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    Default Measuring an unknown world / solar system

    A thought experiment. You find yourself on an unfamiliar planet in an unknown solar system. Instead of wondering how you survive (magic) you set out to measure out your planet and the rest of the system.
    How could you go about it? What would you need? What would be the mot low tech but sufficiently accurate methods to get things like size of your planet, mass of your planet, distance to the star, moon, other planets....
    How different would things be if you'd not be sure fundamental constants like G or c still apply?

    I ask because I genuinely have little idea where I'd start or what would be the simplest thing.
    I guess a first goal could be estimating the circumference of the planet based on falling shadows a la... who did that? Pythagoras? Some Egyptian? I forget. But after that I'm rather stumped.
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    Default Re: Measuring an unknown world / solar system

    It was. This Wikipedia article has some information about that experiment.
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    Default Re: Measuring an unknown world / solar system

    My favorite part is how they measured the distance of Alexandria to Syene. They had a guy walk there while counting the steps his camel made. Camels have ridiculously even steps.
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    Default Re: Measuring an unknown world / solar system

    If there are moons with vaguely similar orbits to Earth's Moon, you can estimate their distances by:
    1. measuring parallax from widely separated observing points; or
    2. measuring parallax between different times of day (diurnal parallax); or
    3. measuring the size of your planet's shadow on a moon during a lunar eclipse

    The latter two methods need your previously estimated diameter of the new earth.
    Or you could use radar, if you are willing to use 20th century technology.

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    Default Re: Measuring an unknown world / solar system

    The repair manual for the FC3000TM Time Machine will be helpful, depending on the state of the planet you arrive on.

    Other than that, you'll mostly need a telescope, a protractor, a ruler/tape measure, Algebra, Trigonometry, and some Calculus. And time. Lots of time.

    For the mass of the planet, you'll need a stopwatch and a ruler (and the planet's approximate diameter, which Farothel already told you how to get). You'll want to measure the acceleration a dropped object experiences at 'ground' level, and measure again at a higher (or lower) elevation. Using the difference between those two accelerations you can calculate the mass of the planet.

    After you've figured out the mass of the planet (should we call it Planet Bob?), you can calculate the distance to any local moons by calculating the time it takes each moon to orbit Bob (you can get this by tracking the moon against the stars behind it). Using the mass of Bob you calculated previously, you can then plug back into Newton's Laws of Motion to get a pretty accurate distance to the moon.

    For the distance to the sun (let's call it "Suzy"), you wait until the moon is exactly half full (or half empty, depending on how you look at it). Using your protractor, you measure the angular distance between the two. You now have a right triangle, and you know two of the angles and the length of one of the legs. You can then calculate the other angle (the three angles add to 180o) and the length of the other leg, which equals the distance between Bob and Suzy.

    To get the mass of Suzy, you need to know how long it takes Bob to go around once. Track the locations of the stars visible in the night sky to determine when you've completed one orbit. With that (and the distance to Suzy you already calculated) and Newton's Laws you can figure out how massive Suzy is.

    To get the distance to inner planets, measure the angular distance between Suzy and the point in their orbit when they are farthest from Suzy. If your telescopes are really good, you should be able to tell that they are at their "half full" phase at that point. A bit of Geometry (or Trig) later, and you have their orbital distance.

    Outer planets are a bit trickier, but by carefully plotting their location in the sky you can determine their orbits. Tycho Brahe did this several hundred years ago. Kepler used his notes to determine that planets orbit in ellipses instead of circles.

    Edit: Here's a website you might find useful: https://www.universetoday.com/117843...ce-to-the-sun/
    Last edited by Lord Torath; 2019-06-19 at 12:38 PM.
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    Default Re: Measuring an unknown world / solar system

    Quote Originally Posted by Lord Torath View Post
    The repair manual for the FC3000TM Time Machine will be helpful, depending on the state of the planet you arrive on.


    For the mass of the planet, you'll need a stopwatch and a ruler (and the planet's approximate diameter, which Farothel already told you how to get). You'll want to measure the acceleration a dropped object experiences at 'ground' level, and measure again at a higher (or lower) elevation. Using the difference between those two accelerations you can calculate the mass of the planet.
    If you already know G&r (and the base units) then you only need one acceleration (I.E at ground level).

    Doing more will allow you to check that you really did know, and catch a few anomalies (e.g. if centre of mass and centre of volume didn't coincide).

    Although to reliably measure the difference, then the height elevation you need is significant (~3km for a 1% change in g on earth), so I think you'd need something more subtle...

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    Default Re: Measuring an unknown world / solar system

    Quote Originally Posted by Lord Torath View Post
    For the mass of the planet, you'll need a stopwatch and a ruler (and the planet's approximate diameter, which Farothel already told you how to get). You'll want to measure the acceleration a dropped object experiences at 'ground' level, and measure again at a higher (or lower) elevation. Using the difference between those two accelerations you can calculate the mass of the planet.
    A pendulum should be a more accurate way of measuring gravity. You'll still need a ruler and a timing device, but you won't need to be as precise on the timing. To avoid modern technology use a pocket watch with a torsion pendulum, or your own resting heart rate. Changes in fundamental constants will screw this up though. If mass changes then the torsion pendulum will be off, and any such change might be quite exciting (or fatal) so will mess with your resting heart rate.
    Last edited by Excession; 2019-06-19 at 06:40 PM.

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    Default Re: Measuring an unknown world / solar system

    The distance from your planet to its sun is going to be the hardest one. It's not too hard to get the relative distances of all of the planets, but you still need to set the scale (i.e., you can get all distances in AU, but you don't know how big an AU is). You can get an extremely imprecise (as in, the error bars are likely to include infinity) estimate from the angle between a moon and the Sun at exactly half-moon, but that's a difficult measurement (and depends on you even having a moon, which you might not). If you have a telescope and can observe the moons of some other planet, and know the speed of light, you can try using Ole Roemer's observation in reverse, but Roemer's observations were only good to within about 50%. Beyond that, it's either invent very good chronometers and wait for an inner planet to transit (if you have any inner planets), or invent radar powerful enough to reach across worlds.

    For the mass of your planet, it's much easier to use one pendulum to get g (the gravitational field), and measure the planet's size using the shadows method. And if you're really paranoid about the possibility that G (Newton's constant) might be different, you'll need to repeat the Cavendish experiment (measuring the force between a couple of cannonballs in the laboratory); for any other experiment you conduct, all you'll ever find will be the product of G and some astronomical mass.
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    Default Re: Measuring an unknown world / solar system

    You should look into the history of the accurate determination of longitude.

    I highly recommend the book Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time by Dava Sobel (2007.)

    You can look up the technical details of all the experiments, observations, and inventions on Wikipedia, but I also highly recommend the way Dava Sobel puts together the essentials and tells the story.
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    Default Re: Measuring an unknown world / solar system

    First off, thanks for all the input! I'll have to check the links when I have more time.

    Ah, right, I should have remembered getting my planetary mass with a pendulum as long as I know G and have found the planet's size.

    Is there another method you could use to measure the planet's circumference? Not that the shadow isn't accurate or primitive enough, but still. I feel like you could turn the 'how far is the horizon' calculation around but it seems you'd need really precise methods (or large objects) to get good results from them.
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    Default Re: Measuring an unknown world / solar system

    Quote Originally Posted by Kato View Post
    First off, thanks for all the input! I'll have to check the links when I have more time.

    Ah, right, I should have remembered getting my planetary mass with a pendulum as long as I know G and have found the planet's size.

    Is there another method you could use to measure the planet's circumference? Not that the shadow isn't accurate or primitive enough, but still. I feel like you could turn the 'how far is the horizon' calculation around but it seems you'd need really precise methods (or large objects) to get good results from them.
    The distance to horizon method is kind of tricky. You're right that you're going to need some very precise instruments (you need that for the distance to the sun, as well). You're also going to need a perfectly flat spherical bit of land to get an accurate measurement. What that generally means is a lake or sea, and it's very hard to measure distance across the surface of a liquid. You could measure the height of a tree just visible over the horizon across a lake. But you can run into air distortion effects in your line of sight, and the lake needs to be at least a couple of miles across. And you need to be able to tell exactly how far away that tree is, which can be tricky with primitive measuring tools.
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    Default Re: Measuring an unknown world / solar system

    Quote Originally Posted by Lord Torath View Post
    The distance to horizon method is kind of tricky. You're right that you're going to need some very precise instruments (you need that for the distance to the sun, as well). You're also going to need a perfectly flat spherical bit of land to get an accurate measurement. What that generally means is a lake or sea, and it's very hard to measure distance across the surface of a liquid. You could measure the height of a tree just visible over the horizon across a lake. But you can run into air distortion effects in your line of sight, and the lake needs to be at least a couple of miles across. And you need to be able to tell exactly how far away that tree is, which can be tricky with primitive measuring tools.
    Hm... Excluding having a perfect spherical planet, I wonder how well a buoy could work. I mean, it won't get me the perfect value but I wonder if it will work better than the shadows (if I don't have a camel to perfectly measure dozens of miles)

    Also, any better way to get the size of other planets than knowing the distance and having a really good telescope?
    I guess I can get their mass if they have visible moons with a bit of patience and clever math (well, most is clever math)
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    Default Re: Measuring an unknown world / solar system

    Radius and mass of planets will both depend on knowing their distance: The mass calculation requires knowing the size of the moons' orbits, which again requires distance.

    Although, come to think of it... If you can get a telescope with good enough resolution, and a spectroscope, and can get a recognizable spectrum off of a moon, to enough precision to get a Doppler shift, you could also determine the moon's orbit (and hence its distance, and hence all the other solar system distances) that way. It probably wouldn't be as precise as radar or a transit of an inner planet, but it probably would take less tech. It's easiest if the moon's orbit is very close to circular, but fortunately, that tends to be true of most moons.
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    Default Re: Measuring an unknown world / solar system

    Quote Originally Posted by Kato View Post
    Hm... Excluding having a perfect spherical planet, I wonder how well a buoy could work. I mean, it won't get me the perfect value but I wonder if it will work better than the shadows (if I don't have a camel to perfectly measure dozens of miles)

    Also, any better way to get the size of other planets than knowing the distance and having a really good telescope?
    I guess I can get their mass if they have visible moons with a bit of patience and clever math (well, most is clever math)
    I think almost none. Kind of by definition anything sight based will need to have to resolve something planetary size.
    Anything gravitational based will be independent of radius (unless you know the density so mass and radius are linked)
    They can conclude things about stars though.
    One possibility would be if you know the parameters of a moons orbit, and you can measure the time it takes to eclipse the planet. This would probably still need a good telescope, but might be a bit more accurate to measure.
    Another might be via light luminosity (the temperature/peak wavelength will depend on the distance).

    Finally there must be some atmospheric reactions that depend on 'g' and give a characteristic wavelength, maybe something that is indirectly observable.
    Spoiler: A possible option on that lines for god-like observers
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    Any hydrogen must be in a potential that varies with depth. The electron wavefunction is effectively slightly pulled towards the planet. This would make the energy levels ever so slightly different (the difference would be ridiculously many orders of magnitude less than a myriad other factors affecting it (let alone the measurement itself), including quantum-uncertainty effects, sods law it's probably comparable to the effect on the photon of leaving the planet).

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    Default Re: Measuring an unknown world / solar system

    Quote Originally Posted by farothel View Post
    It was. This Wikipedia article has some information about that experiment.
    Quote Originally Posted by Fyraltari View Post
    My favorite part is how they measured the distance of Alexandria to Syene. They had a guy walk there while counting the steps his camel made. Camels have ridiculously even steps.
    They knew Earth's diameter long before Eratosthenes as this machine testifies. The Antikythera mechanism required thousands of years of observations, hundreds of years of mathematics, and decades of craftmanship. And if they could build it, they knew enough to calculate the Earth's diameter and the distance to the Moon.

    Earth's diameter is easy to calculate if you don't happen to have a well handy. Just have two observers is different cities measures the azimuth and zenith of a lunar eclipse. The difference in its zenith is the difference in the cities latitude, which verifies the measurements. The difference in azimuth is the difference in the cities longitude. Yes, the ancients knew the relative longitude of their cities.

    To find the distance to the Moon, they would have measured the angles between the lunar eclipse and nearby stars. The difference in two is the parallax and they could have calculated the distance to the Moon with it.

    The distance to the Sun can be calculated by knowing the angle between the Sun and Moon, the distance to the Moon, and the angle of the Moon's terminator. This is another parallax. But I don't know if the ancients actually did this.
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