----- Forwarded message from Amara Graps <[EMAIL PROTECTED]> ----- From: Amara Graps <[EMAIL PROTECTED]> Date: Mon, 14 Jun 2004 08:41:08 +0100 To: [EMAIL PROTECTED] Subject: [extropy-chat] Mars and Titan Reply-To: ExI chat list <[EMAIL PROTECTED]>
More about the atmospheres of Mars and Titan.. for curiousity's sake, I calculated the escape velocities and molecular velocities in order to see how well the two bodies kept their atmosphere. The depth of the atmospheric pressure at each body is due to factors I don't know very much about, so I won't talk about that, but perhaps the following equations and numbers are interesting to you. The key to know if a body can keep its atmosphere is a rule-of-thumb: v_escape ~>= 10 * v_molecular velocity. If it is true, then it can keep it, if it is not true, then it cannot. v_escape = SQRT ( (2 * G * M_planet) / R_planet) v_molecular_velocity = SQRT ( (3 * k_b * T_planet) / m_molecular_velocity) G = gravitational constant k_b = Boltzmann's constant The v_escape is the the velocity of escape of any body from the surface (=R_planet) of the planet. The mass of the body on the surface doesn't matter (cancels out). The v_molecular_velocity is the kinetic energy of the molecule, which is strongly dependent on the temperature of the environment. Titan is *much colder* than Mars. Titan ------ Atmosphere ~82% N2 6% CH4 6% Ar Then molecular weight = (.82)(28.02) = (0.06)(16.042)+(0.06)(39.95) = 26.336 amu = 4.375x10^(-26) kg T ~70K M_planet = 1.34x10^(23) kg R_planet = 2.575x10^6 m v_escape = 2.635x10^3 m/sec v_molecular_velocity = 257.38 m/sec 2,635 m/sec >= 2,574 m/sec Yes, can just barely hang onto its atmosphere Mars ---- Atmosphere 95% CO2 2.7% N2 1.6% Ar 0.006% H2O Then molecular weight = (.95)(44.0)+(0.027)(28.03)+(0.026)(39.95)+(0.00006)(18.016) = 43.20 amu = 7.18x10^(-26) kg T ~300 K (>200km) M_planet = 6.42x10^(23) kg R_planet = 2.396x10^6 m v_escape = 5.022x10^3 m/sec v_molecular_velocity = 418.84 m/sec 5,022 >= 4188 m/sec Yes, no problem to keep this atmosphere -------------- So then compare parameters. Mars atmosphere is ~1.5 x more massive by molecular weight than the Titan atmosphere Mars is ~5 x more massive than Titan Mars is ~30% larger than Titan The escape velocity of any object from Mars is ~2x higher than for Titan (5 km/sec vs. 2.6 km/sec). The molecular velocity of the Martian atmosphere is higher than the molecular velocity of Titan's atmosphere (419 m/sec vs. 257 m/sec). * Would Titan be able to keep a Martian atmosphere? Yes. * Would Mars be able to keep a Titan atmosphere? No. (because then the molecular velocity would be higher: 533 m/sec and the atmosphere would escape) -- ******************************************************************** Amara Graps, PhD email: [EMAIL PROTECTED] Computational Physics vita: ftp://ftp.amara.com/pub/resume.txt Multiplex Answers URL: http://www.amara.com/ ******************************************************************** "It's not the pace of life I mind. It's the sudden stop at the end." --Calvin _______________________________________________ extropy-chat mailing list [EMAIL PROTECTED] http://lists.extropy.org/mailman/listinfo/extropy-chat ----- End forwarded message ----- -- Eugen* Leitl <a href="http://leitl.org";>leitl</a> ______________________________________________________________ ICBM: 48.07078, 11.61144 http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net
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