[extropy-chat] Mars and Titan

[Amara Graps]

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: amara at amara.com
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