CU\'s MAVEN mission is currently making measurements of the Martial upper atmosp
ID: 2077006 • Letter: C
Question
CU's MAVEN mission is currently making measurements of the Martial upper atmosphere in an effort to determine how much atmosphere could have been lost to space over time. The radius of Mars is ~3400 km and its gravitational acceleration is ~3.7 m/s^2. a. The measurements indicate that the present-day escape rate from the atmosphere is on the order of 10^26 particles per second, and perhaps higher. Let's assume every one of those particles is an atomic oxygen on that came from a CO_2 molecule, and that the escape rate has been constant for the past 4 billion years (almost certainly a huge underestimate!). How much atmosphere in units of mbar, has been lost to space over the past 4 billion years? b. There was clearly liquid water flowing on the Martian surface earlier in its history. If, contrary to part (a), we assume every escaping particle originally came from a water molecule, then how thick is the global layer of surface water represented by this loss (The density of water is 1 g/cm^3)Explanation / Answer
escape rate = 1.0e+26 particles/s (oxygen atom)
total particle last over 4 billion years
= 1.0e+26 *4.0e+9 *365*24*3600 = 1.26144e+43
mass of oxygen atom = 15.994915*1.660538e-27 kg
Total mass of atomosphere lost = 1.26144e+43*15.994915*1.660538e-27 kg
= 33.50 e+16 kg
gravity on Mars g = 3.7 m/s2
weight of the matter lost = mg = 33.50e+16/3.7 = 123.965e+16 N
Mars radius R = 3.4e+9 m
surface area A = 4*3.14*(3.4e+6)2 = 1.453e+14 sq.m
pressure lost = F/A = 123.965e+16/1.453e+14 = 8.53e+2 N/m2
= 8.53 mbar ( 1 bar = 1.0e+5 N/sq.m)
2) If the oxygen has cpme from water molecule then for every oxygen atom 1 water molecule is lost
number of water molecules lost = 1.26144e+43
mass of water lost = 1.26144e+43 *(18/6.02e+23) ( one mole water contains NA = 6.023e+23 molecules)
= 3.77e+20 gm
volume of water lost = 3.77e+20 cc = 3.77e+14 cu.m
Thickness of water layer lost = 3.77e+14/1.453e+14 = 2.6 m