I just signed up for blog365, a sort of year-long blogging NaNo. This is partly to console myself after my inglorious failure at said NaNo last year. The idea is to post something every day for the year – something I’m sure those of you bemoaning my infrequent articles must be gladdened to hear. Don’t all clamour at once…

In principle, I’ve already lost blog365 because I didn’t post anything yesterday – but fortunately there’s a leap day coming up which I’ll use to catch up. Anyway, today’s article is inspired by something in the blog365 headline which mentions a lap around the Sun. I wondered: how fast is the Earth moving?

The geocentric days are gone, the Earth is still a sphere

Objects in the mirror may be just as they appear

We spin around the Sun and call each trip we make a year…

Steve Forbert, Thirty More Years

When I was young, my dad (Ken) asked me how far I thought I could see – I thought I was being smart when I said ‘a mile!’ but he told me that the Sun was 93 million miles away, so I could see at least that far. Nobody likes a smartarse. If nothing else, it did imprint the distance between the Sun and Earth firmly on my mind. Now, though, I convert it to 150 million kilometres, which is a much rounder number.

Let’s assume that Earth’s orbit is circular. It isn’t really – it’s slightly elliptical (it varies between about 147 and 152 million km, but for the sake of a few per cent I’ll stick to a circular orbit with r = 150 million km). The length of the Earth’s orbit is then 2πr, about 940 million km.

As Steve Forbert so astutely notes, this trip takes a year – a little under 365 and a quarter days. That turns into 8,766 hours, which I’m going to call 8,800 hours – I want a ballpark figure, not something too precise. Speed is measured in kilometres per hour, of course, which tells us straight away that the formula is distance (km) divided by (per) time (hour) , giving us speed = 940,000,000km / 8,800h.

That’s a recipe for getting the answers wrong by an order of magnitude. Let’s rewrite it in scientific notation to make it simpler: speed = 9.4 10^8 km / 8.8 10^3 h. That gives us 1.07 or so, dividing the number bit (the mantissa, if you prefer), times 10^5 (subtracting the exponents) – we’re orbiting the Sun at over 100,000km/h! (Wikipedia says 107,218 km/h – even with rough numbers, we’re correct to 3 significant figures).

It’s worth remembering that we’re spinning around the Earth’s axis as well. Are we spinning faster than we orbit? Well, the radius of the Earth is about 6,000 km, so at the equator the circumference is about 40,000km. (These are even rougher numbers than before, but again they’ll do). At Bozeman’s latitude* of about 46ºN, we only travel about 70% of that**, so 28,000km, over the 24 hours of a day. That means we’re spinning around the Earth’s axis at over 1,000km/h – about a hundredth of the orbital speed.

Take-home messages of the day:

- nobody likes a smartarse;
- the geocentric days are gone and the Earth is still a sphere; and
- sums with astronomical numbers in are much easier if you use scientific notation.

*Need maths tuition online? Check out OxfordMathsTutoring.wsnw.net* *– mention Kensson’s Ramblings and get a 5% discount!*

* lines of latitude are lateral; lines of longitude are equally long.

** cos(46º) = 0.695.

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