The pattern for satellite speed in a circular orbit can be used to obtain the first space velocity for a planet.
This is because the first cosmic velocity for any planet is equal to the velocity that the body must have in order to sustain itself in a circular orbit at a distance from the center of the planet exactly equal to that of the planet .
So you have to substitute the radius of the planet and the mass of the planet to get the pattern.
Warning:
The first cosmic speed for a planet is the highest speed a body can have on a stable circular orbit. With the pattern of orbital orbit velocity it follows that with the increase of the radius the orbiting velocity decreases (yes, although many expect the inverse relationship ...). Of course it is not possible to orbit the interior of the planet and therefore the value of the planet's radius is the limit (the smallest) value for the radius of the circular orbit.