Explanation on equations please

Question

I've got seemingly two different equations for velocity in orbit:

$$v_1 = \sqrt{ \frac{2GM}{R}} $$

and $$v = \sqrt{ \frac{Gm_e}{R}}$$

What is the difference between these two? I'm quite sure that $G$ is the gravitational constant, $m_e$ is the mass of the earth. $R$ is the radius of orbit in both cases. I'm not sure what the sub script $1$ is but it has something to do with energy conservation.

Answer 1

Comment turned answer per request.

• $v_1$ is the escape velocity. If you throw a rock straight upward with this velocity, the rock with escape to infinity.
• $v$ is the orbital speed for an object to rotate around earth in a circular orbit of radius $R$ without falling back to earth.