A Metre in Light-Years

solved Units

Q. A light-year is the distance light goes in a year. What is one metre $l = 1$ m in light-years?

Inputs

metre

l

1.00 m

Outputs

light years

l

How it's solved

Solved with Units

Given

$l = 1$ m

Find $l$ .

Working

$l = 1$ m $= 1.05700083 \times 10^{−16}$ ly
$l \approx 1.06 \times 10^{−16}$ lyto 3 significant figures

Conclusion

A light-year is a length, the distance light goes in a year, so one metre is a tiny fraction of it.

The web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb

1require_relative "../physics"23question :a_metre_in_light_years do4  kind :numerical5  describes "A light-year is the distance light goes in a year. What is %{metre} %{light_years}?"6  given metre: "1 m", as: "one metre"7  asks light_years: "in light-years"8end

solution.rb

1require_relative "../questions/a_metre_in_light_years"2require_relative "../science/units_and_measurement/units"34solve :a_metre_in_light_years, using: Units do5  take metre: :l6  take light_years: :l7  answer find_value(:light_years, in: "ly", figures: 3)89  conclusion "A light-year is a length, the distance light goes in a year, so one metre is a tiny " \10             "fraction of it."11end

playground.rb

1require_relative "../solutions/a_metre_in_light_years"23play_with :a_metre_in_light_years do4  title "A Metre in Light-Years"5end

The laws it drew on

quantity	written	units	within	from
speed of light	$c$	m/s	—	Units
avogadro constant	$N_{A}$	mol⁻¹	—	Units
length	$l$	m	0 … ∞	Units
mass	$m$	kg	—	Units
time	$t$	s	0 … ∞	Units
electric current	$I$	A	—	Units
temperature	$T$	K	—	Units
amount of substance	$n$	mol	—	Units
luminous intensity	$I_{v}$	cd	—	Units
arc length	$s$	m	—	Units
radius	$r$	m	0 … ∞	Units
plane angle	$θ$	—	—	Units
area	$A$	m²	—	Units
solid angle	$Ω$	—	—	Units
light time	$t_{light}$	s	—	Units
light distance	$d_{light}$	m	—	Units
number of entities	$N$	—	—	Units
baseline	$B$	m	—	Units
distance away	$D$	m	—	Units
parallax angle	$θ_{p}$	—	—	Units

θ = \frac{s}{r}

arc over radius

Ω = \frac{A}{r^{2}}

area over radius squared

d_{light} = c \cdot t_{light}

distance at light speed

N = n \cdot N_{A}

entities in moles

θ_{p} = \frac{B}{D}

baseline over distance