Mars, the fourth planet in our solar system, has a mass M_planet of 6.40 times 1
ID: 802473 • Letter: M
Question
Mars, the fourth planet in our solar system, has a mass M_planet of 6.40 times 10^23 kg and a radius r_planet of 3, 390 km. The Martian atmosphere is comprised of 96% carbon dioxide. 2% nitrogen, and 2% argon by partial pressure. The pressure of the atmosphere at the planetary surface is 600 Pa absolute. Mars has a tropopause at 65 km. and a stratosphere that extends to an elevation of 100 km with a constant temperature of 145 deg K. The lapse rate is 1.15 times 10^-3 K/m. Newton's universal law of gravitation suggests that the gravitational acceleration g_planet of any planet depends on its radius and mass g_PLANET = G M_PLANET/(r_PLANET)^2 with universal gravitational constant G. Find (with a cited reference) and use physical constants for earth to evaluate G, and be sure to include units, Calculate and compare the planet density rho_planet for earth and Mars. We will discover later that the density rho_s of most sediment in the earth's rivers is 2, 650 kg/m^3-how does this compare to your two rho_planet values? What is the density of the Martian atmosphere at the ground surface? Be sure to compute the physical constants for Mars, rather than dialing them up on an electronic device, Plot your model of the temperature T(z) and pressure p(z) profiles of the Martian atmosphere to the top of the stratosphere.Explanation / Answer
a.G=g planet*( rplanet)^2/Mplanet
We know that g= gravitational acceleration of earth=9.8ms-2
Mass of earth=5.972*10^24 kg
Radius of earth=6371 km=6371000 m
G=9.8(6371000)^2/5.972*10^24
=9.8*4.06*10^-13/5.972*10^24
=39.78*10^13/5.972*10^24
=6.66*10^13*10-24
=6.66*10-11m3 kg-1s-2
b. Since density= mass/ volume
we know the mass of earth=5.972*10^24kg=5.972*10^24*10^3=5.972*10^27g
volume of earth=4/3pi r3
r= radius of earth=6371 km=6371*10^5cm
Density of earth=5.972*10^27/(4/3pi(6371*10*5)^3)
=5.972*10^27/(4/3pi *2.58*10^11*10^15
=5.972*10^27/10.8*10^26
=0.5529*10
=5.529gcm-3
=5.53gcm-3
Now density of mars=mass of planet/volume of planet
mass of mars=6.4*10^23kg=6.4*1024*10^3=6.4*10^26
volume=4/3pi r3
r=3390km=3390*10^5cm
=4/3*3.14*(3390*10^5)^3
=4/3*3.14*3.89*10^10*10^15
=4/3*3.14*3.89*10^25
=48.85/3*10^25
=16.2*10^25cm3
Density=6.4*10^26/16.2*10^25
=0.395*10
=3.95g/cm3
c. To calculate the density of Martian atmosphere
r=p/0.1921*T
where r= density
p=pressure=600pa=6 mb
T=145 degree Kelvein
r=6/0.1921*145
=6/27.8
=0.21
=600/80.3
=7.47
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