Selected Questions - Answers From All Experts Astronomy Forum (Ratio of Planets' Orbital velocities)

Question: How would a person calculate the ratio of the orbital velocities of two planets, say Earth and Venus?

Answer:    This is a relatively straightforward astronomical computation, using the ratio relation:

V2/V1 = (a2/a1) (T1/T2)

Where a2, and a1 are the respective semi-major axes of the orbits (i.e. the mean distances from the Sun) and T2, T1 are the respective periods.

By convention we assign '1' to the inner planet (e.g. Venus) and '2' to the outer (Earth).

Then we have a2 = 1 AU,  and for Venus  we need to obtain T1 from Kepler's third law:

(T1/ T2) 2      = k(a1/ a2) ³ 

Now, obtaining Venus' period in days (224.69) from planetary data, we can convert it to years, e.g.

T1 = (224.69/365.25) yr. = 0.615 yr.

And Venus' semi-major axis is:
 
a1 = {[T1] ² }1/3   = [(0.615)²] 1/3 


a1 = 0.723 AU

Therefore:

V2/V1 = (1/ 0.723)(0.615/ 1)


V2/V1 = 0.615/ 0.723   = 0.851

Or, in terms of the ratio of Earth's orbital speed to Venus':   1/ 0.851  =1.175

This can be checked  using a Table of Orbital Velocities found in Astrometric & Geodetic Data, from which one finds:

V(Venus) = 35.02 km/s

V(Earth) = 29.78 km/s

Take the ratio:

V(Venus)/V(earth) = (35.02 km/s)/ (29.78 km/s) = 1.175

So, Venus' orbital velocity is 1.175 times Earth's