The way I remember Earth's approximate mass is the fact it's 10 times Avogadro's number in kg.
My physics teacher always had a great way of drilling in these tidbits.
My physics teacher always had a great way of drilling in these tidbits.
They also made things complex by then picking a unit of mass that’s inconsistent with that: a gram isn’t the mass of 1m³ of water, but of 1/10⁶ m³ of water (a cubic meter is 10³ liters, and a liter of water weighs 10³ grams)
Centimeter-gram-second (https://en.wikipedia.org/wiki/Centimetre–gram–second_system_...) really is superior in that sense (but of course, that’s relative to the arbitrary choice of using water to convert between mass and volume, and from that, length)
Exploring a bit, picking 4 times that, as an estimate of the circumference, would give us a basic length unit of 4 cm (a pretty reasonable unit—bit over an inch and a half, fits right in with the variety of Chinese cun standards, for example). Then our immediate volume unit is 64 mL, which seems kind of small (on the scale of 2 floces), but ten of them make a decent "pint", so I think it can work—it's ~13% bigger than an imperial pint instead of ~12% smaller. the corresponding mass unit, at ~64 g, which again seems a bit small but manages to line up an average person's weight right around 1 kilo.
Avogadro's number is close to 24!, so we could redefine our mass unit as exactly 24! hydrogen atoms (or 4!!) and that comes out to within about 3% of a gram while being significantly easier to communicate to an extraterrestrial civilization.
[1]: https://en.wikipedia.org/wiki/Earth's_circumference
[2]: https://en.wikipedia.org/wiki/Metre#Meridional_definition
>o their 1793 measurement of the distance from the equator to the North Pole was off by less than 2 km....
They spent several years making lots of smaller measurements that were added up.
Each measurement was done twice to ensure correctness. One of the distances had two conflicting measurements, but due to a war, they could not return to make a third measurement and had to just choose one of them (the wrong one).
They chose not to tell anyone because they feared politicians would use it to discredit the metric system.
For me, it's: Earth is a blue marble - in "Mega-view" (Mm zoomed to mm) - with a diameter of a baker's dozen Megameters. The volume of a ball is one half of its enclosing box, so that's ~(1E7)^3 or 1E21 m^3. Earth is rock (3 Mg/m^3) and iron (8 Mg/m^3) and averages 5 Mg/m^3. Or just bracket it - water,lead,gold is ~ 1,10,20 Mg/m^3). Giving an Earth mass of 5E24 kg. Actual value 6E24 kg. Brackets of water and lead give 1E24 to 11E24 kg.
> a great way of drilling in these tidbits
For me it's: Arm-sized, hand-sized, fingernail-sized, and "tiny"-sized, are 1000, 100, 10, and 1 mm. Zooming these by 1000^n gives scale-model "views". Mega-view with planet balls, kilo-view with cities in your palm, meter-view with buildings in hand, micro-view with red blood cell M&M's (yum), nano-view with virus balls (chewy shell, stringy inside), pico-view with H2O bumpy basketballs, femto-view with nuclei marbles. It's easier to remember how big things are, once they're toy-sized, and you've handled and played with them.
Just something I crafted years back. Resulting videos didn't seem to user test well. I was set to dust it off, doing rapid iterative development over gorilla street usability testing... in Spring 2020. Ah well.