Formula sheet

Some possibly useful constants and formulaeM earth =5.974×10 24 kgM sun =1.9891×10 30 kgM uranus =8.66×10 25 kgM Jupiter = 1.9×10 27 kgR sun = 6.96×10 8 m1 Astronomical Unit (A.U.) = 1.495978707×10 11 mMass Proton =1.672622×10 -27 kgMass electron =9.10938×10 -31 kgc = 2.99792458×10 8 m/s(Speed of Light)R = 8.314 J mole -1 K -1(Universal Gas Constant)k= 1.3807×10 -23 J/K (Boltzmann Constant)G = 6.674×10 -11 Nm 2 /kg 2 (Gravitational Constant)σ = 5.67×10 -8 Wm -2 K -4(Stefan-Boltzmann constant)L=3.85×10 26 W(Total Solar Output Power)ρ=M/Vg = GM/R 2r 3 = GM * P 2 /4π 2V 2 p = GM * /rM p sin I = M * K/V pΔf/f * = (R p /R * ) 2(Bulk Density)(Surface gravity)(Kepler’s third law for an extrasolar planet)(Velocity of an extrasolar planet)(Mass of an extrasolar planet: radial velocity)(flux ratio for extrasolar planet transit)N p (r) = Q p exp(-r/R p )/4πrv p (number density of parent molecules in coma)N d (r) = Q p R d ( exp(-r/R d )-exp(-r/R p ) )/(4πrv d (R d -R p )) (daughter molecules in coma)ρ=nm (Mass density for a gas with n molecules each of mass m)q=a(1-e)(perihelion distance)L=rxp=Iω (Angular Momentum)I=0.4MR 2 (Moment of Inertia of a uniform sphere of mass M and radiusR rotating about an axis passing through its center)S=4πr 2(Surface Area of a Sphere)V=4/3πr 3(Volume of a Sphere)K.E. = 1/2mv 2 (Kinetic Energy)PV=nRT or P=nkT (Ideal Gas Equation)F grav =GMm/r 2 (Gravitational Force)F centripetal =mv 2 /r (Centripetal Force)dp/dz=-ρg (Hydrostatic Equilibrium)P.E.=-GMm/r (Gravitational Potential Energy between two bodies of mass Mand m separated by a distance r)F=L/4πr 2(Flux of sunlight at distance r from the sun)P=σT 4(Stefan-Boltzmann Law)

E g =3GM 2 /5R (Total gravitational energy E g released in formation of aspherical body with mass M and radius R)F=TAForce required to break apart a body held together by tensilestrength T assuming cross-sectional area at equator is A∂T/∂t=-κ/(ρC p )(∂ 2 T/∂z 2 ) Thermal diffusion equationdQ/dt=-κAdT/dx (Heat flow equation with κ thermal conductivity, A surfacearea, dT/dx temperature gradiant, Q heat)q= dQ/dt (1/A) (Heat flux)V 2 =GM(1/r-1/2a) (Vis-viva Equation)