= The View from Deimos and Phobos =

The mean radius of [[http://wikipedia.com/wiki/Mars | Mars ]] is 3389.5 km, varying from 3396.2 km at the equator to 3376.2 km at the poles.  This page computes the fraction of a smooth spherical Mars visible from Deimos, Phobos or a single artificial satellite, as a function of elevation angle above the horizon.  

The real planet has topography, so the equatorial side of high latitude mountaintops will have more visibility, the poleward sides less, valleys mostly less.  An array of relay satellites can offer almost complete visibility, except for the bottom of steep trenches.  Temporary relay towers can be placed at the rim of trenches while they are occupied by robots.  

Mars exploration will be complicated, but does not require line-of-sight to either Martian moon; not even the Sun if the robots are powered by isotope or fission thermal generators.   

With an axial tilt of 25.2 degrees, and a 686.97 (Earth) days per year, Mars will have polar winter darkness times about twice as long as the 23.4 degree tilted, 365.24 days per year Earth.  Mars polar surface rovers will spend half their time operating at night, with neither Mars moon visible; some important (and so-far undiscovered) surface phenomena may not be visible at any other time, so relay satellites in high inclination are essential for a complete scientific exploration of Mars.  This transforms the question of visibility to '''which Martian moon provides the lowest round-trip speed-of-light delay to the Martian poles with a smallish number of relay satellites?'''  A Deimos station may be able to see more high-altitude relay satellites.

The Martian moons are approximate ovoids, tide-locked and synchronous with their long axis pointed towards Mars.  Important characteristics as manned or "big computation" outposts are:

||        ||<-3:>   Orbit Radius (km)   || Period||<-2>Orbit Speed,Inclination||<-2>Body Radius (km)|| Mass  || Gravity || Escape ||
||        ||Periapsis||Apoapsis||Semimaj|| (sec) || (km/s)    || degrees   || Maximum || Minimum || (kg)     ||   gee   || V (m/s)||
|| Phobos || 9234.42 || 9517.58||9376.00||27553.8|| 2.138     ||1.093 Mars || 27      || 20 × 24 || 1.066e16 ||  5.8e-4 || 11.4   ||
|| Deimos || 23455.5 || 23470.9||23463.2||109123 || 1.352     || 0.93 Mars || 15      ||12.2 × 11|| 1.476e15 ||  3.1e-4 || 5.56   ||
||<-12> '''Example Relay Satellites''' . . . . . . Mars Standard Gravitational Parameter = 42828.37 km³/s², period = (r^1.5) / 32.937 ||
||<-3> 12/sol, 515 km altitude || 3901  ||  7398 || 3.133     ||
||<-3> 6/sol, 2897 km altitude || 6193  || 14786 || 2.630     ||
||<-4)>           '''Mars day:''' (sol) || 88775 || 24.077    ||25.19 tilt || 3396.2  || 3376.2  || 6.417e23 ||   0.376 || 5027   ||

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== Estimated satellite roundtrip relay delay to farside, in seconds ==

Elevation is the minimum angle of the antenna above the horizon, avoiding topographic blockage and atmospheric attenuation.   The Mars atmosphere is thin, but the molecular resonances of CO₂ may make laser communication difficult.

||<-2>               ||<-3:> Elevation = 0 degrees ||<-3:>Elevation = 10 degrees ||<-3:>Elevation = 20 degrees ||
|| Station ||  Relay || Coverage || Hops || Delay  || Coverage || Hops || Delay  || Coverage || Hops || Delay  ||
|| Deimos  ||  6/sol || 0.4276 || 1 || '''0.224''' || 0.3439 || 2 || '''0.274''' || 0.2667 || 2 || '''0.258''' ||
|| Phobos  ||  6/sol || 0.3189 || 1 || '''0.127''' || 0.2342 || 2 || '''0.178''' || 0.1793 || 2 || '''0.162''' ||
|| Deimos  || 12/sol || 0.4276 || 2 || '''0.206''' || 0.3439 || 3 || '''0.207''' || 0.2667 || 4 || '''0.205''' ||
|| Phobos  || 12/sol || 0.3189 || 2 || '''0.109''' || 0.2342 || 3 || '''0.115''' || 0.1793 || 5 || '''0.130''' ||


Multiple relay hops can have nearly zero elevation, but the relays may have latency, congestion, and non-optimal spacing, so these estimates are '''not''' exact.  The farside delays (ranging from 109 milliseconds to 274 milliseconds) must be compensated for by predictive/adaptive software and operator skill.  The delays are smaller than the 600 millisecond round trip ping time halfway around the Earth via GEO comsat, and comparable to the 300 millisecond delay through a chain of MEO relay satellites.  

Deimos delay to farside ranges from 54 to 88 percent slower than Phobos delay because of its greater distance, but its direct coverage without relay ranges from 43 to 27 percent, while Phobos ranges from 32 to 18 percent.  If robotic surface operations are limited to daytime, without relay satellites, they will be frequently interrupted, and human operator time wasted.  Robots and relays maximize human potential.

Spreadsheets (including calculations for dangling loop elevators): [[ attachment:DeimosPhobos.ods | LibreOffice.ods ]] [[ attachment:DeimosPhobos.xlsx | Excel.xlsx ]]