Question

How did scientists determine how fast earth's orbit is around the sun?

Answer 1

The orbital speed of the Earth is easy to calculate using geometry - we can find the circumference (distance) and divide it by a year (time)

Explanation:

The Earth completes one full orbit, `360^@`, in one year, which is 365.256 days, or exactly 31,556,926 seconds.

The Earth's orbit is slightly elliptical, but is pretty close to circular. The mean (semi-major) distance from the sun to Earth is 149.6 million km. Remembering our geometry a circle with a radius of 149.6 million km is:

`c=2 pi r`
`c=2*pi*149600000 km`
`c= 939964522 km`
or
940 million km.

the orbital speed can be calculated using:
`v=d/t`
`v=(940000000km)/(31556926s)`
`v=29.79 (km)/s`