references: THe physics of every day phenomena - A conceptual introduction to Physics - McGraw-Hill
Conceptual Physics, Paul Hewitt
1) REmember the circular motion of the planets? we supposed the motion to be uniform. We supposed the orbit to be
circular and we suppose the planet to move at a constant speed. (2 pi R / T ). T is the orbital period and R the radius of the orbit.
The force acting on the planet is the gravitational force Fc perpendicular to the motion and to the velocity V.
the planet, because of inertia, wants to keep moving at a constant speed, along a straight line, but the gravitational
force bring it back on its orbit. It is like the planet is constantly falling toward the Sun.
 | The magnitude of V is constant. |V| = 2pi R / T but its direction is constantly changing. There is no tangential acceleration since |V| is constant at = 0 but there is a centripetal acceleration ac (normal to V ). REmember ? a velocity is a vector so it as a magnitude and a direction. the magnitude is constant but the direction is not, because of the centripetal force. The centripetal acceleration is ac = V2 / R also Fc = m ac so m g(R) = m ac g(R) is the gravitaional field at a distance R from the Sun so g(R) = V2/R So the circular speed does not depend on the mass of the planet orbiting but only on the distance and on the gravitational field. The field g(R) depends on the Mass of the Sun and on the distance R. g(h) = G M / R2 G is the gravitational constant = 6.67 10-11 V = sqrt ( G M / R) |
2) In the particular cases of planets or moon moving along a circle, the motion is uniform.
The force and the velocity are perpendicular to each other and the magnitude of V is constant.
nice applet here