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

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,

** speed at perihelion is 30,300 m/s and at aphelion it’s 29,300 m/s.**