Angular Momentum L = Iω, where L is the angular momentum, I is the object’s moment of inertia, and ω is the object’s angular velocity (Chapter 2).
Area of a Circle A = πd2/4, where π is approximately 3.14, and d is the diameter of the circle (Chapter 3).
Average Density ρ = m/V, where ρ is the average density, m is the total mass, and V is the volume of the object (Chapter 5).
Distance from Parallax d = 1/p where d is the distance in parsecs and p is the parallax angle in arcseconds, or dly = 3.26/p, where dly is the distance in light-years (Chapter 11).
Distance-Magnitude Relationship M = m − 5 log(d/10), where M is the star’s absolute magnitude, m is its apparent magnitude, and d is its distance in parsecs (Chapter 11).
Doppler Shift ∆λ/λo = v/c, where ∆λ is the change in wavelength (λ − λ0), λ is the observed wavelength, λ0 is the wavelength the object emits as seen by someone not moving toward or away from it, v is the speed of the object toward or away from the observer, and c is the speed of light (Chapter 4).
Drake Equation N = R*fpneflfifc L, where N is the number of advanced civilizations in our Galaxy estimated by the equation, R* is the rate at which solar-type stars form in the Galaxy, fp is the fraction of stars that have planets, ne is the number of planets per star system suitable for life, fl is the fraction of habitable planets on which life arises, fi is the fraction of lifeforms that develop advanced intelligence, fc is the fraction of species that develop technology and send signals into space, and L is the lifetime of technological civilizations (Chapter 19).
Energy Flux F = σT 4, where σ is Stefan’s constant and T is the blackbody’s temperature in K (Chapter 4).
Energy-Mass Equation E = mc2, where c is the speed of light and E is the energy released when mass m is converted to energy (Chapter 10).
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Gravitational Force F = G(m1m2/r2), where G is the gravitational constant, m1 and m2 are the masses of the two interacting objects, and r is the distance between them (Chapter 2).
Gravitational Potential Energy (always true) PE = GmM/r, where PE is the potential energy, G is the gravitational constant, m is the mass of the object whose gravitational potential energy you are measuring, M is the mass of the object creating the gravitational potential, and r is the distance between the centers of the two (Chapter 2).
Gravitational Potential Energy (near Earth) PE = mgh, where m is the mass of the object whose gravitational potential energy you are measuring, g = 9.8 m/s2, and h is the height of the object above Earth’s surface (Chapter 2).
Kepler’s Third Law P2 = a3, where P is the sidereal period in Earth years and a is its semimajor axis in astronomical units (Chapter 2).
Kinetic Energy KE = ½ mv2 = p2/2m = L2/2I, where KE is its kinetic energy, m is its mass, v is its speed, p is the momentum, L is the angular momentum, and I is the object’s moment of inertia. The first two equalities apply if the object is moving in a straight line. The last equality applies if the object is revolving or rotating (Chapter 2).
Luminosity L = F · 4 πr2, where L is the luminosity (total energy per second) emitted, F is the energy flux, and r is the radius of the object (Chapter 4).
Magnification M = fo/fe, where fo is the focal length of the primary mirror or objective lens and fe is the focal length of the eyepiece (Chapter 3).
Momentum p = mv, where p is the momentum, m is the mass, and v is the velocity (Chapter 2).
Newton’s Force Law F = ma, where F is the force acting on an object, m is its mass, and a is its acceleration (F and a are in boldface to denote that they act in some direction or other) (Chapter 2).
Newton’s Version of Kepler’s Third Law for Binary Star Systems M1 + M2 = a3/P2, where M1 and M2 are the masses of the stars, a is the average distance between them, and P is the period of their orbit in years (Chapter 11).
Photon Energy E = hc/λ, where E is the photon’s energy, h is Planck’s constant, c is the speed of light, and λ is the wavelength of the light (Chapter 3).
Pressure P = F/A, where P is the pressure, F is the force, and A is the area over which the force acts (Chapter 6).
Recessional Velocity of Galaxies v = H0 × d, where v is the recessional velocity in kilometers per second, H0 is the Hubble constant, and d is the distance to the galaxy in megaparsecs (Chapter 16).
Schwarzschild Radius of a Black Hole RSch = 2 GM/c2, where RSch is the Schwarzschild radius in meters, G is the gravitational constant, M is the mass of the black hole in kilograms, and c is the speed of light (Chapter 14).
Size of a Distant Object D = R × tan θ, where D is the physical diameter of an object, R is the distance to it, and tan θ is the tangent of the angle it makes in the sky (Chapter 1).
Wien’s law λmax = 2.9 × 103/T, where λmax is the peak wavelength of the blackbody and T is the blackbody’s temperature in kelvins (Chapter 4).
Work W = Fd, where W is the work, F is the force acting, and d is the distance moved in the direction that the force acts (Chapter 2).