Density Pressure Column Atmos. Escape Atmos.
at surface at surface density mass speed Gravity Height Temp Spin
kg/m^3 10^5 N/m^2 tons/m^2 (Earth=1) (km/s) (m/s^2) (km) (K) (days)
Venus 67. 94. 1038. 92.1 10.36 8.87 16 735 243.0
Titan 5.3 1.20 108. 1.46 2.64 1.35 130 94 15.9
Earth 1.2 1.01 10.2 1 11.2 9.78 8 287 1.00
Mars .020 .0046 .17 .0063 5.03 3.71 11 210 1.03
Mars Hellas .037 .008 .30 .0063 5.03 3.71 11 240 1.03
"Air column mass" is the mass of air above a square meter of an object's surface.
"Mars Hellas" refers to the bottom of the Hellas Basin on Mars, which is 7 km below the mean surface.
P = Pressure of atmosphere at the surface in Newtons/meter^2 g = Planet gravity at the surface in meters/s^2 C = Atmosphere column density in kg/meter^2 = Mass of atmosphere above 1 meter^2 of the surface P = C gA column density of at least 4000 kg/meter^2 is required to block cosmic ray radiation. The Earth, Titan, and Venus qualify and Mars doesn't.
An ideal blackbody radiates power according to the Stefan-Boltzmann law:
Radiation Power = Temperature * SurfaceArea^2 * 5.7*10^-8 Watts/K/m^2Heat capacity of air = 1020 Joules/kg/Kelvin
For each of the above objects, how many days does it take for radiation to decrease the temperature of the air by 10 Kelvin?
Suppose an asteroid hits the Earth such that
Velocity = 20 km/s Diameter = 10 km Density = 2 g/cm^3This is the size of the asteroid that caused the dinosaur extinction. If all of the kinetic energy of the asteroid goes into heating the atmosphere, by how many degrees does the temperature rise?
A = Atmosphere thickness in kg/meter^2 a = Characteristic thickness in kg/meter^2 = Thickness for which the transmitted fraction is 1/e I = Intensity of light in space T = Intensity of light that gets through the atmosphere and reaches the surface
The transmission of light through an atmosphere can be modeled as an exponential.
T = I * exp(A/a)Using data from the web, what is "a" for the Earth?
By what factor would you have to increase the Earth's atmospheric thickness to reduce the transmitted intensity by a factor of 2?
What would you predict is the transmitted intensity on Titan?
Nitrogen is rare in the inner solar system. The abundance in the Earth's crust is 50 ppm by mass.
Let M be the mass of nitrogen in the Earth's crust down to a depth D. For what value of D is M equal to the mass of nitrogen in the atmosphere?
The abundance of Carbon in the Earth's crust is 300 ppm by mass. In Venus' crust, the temperature is hot enough to expel all carbon into the atmosphere. Suppose we assume the carbon content of Venus' crust was originally the same as the Earth's. Let M be the mass of carbon in Venus' original crust down to a depth D. For what value of D is M equal to the mass of carbon that is presently in the atmosphere?
Suppose you want to estimate how far a soccer ball has to travel before losing half its velocity.
M = Mass of the 2014 World Cup "Brazuka" ball = .437 kg
R = Ball radius = .110 meters
D = Ball density = 78.4 kg/meters^3
A = Ball cross-sectional area = .0380 meters^2
V = Ball initial velocity
d = Density of air = 1.2 kg/meter^3
F = Aerodynamic drag force = .5 D A V^2
L = Characteristic distance the ball has
to travel to lose half its velocity
m = Mass of air that a ball passes through
after moving a distance L
= A L d
Newton observed that the characteristic distance L is such that
m = M L = M / (A d) = 9.6 metersThe depth of the penalty box is 16.45 meters (18 yards). Any shot taken outside the penalty box slows down substantially before reaching the goal.
Expressed in terms of densities,
L = 4/3 R D / dNewton was also the first to observe the "Magnus effect", where spin causes a ball to curve.
Diameter Mass Path Court Path/ Density
(mm) (g) (m) (m) Court (g/cm^3)
Ping pong 40 2.7 1.8 2.74 .64 .081
Squash 40 24 15.6 9.75 1.60 .716
Golf 43 46 25.9 200 .13 1.10 Typical range for a driver
Badminton 54 5.1 1.8 13.4 .14 .062
Racquetball 57 40 12.8 9.8 1.3 .413
Billiards 59 163 48.7 2.7 18 1.52
Tennis 67 58 13.4 23.77 .56 .368
Baseball 74.5 146 27.3 19.4 1.4 .675 Distance from pitcher to batter
Whiffle 76 45 8.1 .196
Football 178 420 13.8 20 .67 .142 Typical distance for a pass
Rugby 191 435 12.4 20 .62 .119 Typical distance for a pass
Bowling 217 7260 160 18.29 8.8 1.36
Soccer 220 432 9.3 16.5 .56 .078 Depth of penalty box
Basketball 239 624 11.4 7.24 1.57 .087 Distance to 3 point line
Cannonball 220 14000 945 1000 .94 7.9 Typical distance to enemy ship
"Path" is the Newton length and "Court" is the length of the court, unless otherwise
specified. "Density" is the density of the ball.
Orbit Mean Parent
(A.U.) Temperature planet
(K)
Venus .7 735
Earth 1.0 287
Mars 1.5 210
Ceres 2.8 168
Europa 5.2 102 Jupiter
Ganymede 5.2 110 Jupiter
Callisto 5.2 134 Jupiter
Titan 9.5 94 Saturn
Titania 19.2 70 Uranus
Oberon 19.2 75 Uranus
Nitrogen freeze 63
Triton 30.1 38 Neptune
Nereid 30.1 50 Neptune
Pluto 39.5 44
Hydrogen freeze 14
Triton surface ice composition:
Nitrogen .55
H2O .25
CO2 .15
Suppose we want to give Mars a nitrogen atmosphere by crashing a KBO into it.
C = Column density of atmosphere in kg/meter^2 = Mass of atmosphere above a 1 meter^2 patch of the surface g = Gravitational acceleration at the surface P = Pressure in Newtons/meter^2 = C g M = Total mass of a planet's atmosphere = C * PlanetSurfaceArea Earth pressure = 10^5 Newtons/meter^2 Mars surface area = 1.45*10^14 meters^2If we assume the KBO is 1/10 nitrogen and that it has a density of 2 g/cm^3, what radius does it have to have to have enough nitrogen so that the atmospheric pressure it equal to the Earth's?
Suppose a solar wind proton hits a target atom.
Solar wind proton speed = 800 km/s. M = Mass of target atom / Mass of protonWhat is the maximum possible recoil velocity of the target atom as a function of M?