I may have to look up tangential velocity then
Calculating the tangential velocity based on orbit parameters like distance/eccentricity:
v = sqrt((G*M/a)*(1 + e)/(1 - e)).
The planet Mercury's semi-major axis a = 57909176e3 metres, and has an orbit eccentricity e = 0.20563069:
v = sqrt((6.6742e-11 * 1.988435e30 / 57909176e3) * (1 + 0.20563069) / (1 - 0.20563069)),
v = 58976.3015.
That's very close to the maximum orbit speed of Mercury, as 58980 m/s on wikipedia.org.
(Note, 1.988435e30 == Sun's mass)
Oppositely, for the apoapsis velocity:
v = sqrt((G*M/a)*(1 - e)/(1 + e)),
v = 38858.47.
For a circular orbit, the eccentricity is 0.
These calculations help you find the length of the tangential velocity vector. As for finding the direction of the tangential velocity vector, the cross product operation will help you (if your orbit plane is nice and aligned with the coordinate system, it's very straightforward).