Sunlight on Its Way

solved Units

Q. Suppose the unit of length were the distance light goes in one second $c = 1$ m/s. Sunlight takes 8 minutes 20 seconds $t_{light} = 500$ s to reach us. How far is the Sun in that unit?

Outputs

distance

d_{light}

How it's solved

Solved with Units

Given

$c = 1$ m/s from “the distance light goes in one second”
$t_{light} = 500$ s from “8 minutes 20 seconds”

Find $d_{light}$ .

Working

distance at light speed $d_{light} = c \cdot t_{light}$
$d_{light} = 1 \cdot 500$
$d_{light} = 500$ m
$d_{light} \approx 500$ mto 3 significant figures

Conclusion

Choose light's own travel as the unit of length and its speed becomes one, so a distance and its travel time are the same number.

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 :sunlight_on_its_way do4  kind :numerical5  describes "Suppose the unit of length were the distance light goes in one second. Sunlight takes 8 minutes 20 seconds to reach us. %{distance}?"6  asks distance: "How far is the Sun in that unit"7end

solution.rb

1require_relative "../questions/sunlight_on_its_way"2require_relative "../science/units_and_measurement/units"34solve :sunlight_on_its_way, using: Units do5  deduce_from "the distance light goes in one second", c: 1.06  deduce_from "8 minutes 20 seconds", t_light: "500 s"7  take distance: :d_light8  answer find_value(:distance, figures: 3)910  conclusion "Choose light's own travel as the unit of length and its speed becomes one, so a " \11             "distance and its travel time are the same number."12end

playground.rb

1require_relative "../solutions/sunlight_on_its_way"23play_with :sunlight_on_its_way do4  title "Sunlight on Its Way"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