SI Units for Astronauts
The doors of the craft open into the cold, hazy atmosphere of Proxima Centauri b. Plans are afoot for a new workshop, fully equipped with sets of super-high-precision callipers, but alas! the cabin boy forgot to pack the International prototype metre he picked up on his trip to Paris.
Thankfully, as of 2019, we can work out all of our SI units from natural physical constants, let's get to work...
Firstly, a reminder of our units:
- Time - seconds (
s) - Distance - metres (
m) - Current - amperes (
A) - Mass - kilograms (
kg) - Temperature - kelvin (
K) - Luminous intesity - candelas (
cd)
(We're going to ignore Moles).
At various points in time, we've had lumps of metal in Paris that were the official kilogram, metre etc. These kind of definitions have some issues - notably that they can change (the kilo has got a bit lighter) and they're not universal (as in we'd have to drag one all the way to Proxima Centauri b). For our new definitions, we've fixed the constants (eg. the speed of light in a vacuum) and we derive the units from them.
Time depends on none of the other SI units for its definition.
Vibrate some caesium. Like a tuning fork, it has natural frequencies. Count 9,192,631,770 back and forths, and that was a second.
Distance is a function of time and a constant.
Measure the distance some light travels, in a vacuum, in 1 / 299,792,458 seconds, that was a metre.
Current is a function of time and a constant.
A unit of electrical charge is 1.602176634 × 10−¹⁹. The unit of this number is A ⋅ s..
Mass is a function of time, distance and a constant.
The Planck constant is 6.62607015 × 10⁻³⁴. The unit of this number is kg ⋅ m² ⋅ s⁻¹.
Using a Kibble balance, measure the electrical power (kg ⋅ m² ⋅ s⁻³) required to counteract some weight.
Temperature is a function of time, distance, mass and a constant.
The Boltzmann constant is 1.380649 × 10⁻²³. The unit of this number is kg ⋅ m² ⋅ s⁻² ⋅ K⁻¹.
Luminous intensity is a function of time, distance, mass, an angle and a constant.
The constant is 683. The unit of this number is cd ⋅ sr ⋅ kg⁻¹ ⋅ m⁻² ⋅ s³ where sr is a dimensionless way of measuring angles in 3D.