Article

Question

How was the speed of light determined and who found it, when? How close was the estimate of 186,000 mps to the 'actual' speed of light?
Asked by: Chuck Baker

Answer

Although Galileo was the first person of record to try to determine the speed of light, he was not successful. His experiments took place over terrestrial distances and the timing methods available to him were far to crude to make a successful determination given such distances and the very great speed of light. 

It was the Danish astronomer, Olaus Roemer, who, in 1676, first successfully measured the speed of light. His method was based on observations of the eclipses of the moons of Jupiter (by Jupiter). 

Roemer noted that the observed time interval between successive eclipses of a given moon was about seven minutes greater when the observations were carried out when the earth in its orbit was moving away from Jupiter than when it was moving toward Jupiter. He reasoned that, when the earth was moving away from Jupiter, the observed time between eclipses was increased above the true value (by about 3.5 minutes) due to the extra distance that the light from each successive eclipse had to travel to reach the earth. Conversely, when the earth was moving toward Jupiter, the observed interval between eclipses was decreased (by about 3.5 minutes) because of the decreased distance that the light had to travel on each successive eclipse. 

Had the earth not been moving, the light from successive eclipses would have to travel the same distance to the earth, so that the true interval between eclipses would be observed. However, when the earth was moving away from Jupiter, the light had to travel a greater distance to reach the earth from each successive eclipse, and conversely a smaller distance when the earth was moving toward Jupiter. Since the speed of the earth in its orbit was known, the distance that the earth had moved between eclipses could be calculated. The speed of light was then estimated to account for the seven minute overall variation of the observed interval between successive eclipses. 

Roemer's estimate for the speed of light was 140,000 miles/second, which is remarkably good considering the method employed. 

Physical notations

Physical notations

Symbol	Meaning	SI unit of measure
${\displaystyle A}$	area	meter squared (m2)
	magnetic vector potential
	amplitude	meter
${\displaystyle \mathbf {a} }$	acceleration	meters per second squared (m/s2)
${\displaystyle \mathbf {B} }$	magnetic flux density also called the magnetic field density or magnetic induction	tesla (T), or equivalently, weber per square meter (Wb/m2)
${\displaystyle C}$	capacitance	farad (F)
	heat capacity	joule per kelvin (J K−1), or equivalently, joule per degree Celsius (J °C−1)
	constant of integration	varied depending on context
${\displaystyle c}$	speed of light (in vacuum)	299,792,458 meter per second (m/s)
	speed of sound	340.29 meter per second (m/s)
	specific heat capacity	joule per kilogram per kelvin (J kg−1 K−1), or equivalently, joule per kilogramper degree Celsius (J kg−1 °C−1)
	viscous damping coefficient	kilogram per second (kg/s)
${\displaystyle \mathbf {D} }$	electric displacement field also called the electric flux density	coulomb per square meter (C/m2)
${\displaystyle D}$	density	kilograms per cubic meter (kg/m3)
${\displaystyle d}$	distance	meter (m)
	direction	unitless
	impact parameter	meter (m)
	diameter	meter (m)
differential(e.g. ${\displaystyle dx}$)
${\displaystyle d\mathbf {A} }$	differential vector element of surface area A, with infinitesimally small magnitude and direction normal to surface S	square meter (m2)
${\displaystyle dV}$	differential element of volume V enclosed by surface S	cubic meter (m3)
${\displaystyle \mathbf {E} }$	electric field	newton per coulomb (N C−1), or equivalently, volt per meter (V m−1)
${\displaystyle E}$	energy	joule (J)
${\displaystyle e}$	eccentricity	unitless
	2.71828... (base of the natural logarithm), electron, elementary charge
${\displaystyle \mathbf {F} }$	force	newton (N)
${\displaystyle f}$	frequency	hertz (Hz)
	function
	friction	newton (N)
${\displaystyle G}$	the gravitational constant	newton meter squared per kilogram squared (N m2/kg2)
${\displaystyle g}$	acceleration due to gravity	meter per second squared (m/s2), or equivalently, newton per kilogramme(N/kg)
${\displaystyle \mathbf {H} }$	magnetic field strength also called just magnetic field	ampere per meter (A/m)
${\displaystyle H}$	Hamiltonian	joule (J)
${\displaystyle h}$	height	meter (m)
	Planck's constant	joule second (J s)
${\displaystyle \hbar }$	reduced Planck's constant ${\displaystyle \textstyle \left({\frac {h}{2\pi }}\right)}$	joule second (J s)
${\displaystyle I}$	action	joule second (J s)
	intensity	watt per square meter (W/m2)
	sound intensity	watt per square meter (W/m2)
	electric current	ampere (A)
	moment of inertia	kilogram meter squared (kg m2)
${\displaystyle i}$	intensity	watt per square meter (W/m2)
	imaginary unit
${\displaystyle \mathbf {\hat {i}} }$	Cartesian x-axis basis unit vector	unitless
${\displaystyle \mathbf {J} }$	free current density, not including polarization or magnetization currents bound in a material	ampere per square meter (A/m2)
	impulse	kilogram meter per second (kg m/s)
${\displaystyle \mathbf {\hat {j}} }$	Cartesian y-axis basis unit vector	unitless
${\displaystyle K}$	kinetic energy	joule (J)
${\displaystyle k}$	Boltzmann constant	joule per kelvin (J/K)
	wavenumber	radians per meter (m−1)
${\displaystyle \mathbf {\hat {k}} }$	Cartesian z-axis basis unit vector	unitless
${\displaystyle L}$	inductance	henry (H)
	luminosity	watt (W)
	angular momentum	newton meter second (N m s or kg m2 s−1)
${\displaystyle l}$	length	meter (m)
${\displaystyle M}$	magnetization	ampere per meter (A/m)
	moment of force often simply called moment or torque	newton meter (N m)
${\displaystyle m}$	mass	kilogram (kg)
${\displaystyle N}$	normal vector	unit varies depending on context
	atomic number	unitless
${\displaystyle n}$	refractive index	unitless
	principal quantum number	unitless
${\displaystyle P}$	power	watt (W)
${\displaystyle \mathbf {p} }$	momentum	kilogram meter per second (kg m/s)
	pressure	pascal (Pa)
${\displaystyle Q}$	electric charge	coulomb (C)
	Heat	joule (J)
${\displaystyle q}$	electric charge	coulomb (C)
${\displaystyle R}$	electrical resistance	ohm (Ω)
	Ricci tensor	unitless
	radiancy
	gas constant	joule per kilogramme kelvin (J/kgK)
${\displaystyle \mathbf {r} }$	radius vector (position)	meter (m)
${\displaystyle r}$	radius of rotation or distance between two things such as the masses in Newton's law of universal gravitation	meter (m)
${\displaystyle S}$	surface area	m2
	entropy	joule per kelvin (J/K)
	action
${\displaystyle s}$	arc length	meter (m)
	displacement
${\displaystyle T}$	period	second (s)
	thermodynamic temperature also called absolute temperature	kelvin (K)
${\displaystyle t}$	time	second (s)
${\displaystyle \mathbf {U} }$	four-velocity	meter per second (m/s)
${\displaystyle U}$	potential energy	joule (J)
	internal energy	joule (J)
${\displaystyle u}$	relativistic mass	kilogram (kg)
	energy density	joule per cubic meter (J/m3) or joule per kilogram (J/kg) depending on the context
${\displaystyle V}$	voltage also called electric potential difference	volt (V)
	volume	cubic meter (m3)
	shear force
${\displaystyle \mathbf {v} }$	velocity	meter per second (m/s)
${\displaystyle W}$	mechanical work	joule (J)
${\displaystyle w}$	width	meter (m)
${\displaystyle x}$	a generic unknown	varied depending on context
	displacement	meter (m)
${\displaystyle Z}$	electrical impedance	ohm (Ω)

Greek characters[edit]

Symbol	Name	Meaning	SI unit of measure
${\displaystyle \alpha }$	alpha	angular acceleration	radian per second squared (rad/s2)
${\displaystyle \beta }$	beta	velocity in terms of the speed of light c	unitless
${\displaystyle \gamma }$	gamma	Lorentz factor	unitless
		photon
		gamma ray
		shear strain
		Heat capacity ratio	unitless
${\displaystyle \Delta }$	delta	a change in a variable (e.g. ${\displaystyle \Delta x}$)	unitless
		Laplace operator
${\displaystyle \delta }$	delta	displacement (usually small)
${\displaystyle \epsilon }$	epsilon	permittivity	farad per meter (F/m)
		strain	unitless
${\displaystyle \zeta }$	zeta	damping ratio	unitless
${\displaystyle \eta }$	eta	energy efficiency	unitless
		coefficient of viscosity also called simply viscosity	pascal second (Pa s)
${\displaystyle \theta }$	theta	angular displacement	radian (rad)
${\displaystyle \mathrm {K} }$	kappa	torsion coefficient also called torsion constant	newton meter per radian (N m/rad)
${\displaystyle \Lambda }$	lambda	cosmological constant	per second squared (s−2)
${\displaystyle \lambda }$		wavelength	meter (m)
${\displaystyle \mathbf {\mu } }$	mu	magnetic moment	ampere square meter (A m2)
		coefficient of friction	unitless
		dynamic viscosity	Pascal second (Pa s)
		permeability (electromagnetism)	Henry per meter (H/m)
		reduced mass	kilogram (kg)
${\displaystyle \nu }$	nu	frequency	hertz (Hz)
		kinematic viscosity	meters squared per second (m2/s)
${\displaystyle \pi }$	pi	3.14159... (irrational number)
${\displaystyle \rho }$	rho	mass density usually simply called density	kilogram per cubic meter (kg/m3)
		free electric charge density, not including dipole charges bound in a material	coulomb per cubic meter (C/m3)
		resistivity	Ohm meter (${\displaystyle \Omega }$ m)
${\displaystyle \Sigma }$	sigma	summation operator
${\displaystyle \sigma }$	sigma	electrical conductivity	Siemens per meter (S/m)
		normal stress
${\displaystyle \tau }$	tau	torque	newton meter (N m)
		shear stress
		time constant	second (s)
		6.28318... (2π)
${\displaystyle \Phi }$	phi	field strength	unit varies depending on context
		magnetic flux	Weber (Wb)
${\displaystyle \phi }$	phi	electric potential Higgs Field
${\displaystyle \Psi }$	psi	wave function	unitless
${\displaystyle \omega }$	omega	angular frequency	radian per second (rad/s)
${\displaystyle \Omega }$	omega	electric resistance	ohm