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I'm trying to figure out answer to this task:

At a certain level of development of the Martian civilization, scientists of this planet began to measure distances. Will their measurements be more or less accurate: a) to the planets of the solar system; b) to the nearest stars according to the measurements of earthlings? Consider that the development of the sciences of the terrestrial and Martian civilizations followed approximately the same path.

The Mars's orbit is only different from Earth's by being more elongated. Does it give some advantages?

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    $\begingroup$ I guess the way to go about this is to think of how our methods of measuring distances are depending on the orbit of a planet.. $\endgroup$ Nov 4, 2021 at 15:21
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    $\begingroup$ Hint: How was a parsec originally defined? $\endgroup$
    – Connor Garcia
    Nov 4, 2021 at 15:35
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    $\begingroup$ Oh, I see. So because Mars's orbit is more elongated if the Martians used their average distance to the Sun in parsec they would get greater mistake. $\endgroup$
    – ALiCe P.
    Nov 4, 2021 at 17:59
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    $\begingroup$ @ALiCeP. yes, but instead of "is more elongated" just say "is larger" and instead of "greater mistake" say "a larger motion" or better yet simply "larger parallax". I think you can write an answer to your own question now if you like! :-) $\endgroup$
    – uhoh
    Nov 4, 2021 at 19:38
  • $\begingroup$ A good part of the “cosmic ladder” was figuring the diameter of the Earth, the distance and size of the Moon, and the distance and size of the Sun. Mars has small moons, which might make it more difficult to measure their size and distance. Also, they orbit Mars much faster than Earth’s Moon, adding to the difficulty. $\endgroup$ Nov 5, 2021 at 23:41

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It would be more accurate to determine the parallaxes of stars, and thus their distances from the Solar systerm, from the surface of Mars than from the surface of the Earth.

The orbit of the planet Earth has a semi-major axis of 1 Astronomical Unit (AU).

Imagine that a star is observed at the moment when there is astraight line from the center of the Sun through the center of the Earth to the celestial longitude of the star, i.e. when the star's celestial longitude is directly opposite to the Sun as seen from Earth.

Now imagine that the star is observed 3 months or 1 quarter year before then. The line between Earth and the Sun will be at right amgles to the line between the Sun and the Star, and will be 1 AU long. Imagine that the angle to the star is measured very precisely.

Now imagine that the star isobserved, and the angle to it measured, six months after is angle is measured the first time. The planet Earth will now be opposite in its orbit to where it was six months before, and the line between Earth and the Sun will be at right angles to the line between the Sun and the Star. Imagine that the angle to the star is measured very precisely.

Because of theincredibly vast distances to the stars, the two measurements of the angle to the star should be very slightly different despite being measured from points which are two AU apart. The difference between the two angle measurements is called the parallax of the star, and the parallax can be used to calculate the distance to the star.

The orbit of Mars has a semi-major axis of 1.52 AU. So two measurements of the Angle to a star made 0.94 Earth year, or half a Martian year, apart would be made from positions 3.04 AU apart. That is 1.52 times as far as the baseline used in parallax measurements from Earth, so that will makeparallex measurements a little bit easier and more accurate.

For example, it is a little easier to measure an angle of 0.0015 arc second than an angle of 0.001 arc second.

So it is theoretically more accurate to measure the distances to distant stars from the surface of Mars than from the Earth, although it has not be tried yet.

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  • $\begingroup$ Could you please explain in a little more detail why exactly the measurements made from 3.04 AU apart (1.52 times as far as from Earth's baseline) are more accurate and easy? $\endgroup$
    – ALiCe P.
    Nov 6, 2021 at 6:17
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    $\begingroup$ @ALICe P. I would think that it is obviously easier to measure a larger angle than a smaller angle. Anyway, I added something to that effect to my answer. $\endgroup$ Nov 7, 2021 at 4:58
  • $\begingroup$ You're right, weird that I didn't think of it. Thanks for clarifying this for me once again! $\endgroup$
    – ALiCe P.
    Nov 7, 2021 at 6:56

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