What is the direction of areal velocity of the earth around the sun?

We know that the areal velocity of earth around the sun is given by

….(i)

Where

L⃗ = angular momentum of earth about sun

mass of earth

Now, angular momentum of earth around the sun is given by

…. (ii)

Where

v⃗ = velocity of earth

r⃗ = position vector of earth w.r.t sun

from eqn.(i) and (ii) we have,

Therefore, direction of areal velocity is perpendicular to the plane containing velocity vector and position vector.

Therefore, areal velocity of earth is normal to the plane containing earth and the sun