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

* 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 m^2/kg^2

M=1.989*10^{30} kg

a=1.496*10^{11} 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.

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