Forum Astrophysics and cosmology Helpful Constants and Formulae (21 posts)


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joined September 25, 2007
29 forum posts

Helpful Constants and FormulaeThese will all hopefully be in a file for community access that will be downloadable at a later date. Resources include but are not limited to Dunn, Tony. "Astronomical Formulas." Orbitsimulator.com. Tony Dunn. Web. 26 Nov. 2011. . Cole, G. H. A., and M. M. Woolfson. Planetary Science: the Science of Planets around Stars. Bristol, [U.K.: IoP, 2002. Print. I'll list more later I'll finish this post with constants G is the gravitational constant with a value of 6.67384×10^(11) m^3/(kg s^2) σ is the StefanBoltzmann constant with a value of 5.670400×10^(8) J/(m^2s K^4) L_☉ is 1 Solar Luminosity with the value of 3.846×10^26 W M_☉ is 1 Solar Mass with the value of 1.98892×10^30 kg AU us 1 astronomical unit with a current value of 1.495978707×10^11 m δ_s is the silver ratio 1+2^(1/2) φ is the golden ratio (1+5^(1/2))/2 Minimum mass of dwarf planet based on the smallest known body Saturn I (Mimas) to be in hydrostatic equilibrium 3.75×10^19 kg, this would require to a similar density. Feel free to add to this list. Message has been edited  november 25, 2011

joined September 25, 2007
29 forum posts

Angular Frequencyω = 2π/T ω = 2πf ω = v/r ω is the angular frequency or angular speed (radians per second) T is the period (seconds) f is the ordinary frequency (hertz,sometimes symbolised with ν) v is the tangential velocity of a point about the axis of rotation (meters per second) r is the radius of rotation (meters) The first formula is the easiest to use.

joined September 25, 2007
29 forum posts

Oblateness Constant (simple)q ≡ (aω^2) / g q ≡ (aω^2) * (a^2/GM) q ≡ (a^3 * ω^2)/GM a is equatorial radius (meters) ω is the angular frequency or angular speed (radians per second) g is gravitational acceleration(meters per second) G is the gravitational constant M is mass of body (kilograms) This does not take into account differentiation. To fudge this on can take M and multiply against either a random number between 0.8 and 1.2 or mulitply against a system wide value to represent general differentiation. The second and third formulae, while appearing a little more complex then the first, tend to be easier to use. Message has been edited  november 23, 2011

joined September 25, 2007
29 forum posts

Roche limit advancedd ≈ 2.423R(ρ_M/ρ_m )^(1/3) * (((1+m/3M)+1/3 q(1+m/M))/(1q))^(1/3) d is distance from center of primary ρ_M is density of primary ρ_m is density of satillite M is mass in of primary m is mass in of satillite q is the oblateness constant (also listed as c/R) There is a simple version, but it greatly increases the error sigma.

joined September 25, 2007
29 forum posts

Orbital PeriodP=2π*{ a^3 / [G * (M+m) ] }^(1/2) P is period of orbit (seconds) a is separation distance (meters) M is mass in of primary m is mass in of satillite G is the gravitational constant Message has been edited  november 23, 2011

joined September 25, 2007
29 forum posts

Minimum Rotational PeriodP = 2π*( r^3 / GM )^(1/2) P is period oforbit (seconds) r is equatorial radius (meters) M is mass in of body G is the graviational constant

joined September 25, 2007
29 forum posts

Synchronous Orbitr = (GM/ω^2 )^(1/3) M is mass in of body G is the gravitational constant r is the elevation from the center of the body (meters) ω is the angular frequency or angular speed (radians per second)

joined September 25, 2007
29 forum posts

Synchronous Orbit Velocityv=ωr v is the velocity of the synchronous orbit (meters per second) r is the elevation from the center of the body (meters) ω is the angular frequency or angular speed (radians per second)

joined September 25, 2007
29 forum posts

Effective Planet TemperatureT_eff = {[L_☉ (1A)]/[16πσa^2 ]}^(1/4) T_eff is the effective surface temperature not accounting for greenhouse effect (kelvin) L_☉ is the luminosity in solar units and must be converted to watts L_☉ ∙ 3.846×10^26 W A is the geometric albedo σ is the StefanBoltzmann constant a is the semimajor axis(meters)to get minimum and maximum adjust to peri and apo This does not take into account any greenhouse effect factor,H,to add in H use the following modification to the T_eff formula T_wgh=T_eff + 0.15 ∙ T_eff ∙ H/H ∙ H^(1/2) It is not unusual for H to be a negative value for bodies who either have a highly reflective surface or a thin conductive atmosphere,Mars and Enceladus are prime examples. For gas planets that are in excess of 12 M_♁ black body value for planet should be included at equatorial radius as planet will most likely still be radiating heat from formation.

joined September 25, 2007
29 forum posts

Luminosity Mass RelationshipL=kM^n L is the luminosity of the stellar object k is multiplier factor M is the mass of the stellar object in Solar masses n is the power factor k and n vary according to M M≤0.43,k=0.23,n=2.3 M≤2.00 and M>0.43,k=1,n=4 M≤20.0 and M>2.00,k=1.5,n=3.5 M>20.0,k=1,n=4M/[44+(M/10.25)^2]


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Forum Astrophysics and cosmology Helpful Constants and Formulae (21 posts)
