Question

What is the centripetal force that holds planets in orbit?

Answer 1

Answer: Gravity force

If we approximate the orbit of the planets around the Sun to circular orbits with a uniform circular motion, where the velocity $\vec{V}$ is a vector, whose direction is perpendicular to the radius $r$ of the trajectory; the acceleration $\vec{a}$ is directed towards the center of the circumference (that's why it's called centripetal acceleration).  

Now, according to Newton's 2nd law, the force $\vec{F}$ is directly proportional and in the same direction as the acceleration:  

$\vec{F}=m.\vec{a}$  

Therefore the net force resulting from the movement of a planet orbiting the Sun points towards the center of the circle, this is called Centripetal Force which is a central force that in this case is equal to the gravity force.