Formulas & Constants for “A Classical & Relativistic Trip to a Black Hole”

constant	symbol	value
speed of light	c	3.00 X 10^8 m/s
gravitational constant	G	6.67 X 10^-11 Nm^2/kg^2
mass of Earth	Me	5.98 X 10^24 kg
radius of Earth	Re	6.37 X 10^6 kg
acceleration due to gravity on Earth	g	9.81 m/s^2
equivalencies
1 m^3 = 10^6 cm^3
1 light year = 9.46 X 10^15 m

quantity	symbol	unit	equation	notes
velocity	v	m/s	v = d/t	d = distance, t = time
acceleration	a	m/s^2	a = Dv/t	rate at which velocity changes (Dv = vf - vi)
net force	F	N	F = ma	Newton’s 2^nd law, m=mass in kg
volume of a sphere	V	m^3	V = 4/3pr^3	r is the radius
density	D	kg/m^3	D = M/V	mass per unit volume
centripetal force	Fc	N	Fc = mv^2/r	force that keeps an object in a circular path, directed towards the center of the circle
period of object in circular motion	T	s	T = 2pr/v	time to go around the circle (orbit) once
gravitational force between two objects	FG	N	FG = GmM/r^2	G = gravitational constant, m = mass of small object, M = mass of large object, r = distance between their centers
escape velocity	vesc	m/s	= sqrt(2GM/R)	Escape velocity is the minimum speed to escape an object’s (planet’s or star’s, etc) gravitational field where G = gravitational const., M = mass of object, R = radius of object
Special relativity (time dilation at high velocities)	Dt	s	Dt = Dto/sqrt[1-(v/c)^2]	Dto = change in time from perspective that sees events occur in same place, Dt = change in time from perspective that sees events occur in different places, v = velocity, c = speed of light