Space Simulators in Space Science Education in Hungary (2): Hunveyor Orientations and Astronomical Observations on Martian Surface

Abstract

We developed our Hunveyor simulator, a planetary lander, with capabilities for observations and orientations on the Martian surface. We studied also orientation and space station activities at the Lagrangian points of the Earth+Sun or Earth+Moon system. The basic coordinate transformations were formulated in this course and the space-orientation requirements for planetary surface robotics were also studied. Introduction: Some of us on the Eotvos University who had the possibility to attend International Space Camp, Huntsville, Alabama, (and MSFC) had learned there that various programs with space simulators are the most effective teacher trainings and student works for space science education. Further developing our Hunveyor system [1,2] we studied: how to orient space probe instruments on Martian surface. How the known terrestrial coordinate systems change and how to develop the necessary transformations for astronaut simulator work. What is a useful spatial orientation for a space station in Lagrangian points, where no local visible bodies except light points on the sky can preserve the environment we acustomed on Earth. Mars surface works: The most important think to introduce students to living conditions on Mars is to learn the spatial orientation of the planetary body: that is the orientation and motions of the night sky. Therefore first the real North Pole coordinates of Mars were used to build a II. Equatorial coordinate system for Martian astronauts. Many local calendar parameters are similar or well comparable to the terrestrial ones, so the transformations are simple, (the length of the day = sol is almost 24 hours, the length of a month is almost twice of the terrestrial ones) except the II. Equatorial coordinates. Martian North Pole: Imagine that our spacecraft landed in the Northern Hemisphere of Mars, in the Chryse Plain, at the vicinity of the 40 North latitude and 45 Western longitude, near to the mouth of Kasei riverbeds (almost Viking-1 position). In reproducing the Horizontal and I. Equatorial coordinate systems, the position of the Martian North polar axis on the sky is neeeded. It has been measured on the basis of Viking-1 and -2, and also Pathfinder missions, and it is 317,7 degrees RA (21 hours and 8 mins in traditional RA units) and +52,9 degrees declination given in our terrestrial system [3]. This position is near to the North America Nebula and Deneb in the Cygnus constellation. Therefore the role of Ursa Minor in spatial orientation on Earth (North. Hempisph.) can be replaced by Cygnus on the surface of Mars (North. Hemisph.) Coordinate transformations to Mars: In spherical coordinate transformations the two N. polar points (of Earth and of Mars) and any of the star positions give the basis of the spherical triangle, where to give the spherical sinus and cosinus theorems. Fig. 1. Transformations of the II. Equatorial system of Earth to that of Mars. The arc distance of the two poles is: Q, declination in Terrestrial system DE, in Martian system DM (Fig. 1.) The corresponding complement angles (to 90 degrees) form the two arc-sides of the celestial spherical triangle, together with Q as the third side. The II. Equatorial longitudes of this star are RAE * and RAM * According to sinus theorem: sin (90-DM) = sin (180-RAE*) sin (90-DE) sin RAM* and cosinus theorem: cos (90-DE) = cos (90-DM). cos Q + sin (90-DM) . sin Q . cos RAM* Because RAE * and RAM * are measured from the spherical circle, which connects the two poles, the real RAE and RAM can be transformed by the RAE * = RAE + μ (mu) and the RAM * = RAM + (lambda) formulas, respectively for Earth and Mars (Fig. 2.) Lunar and Planetary Science XXXIV (2003) 1166.pdf