A central force is a type of force that acts on an object towards or away from a fixed point, called the center of force. This force is always directed along the line connecting the object to the center of force.
The three types of orbits under central force are circular, elliptical, and parabolic. A circular orbit is when the object moves in a circular path around the center of force, while an elliptical orbit is an oval-shaped path. A parabolic orbit is a path that is neither circular nor elliptical, but rather a straight line that intersects the center of force.
The motion of an object under central force is described by Kepler's laws of planetary motion. These laws state that the object follows an elliptical orbit, with the center of force at one focus of the ellipse. The object also sweeps out equal areas in equal times and the square of the orbital period is directly proportional to the cube of the semi-major axis of the ellipse.
The equation for calculating the centripetal force in an orbit under central force is F = (m * v^2) / r, where F is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the distance between the object and the center of force.
The central force affects the trajectory of an object by determining the shape and size of the orbit. A stronger central force will result in a smaller orbit, while a weaker central force will result in a larger orbit. The direction of the force also affects the trajectory, as it determines whether the orbit is clockwise or counterclockwise.