# What is the velocity of Earth at perihelion and aphelion? How is this information calculated?

##### 2 Answers

Earth's perihelion velocity is

#### Explanation:

Using Newton's equation, the force due to gravity which the Sun exerts of the Earth is given by:

Where

The centripetal force required to keep Earth in orbit is given by:

Where

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.

#### Explanation:

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.