a careful manner) to confirm they are still in sync. Compare time stamp between A's transmission, and B's reception. Who knows, maybe when you bring them together, clocks A and B aren't in sync, due to some twin-paradox thing. Maybe you can't be careful enough.
> Synchronize A & B in one location. Move A & B apart in a careful manner.
Doesn’t matter how careful you are, SR tells us moving clock will become unsynched. The amount of “unsynching” depends on c (see Lorentz factor) so if c is different in forward vs reverse direction, bringing the clocks back will even it out
I also feel like there is a hidden assumption here, that people were interested in the one-way-speed to see if it is Newtonian additive, like it is "c +/- a tiny little bit from the earth's motion around the sun". It seems like with a sufficiently slow separation of the two clocks, you should be able to see if the you get "0.1c" in one orientation, and "1.9c" in the other. Especially since the Lorentz factor is non-linear [ √(1 - (v²/c²)) ]. Right? ???
> It seems like with a sufficiently slow separation of the two clocks, you should be able to see if the you get "0.1c" in one orientation, and "1.9c" in the other.
No you wouldn’t be able to “see” it. If your clocks are off you dont know that and by how much until you bring it back and compare. That's Special Relativity
"You can't measure one-way speed of light" is formal doctrine in relativity cant, and "true" as far as it goes, in that anything you manage to measure makes no difference without reference to an absolute rest frame. It hinges on formally failing to synchronize clocks at a distance from one another, and people make hay about that, rather pointlessly. They are really talking about "speed of causality", not light, which happens to go at the same speed; and one-way speed of causality doesn't mean anything.
But the cosmic microwave background defines an absolute rest frame that we happen to be measured going 600km/s against. And you can measure one-way speed relative to that, provided you admit that, yes, you really can synchronize displaced clocks entirely adequately for the purpose, as we do absolutely routinely for GPS satellites in wacky orbits thousands of miles apart. Your measurement had better have the time-to-traverse from you to a clock indicating an extra 600km/s in that direction, and short the same in the other direction, and equal toward clocks placed at right angles to those directions. If it doesn't turn out to match CMB asymmetry, you probably get a Nobel prize.
On the subject of the CMB, some of the measurements show a bias exactly aligned with the plane of the solar ecliptic. This is called the "Axis of Evil" in astronomy circles, and is rarely mentioned as it is deeply embarrassing to cosmologists. "Cosmologists are often in error, but never in doubt." -- Lev Landau.
You make an excellent point but as it turns out the CMB would still appear uniform even the speed of light was not the same in all directions. The reason is that if the speed of light is different in one direction, then the effect of time dilation will also be different depending on direction as well and these two factors cancel one another out resulting in what will still appear as a uniform CMB.
The below paper goes into complete technical details giving an example of the speed of light being c / 2 in one direction and instantaneous in another direction (so that it averages out to c), and how the differing time dilations result an isotropic view of the universe.
Although we can't directly measure the one way speed, can't we at least demonstrate that the speed of light is the same for various arbitrary directions? I'm imagining sending a very brief & well columnated laser pulse aimed at e.g. Pluto, such that we have to "lead" the shot based on light travel time. If the outward bound light pulse travels slower/faster than expected, it will arrive at the wrong time & miss the planet, won't it?
You could repeat the experiment at different times of the Plutonian year to verify other directions, etc..
I think there may be practical problems with this method in terms of creating such a well columnated laser pulse, but in principle couldn't we use it to rule out anisotropic light speeds in several (perhaps most/all) directions?
Is it possible to use redshift of photons from the sun? Say if you know the hydrogen transition line frequency, then measure very precisely the observed frequency from solar photons, you could calculate the redshift. I suppose this would rely on knowing the mass of the sun already as well.
“The main causes of electromagnetic redshift in astronomy and cosmology are the relative motions of radiation sources, which give rise to the relativistic Doppler effect, and gravitational potentials, which gravitationally redshift escaping radiation. All sufficiently distant light sources show cosmological redshift corresponding to recession speeds proportional to their distances from Earth, a fact known as Hubble's law that implies the universe is expanding.”
"gravitational redshift (known as Einstein shift in older literature)[1][2] is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy corresponds to a decrease in the wave frequency and increase in the wavelength, known more generally as a redshift. "
Why doesn't it work to have the emitter and sensor together at the same location, synchronize them at that moment, and then move them apart a distance so large the initial delay no longer matters, before running the test? Do we not have accurate enough clock sources to keep the synchronization?
the assumption that time dilation is identical for the same acceleration profiles is equivalent to an assumption of the 1 way speed of light. if you do the full math with a non constant light speed, you find that degree of asymmetry in the 1 way speed of light directly cancels the difference in time dilation
How can that work? I can control both how hard I accelerate, and how far I go with constant velocity. So I can control how much of the clock skew is due to acceleration time dilation. That can't match the speed difference for all possible experimental setups.
For experiment 1, say I accelerate the clocks at 0.1 g for 10 seconds, then drive with constant velocity for 1 hour, then decelerate at 0.1 g for 10 seconds. That acceleration time dilation exactly matches the change in propagation time due to the difference in c? Fine, I'll give you that.
So for experiment 2, I drive at constant velocity for two hours. I've kept the acceleration time dilation the same as in experiment 1, but doubled the distance. If the change in propagation time matched in experiment 1, it can't match now.
Or, for experiment 3, I accelerate at 0.1 g for five seconds, reaching 1/4 of the previous velocity, then drive for two hours. Now the propagation difference is the same as in experiment 1, but the acceleration time dilation is different.
So how is this going to come out "you can't tell" in all three experiments?
1 hour according to who's clock? The point is that if the 1 way speed of light is different, the clocks traveling in opposite directs will measure the 1 hour passing at different speeds.
The (non-GR) time dilation rate difference will be proportional to v^2/c^2 (neglecting 4th order terms and higher). The total time dilation difference will be that times the time in transit, which is d/v (with d being the distance traveled). So the total time dilation difference will be proportional to vd/c^2. By making the velocity small, I can make that term as small as I want.
But what if I don't know what c is? Doesn't matter. I know it's much, much larger than the velocity I'm moving at.
So I don't buy the "according to who's clock" argument. I can make it so that it doesn't matter, just by going slow enough.
the part you're missing is that during the acceleration phase, if the 1 way speed of light is different, the velocities achieved relative to a stationary observer by accelerating for t seconds relative to the clock that is doing the acceleration will be different depending on the direction of acceleration.
To what order in v? I'd like to see your math, but I'm pretty sure I can still minimize that by going slow (relative to the speed of light in any direction).
I can't find the link offhand, but he's discussed this on another page, or possibly in one of his videos (which would explain why I couldn't find it in 30 seconds).
I believe this is an attempt at vulgarization, as the exact opposite effect happens for anglo-saxon non-scientist readers when they come across metric units...
Nah, we don't do anything like as consistent and understandable as that. We use a random mixture of imperial and metric measurements where the "right" one to use in each context is determined by cultural norms.
E.g. we measure petrol in litres, beer in pints, wine in litres (but actually centilitres), long distances in miles, short distances in metres, weights of people in stones, weights of everything else in kilograms (except home cooking which is split between imperial and metric) and fuel efficiency in miles per gallon.
The fuel efficiency one is really dumb given that we buy fuel in litres.
So, without reading, here are my uninformed thoughts on how I would do it:
You could probably figure out the distance by using a technique we use to figure out the distance to nearby stars, measuring the change in position in the sky relative to very far away stars. I think you'd only need to observe two stars to figure out the distance.
Could also use pulsar timing like gps signals to track the location of the Earth throughout its orbit.
Could also take measurements after launching a pair of space probes away from the earth.
Unfortunately, the parallax method depends on knowing the diameter of Earth's orbit, which is (except for a factor of two) the value we are seeking. There's also the issue that the change the Sun's position with respect to the stars over six months is about 180 degrees (with some fluctuation, perhaps, depending on where the earth is in relation to its orbit's major axis when the measurement begins), and will be regardless of the Sun's distance.
The distance of Venus was measured by the parallax method during a transit, with a baseline on the Earth's surface. This then yields all the other planets' distances from their orbital periods. This has me wondering why this had not been done for the Sun's distance, and perhaps the first reason to be considered is the difficulty of observing the Sun eclipsing distant stars.
Update: According to Wikipedia [1], Jeremiah Horrocks came up with reasonable figures for both the size of Venus and the distance of the Earth from the Sun from a single observation of a transit, but the article says he made use of a false premise, so does that just mean he was lucky?
https://phys.org/news/2015-01-distance-sun.html