Science

Introduction | Stars | Planets | Lithospheres | Atmospheres and Oceans | Moons | Life | Chemistry

Introduction

My aim here is to focus on the equations behind my calculations, and leave much of the general explanations to other web sites. So these pages just give some brief discussion of the techniques used, with frequent reference to other sites where appropriate. The most useful general sites I've found are the lecture notes of Nick Strobel.

There is clearly no limit to this subject, so what goes in here may be rather patchy. If neither my notes nor the other Web sites are sufficient, look at the paper references.

If any terms are unfamiliar, check for space terms in the glossary from the Nine Planets pages.

Stars

Strobel on stellar properties and structure and evolution.

For each line in the table, I discuss the calculations

Feature

Symbol

Calculation

Comment

Type

Input or table lookup from mass

Mass ()

M

Input or table lookup from type

Distance from Earth (ly)

D

Input

Age on Main Sequence (Gyr)

Ams

If then else

Age (Gyr)

A

Input

Radius ()

R

Surface gravity (m/s²)

g

Escape Velocity (km/s)

vs

Luminosity ()

L

Absolute magnitude

Mv

Apparent magnitude mv

mv

Input

Surface temperature (K)

T

Peak wavelength (micron)

l

Wien's constant is an input

Ecosphere range (AU)

X

Illumination between 0.53 and 1.02 that of Earth (from Kasting's paper)

Luminosity changes during a star's lifetime as , where ZAMS = Zero Age Main Sequence, ie star formation so all the calculations could be repeated then. A selection have been recalculated to indicade the changes over a planet's lifetime.

Planets

Strobel on Planetary Science. Our solar system is well described in the SEDS Nine Planets site, and the Goddard fact sheets.

General

Feature

Symbol

Calculation

Comment

Type

Mean orbital distance (AU)

x

Input

Eccentricity

e

Input

Eccentricity and axial tilt generate the seasons.

Axial tilt (°)

e

Input

Year (Earth days)

Y

Star system escape velocity (km/s)

Vs

Angular diameter of star (°)

As

Angular diameter of moon (°)

Am

Solar day (hr)

Ds

Radius (km)

r

Input

1/Ellipticity

1/el

Input

Lithospheres

Feature

Symbol

Calculation

Comment

Mass (Earth Masses)

m

Input

Maximum Mass (Earth Masses)

Mmax

Density (kg/m³)

s

Inertia Factor

IF

Typical surface gravity (m/s²)

g

Equatorial surface gravity (m/s²)

ge

Polar surface gravity (m/s²)

gp

Escape velocity (km/s)

v

????

Rotation period (hr)

D

Input

-ve is retrograde

Shortest possible period (hr)

Dmin

Any faster and planet breaks up

Geosynchronous orbit (km)

 

Plate tectonics end (Gyr)

Terrestrial planets only, after this CO2 is locked up in sedimentary rocks reducing the Greenhouse Effect.

Maximum mountain height (m)

h

Roche Limit (km)

L

If the moon gets closer than this it breaks up

Horizon distance (m)

h

at eye level (1.5m)

If you are interested in the details of planetary formation, look at the accrete software, which is dating somewhat.

I did allow planetary interiors to be be modelled as a set of up to 4 concentric spherical shells of fixed density. For the Earth they would correspond to the inner and outer cores, mantle and crust. For simplicity, it is possible to just use one shell. I've disabled this feature as it seemed too complex for the available information on other planets. Let me know if you would find it useful.

Atmospheres and Oceans

Both terrestrial planets and Gas Giants have atmospheres. But while the former have true solid surfaces and atmospheres driven by sunlight, the latter have no clear surface and often receive the majority of their heat from inside due to slow gravitational collapse, and given how little we know about their atmospheric patterns, I've disabled many of the standard calculations rather than give daft results.

Feature

Symbol

Calculation

Comment

Albedo

A

Input

Atmospheric pressure (mbar)

P

Input

Minimum RMM (relative molecular mass, 1/12 of an atom of Carbon 12) for atmosphere (g)

 

The rms velocity of a gas molecule in the exosphere (temperature taken as 1273 K) must be less than a tenth of escape velocity. While molecules have a range of speeds, so few will fall in the high speed tail of the distribution that an appreciable fraction won't leave over geological time

Atmospheric RMM (g)

RMM

Derived from atmospheric gas composition

Atmospheric composition is partly dependant on the elemental distribution in the gas torus from which planets form, and partly on the future evolution of the planet, with some gasses escaping from the atmosphere, some being changed by the geochemical cycle, and some being altered by the presence of life.

Stephen Gillett has written many articles on possible atmospheres and biochemical regimes, which would be impossible to summarise here, but generally the more esoteric systems are normally impractical as either as the elements aren't abundant enough, or chemical energetics argue against them. Elemental abundances can be found from chemistry sites, but I've found no good on-line source of chemical reaction data.

At the moment I assume that all the chemicals quoted in the atmosphere table are true gasses at STP (standard temperature and pressure). In the longer term, with Del Cotter's help, I will extend this to handle general phase properties.

An active ecosphere is needed to maintain an oxygen atmosphere against its tendency to oxidise rocks.

Specific heat capacity (J mol-1 mol-1 K-1)

Cp

Speed of sound at surface (m/s)

v

Temperature range of orbit (°C)

Tmin to Tmax

to

(No greenhouse effect)

Greenhouse Effect

Input

Atmospheric temperatures are strongly influenced by the greenhouse effect, but calculation is so complicated, that I ask users to enter a figure themselves.

Typical Surface temperature

Tsurf

With greenhouse effect

Scale height (m)

H

The height over which atmospheric pressures fall by 1/e, ie to 37%. It is dependant on temperature, gravity and atmospheric RMM.

Dry Adiabatic lapse rate, (°C/km)

DALR

Indicates how quickly an air parcel without moisture will cool as it rises. If a real, moist, air parcel has a lapse rate less than this, it will have cooled less when it reaches a certain altitude, so will be less dense, and continue rising, an unstable situation leading to convection, strong air mixing and rainfall. If the DALR is large enough for temperatures to fall below 0°C at the tropopause before they start rising again, water vapour will freeze out in a 'cold trap', This cold trap is very important for preserving a planet's water supply over geological time, as it prevents its passage above the Ozone layer into the stratosphere where it runs the risk of photo-dissociation from UV light, and the hydrogen escaping into space.

The ozone layer is crucial in preventing UV from reaching the surface, but the calculations there are extremely complicated, so I've not modeled them in any detail here.

I just assume that the peak ozone absorption occurs as a scaled version of Earth's atmosphere, but I have little confidence in the calculation, so the output from the last 3 calculations is disabled at present.

Ozone layer height (km)

????

Tropopause height (km)

Tropopause temperature (°C)

Coriolis effect at 45°N * 1E4

f

The Coriolis parameter is purely dependant on a planet's rotation rate, and determines how easily heat can be transferred from equator to pole, how tight low pressure systems are and how strong are the winds.

Mid-ocean tide height (m)

h



Someone else has set up a standard atmosphere for the Earth, which gives the typical pressure, density and temperature at a particular height in our atmosphere.

The ocean current patterns from the Radar Altimeter on ERS-1 are available.

Moons

The presence of a large moon is important, both because of its impact on the tides and tidal braking, but also to stabilise the axial tilt. Recent work on chaotic obliquity suggests that axial tilts can vary chaotically from 0 to 60°, but the axes of Mercury and Venus were stabilised by tidal dissipation, and the Earth's by the moon. There are no simple calculations that be can be applied here, but a large moon is a good idea.

The relative sizes of the star, moon and planet are checked to see whether total eclipses are possible, as they are always popular with a certain brand of SF author. Later I will add an indication of their length.

The calculations for mass, radius, surface gravity and escape velocity are as for the planet. I will add a Roche limit calculation later, so for the moment the only awkward calculation is that of the Siderial month (the period of orbit of the moon with respect to the stars) and the Synodic month (the period of the phase cycle, New Moon to New Moon).

Siderial Month =

Synodic Month =

Life

Strobel

Martyn Fogg has written extensively on the requirements for planetary life in his Terraforming book, but a rough summary for Earthlike life follows:

Lifeform

Lowest temp (°C)

Highest temp (°C)

Lowest pressure (mbar)

Highest pressure (mbar)

Comments

Microorganisms

-10

110

10

?

composition very variable

Higher plants

0

45

90

?

at least 20 mbar O2, 0,01 mbar CO2, < 21% O2 to avoid fires

Humans

-10

40

140

3700

< 10mbar CO2

Requirements for life

For details of habitable zones round other stars, look at Kasting's paper. More information about the biological possibilities on other planets can be obtained by subscribing to the Marsbugs electronic newsletter, looking at the Life in Extreme Environments page

Chemistry

Not my strongest subject, but luckily others have superb sites for general chemistry and the elements, but not as far as I know, other common chemicals. I current just quote the melting and bioling points for a few elements and compounds, like Hydrogen, Helium, Nitrogen, Oxygen,Argon, Carbon Dioxide, Methane, Ammonia and Water.

Have a look at a developing school chemistry course.