What is the velocity of Earth at perihelion and aphelion? How is this information calculated?
Earth's perihelion velocity is
Using Newton's equation, the force due to gravity which the Sun exerts of the Earth is given by:
The centripetal force required to keep Earth in orbit is given by:
Combining the two equations, dividing by
The value of
At perihelion the distance from the Sun to the Earth is
At aphelion the distance from the Sun to the Earth is
The actual values as calculated using the NASA DE430 ephemeris data are
An alternative approach: Assume that the average velocity 29.7848 km/s is attained when r = a = 1.496 E+08 km. Then the formula v = 29.7848Xsqrt (2a/r -1) gives mini/max 29.22 km/s and 30.29 km/s.
At perihelion, r = a(1 - e) = 1.471 E+08 km and at aphelion r = a(1 + e) = 1.521 E+08 km. e = 0.01671.