A View from the Back of the Envelope top

Round Earth, Tilted People
Where is China? It is down over there...
Kilometers in your hands

The Earth is round, so your neighbors are tilted.

The idea: We all know the Earth is round, and people on the other side are upside-down. But even nearby people, in neighboring cities, can be noticeably tilted. And visualizing the tilt, when thinking of a distant place, or when watching a newscast, can help tie together the place, its distance, and our round Earth.

Consider sunrise in California. I am in New England. A Californian is facing the sun just rising above their horizon. Compared with me, they are tilted back 40 degrees, almost diagonal. They are looking horizontally (for them), straight out at the sun, which for me is half way up the sky (40° up). Even people in New York City, a few hours drive away, are noticeably listing. And from my perspective, even the steeper slopes of the Rockies are flat, horizontal.

Earth circumference is 40 Mm (±<<1%).
So tilt° = distance / 40,000 km × 360°,
or tilt° ~= distance × 0.01 °/km
(~= 1.6 × 10-4 rad/km ~= 0.0002 rad/km).
100 km63 miles1 degree(actually, a bit less)
1000 km630 miles10 degrees(closer to 9 degrees)
10000 km6300 miles100 degrees(closer to 90 degrees)
10000 km6300 miles90 degrees( horizontal )
5000 km3100 miles45 degrees( diagonal )
3333 km2100 miles30 degrees

I am in Boston. New York City is about 300 km to the southwest of me.
So people there are tilted about 3° to the SW (say 0.06 rad).

How much of a tilt is that? Well, a two meter person's head is shifted about 10 cm (and 1 m person's, 5 cm). A hand's breadth. Enough to shift your weight forward onto your toes, or backward onto you heels.

California is about 4000 km away from me to the west,
so people there are tilted about 40 degrees to the west.

Earth's circumference is 40 Mm (40,000 km).
About 1 degree tilt per 100 km distance.
The person's tilt is in the same direction as the person.

A View from the Back of the Envelope
Comments encouraged. - Mitchell N Charity <mcharity@lcs.mit.edu>


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  1999.Mar.02   Created.