question

1/P=1/E+1/S (for inferior planets)

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relates sidereal orbit, P, to a number of days, E

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little dude=D/d*either 360/2pi or 206265

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used to find the angular size of a thing. For big things, use first either, if it's small, use the second

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v=d/t

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velocity

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v=(d1-d2)/(t1-t2)

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used to find average velocity within a time period

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v=2R/t

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general motion of an object in a circle; average speed of an object in circular motion

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F=ma

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force equals mass times acceleration

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F=GmM/d^2

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newtons universal law of gravitation; F is the magnitude of the gravitational force between the two masses, G is the gravitational constant, m is the first mass, M is the second mass, and d is the distance between them

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F(weight)=mg=GmM/R^2

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another version of newton's law of universal gravitation; the force of weight equals mass times surface gravity, or the gravitational constant times the mass of the thing, the mass of the planet divided by the radius of the planet (distance between the thing and the planet) squared

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F(cent)=mv^2/r

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it's like f=ma but for circles; proves that stuff moving in a circle is accelerating; the centripetal force equals the mass times velocity squared divided by the radius of the circle

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L=mvr

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equation for angular momentum; angular momentum equals the mass times velocity times the radius

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P^2=A^3

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relates the period to the distance a thing is away from the thing it's orbiting; P must be in years and A must be in AU

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P^2=4piA^3/Gm+M) or P^2=4piA^3/GM

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Newton's version of Kepler's third law, where the period squared equals four pi times the cube of the average distance in AU divided by the gravitational constant times the mass of the larger body

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v(circ)=√GM/r

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formula for circular velocity; square root of the gravitational constant times the mass of the bigger thing divided by the radius of the orbit (the distance between the two things)

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v(esc)=√2GM/R

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escape velocity equals the sqare root of two times the gravitational constant times the mass of the thing divided by the radius of the thing

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M=v^2r/G

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you can use this to find the mass of a satellite when only knowing its speed; the mass equals the velocity squared times the radius of the orbit divided by the gravitational constant

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λf=c

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wavelength times frequency equals the speed of light

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E=hf=hc/λ

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energy E of a photon equals Planck's Constant times the frequency, or the constant times the speed of light divided by the wavelength

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b=L/4pid^2

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brightness equals luminosity divided by four pi distance squared

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λ(peak)T=.0029mK

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wiens law; the blackbody radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature; m isn't a variable it just stands for meters, K also is useless just ignore it, T is the temperature in Kelvin

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F=little dudeT^4

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Stefan's Law; relates the flux output of a blackbody with its temperature, where F is the flux output (energy per area), the little dude is a constant and the temperature is in Kelvin

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L=4piR^2little dudeT^4

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an extension of Stefan's law; L is luminosity, T is the temperature in Kelvin and the little dude is a constant

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λ(obs)-λ(original)=λ(original)v(r)/c

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used to see how fast something is moving based on an observed and expected wavelength; v is the velocity and c is the speed of light

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P=nkT

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Version of the ideal gas law; P is the pressure, n is the number density, or the number of particles per volume of the gas (huge number), k is the Boltzmann constant, and T is the absolute temperature in Kelvin

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v=√8kT/mpi

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used to find the average speed of a gas; v is the average velocity, k is the Boltzmann constant, T is the temperature in Kelvin, m is the mass and pi is ....pi

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E(k)=1/2mv^2

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formula for kinetic energy; pretty straightforward man

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T=279K*(√1-a/d(AU))^1/2

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no idea when you would use this, but temperature equals 279K (where K is a unit not a variable) times the half power of the square root of one minus acceleration divided by the distance in units of AU. again, what is this for??

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P(f)/P(o)=(1/2)^n

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ok this is weird if you think about it but just add the amount of thing 1 plus the proportional amount of thing 2 it creates and figure out what power of two gets that number and that's the answer

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L prop. M^3.5

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Luminosity is proportional to the mass of the thing to the 3.5 power; handy if the givens do not include a distance

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weird t prop. M^-2.5

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the lifespan of a star is proportional to the mass tot he -2.5 power; the larger the mass, the shorter the lifespan

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d(pc)=1/p(n)

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formula for parallax, or the apparent motion of a star; d is measured in parasecs and the angle p is measure in arcseconds

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m-M=5log(d/10pc)

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used to find the absolute or apparent magnitude when distance is given; the apparent magnitude minus the absolute magnitude equals five times the log of the distance in parasecs divided by 10pc (where pc is a unit not a variable)

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d=10pc*10^.2(m-M)

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used to find distance when both magnitudes are given; distance in parasecs equals 10 pc (where pc is a unit not a variable) times 10 to the power of .2 times the apparent magnitude minues the absolute magnitude

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M2-M1=2.5log(L1/L2)

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to see how much brighter a thing is compared to another thing; absolute magnitude of thing 2 minus the absolute magnitude of thing 1 equals 2.5 times the log of the Luminosity of thing one divided by the luminosity of thing two; the answer will be in terms of thing 1 is x times more luminous than thing 2

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b(1)/b(2)=2.512^m(2)-m(1)

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relates brightness to apparent magnitude; you need distance to use this one

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b(1)/b(2)=10^.4(m(1)-m(2))

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relates brightness to apparent magnitude; you need distance to use this one

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m(1)-m(2)=2.5log(b1/b2)

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relates brightness to apparent magnitude; you need distance to use this one

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