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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