Question

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

Answer 1

Earth's perihelion velocity is `30.28`km/s and its aphelion velocity is `29.3`km/s.

Explanation:

Using Newton's equation, the force due to gravity which the Sun exerts of the Earth is given by:
`F=(GMm)/r^2`
Where `G` is the gravitational constant, `M` is the mass of the Sun, `m` is the mass of the Earth and `r` is the distance between the centre of the Sun and the centre of the Earth.

The centripetal force required to keep Earth in orbit is given by:
`F=(mv^2)/r`
Where `v` is the orbital velocity.

Combining the two equations, dividing by `m` and multiplying by `r` gives:
`v^2 = (GM)/r`

The value of `GM=1.327*10^11km^3s^(-2)`.

At perihelion the distance from the Sun to the Earth is `147,100,000 km`. Substituting the values into the equation gives `v=30kms^(-1)`.

At aphelion the distance from the Sun to the Earth is `152,100,000 km`. Substituting the values into the equation gives `v=29.5kms^(-1)`.

The actual values as calculated using the NASA DE430 ephemeris data are `30.28ms^(-1)` and `29.3kms^(-1)`.

Answer 2

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.