## How fast does the Earth go at perihelion and aphelion? (Intermediate)

I need to find the approximate speeds of the earth's orbit at perhilion and aphelion (this year, for example, if it makes a difference). I have given myself a crash course in astronomy over the course of the last three months and command a fair if somewhat pedantic understanding of the underlying principles. The earth's mean revolutionary velocity is easily found, but i have not found these precise figures and am not much of a math whiz. Can you help me?

The formula for the velocity of an object at some distance r from the Sun is:

v = sqrt[GM*(2/r - 1/a)]

Where G is the universal gravitational constant, M is the mass of the Sun, and a is the planet's semimajor axis.

At perihelion, Earth's distance from the Sun is r=a(1-e) and at aphelion, it's r=a(1+e).

G=6.673*10-11 N m2/kg2

M=1.989*1030 kg

a=1.496*1011 m

e=0.017

So plugging in the numbers, the speed at perihelion is 30,300 m/s and at aphelion it's 29,300 m/s.

#### Britt Scharringhausen

Britt studies the rings of Saturn. She got her PhD from Cornell in 2006 and is now a Professor at Beloit College in Wisconson.

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