How strong is the sun gravitational pull?

How is the planet Mercury's speed relative to its gravitational pull of the sun?

• Scenario: The sun is huge so its gravity must be pretty powerful. Powerful enough to keep all the planets in orbit around it. Mercury is so small, it is closet to the sun, and travels fast. So what is the formula of maintaining this small, fast planet in or bet? How do you figure numbers to find Mercury's weight according to mass. Or how does mass work without weight in gravitational fields?

• Answer:

  Weight is not a meaningful concept for an object in free fall. Weight only exists when something is being held in some way in a gravitational field so it cannot fall. Orbital velocity is calculated as sqrt(G*M/R) where G is the Gravitational Constant, M is the gravitating mass (the Sun in this case) and R is the radius of the orbit. The velocity is, of course, independent of the mass of the orbiting object - dust motes and planet orbit at the same speed/