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.