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Since the sum of all forces is the centripetal force, drawing centripetal force into a free body diagram is not necessary and usually not recommended. Using F net = F c {\displaystyle F_{\text{net}}=F_{c}} , we can draw free body diagrams to list all the forces acting on an object and then set it equal to F c {\displaystyle F_{c}} .
In Newtonian mechanics, gravity provides the centripetal force causing astronomical orbits. One common example involving centripetal force is the case in which a body moves with uniform speed along a circular path. The centripetal force is directed at right angles to the motion and also along the radius towards the centre of the circular path.
Note: This page uses common physics notation for spherical coordinates, in which is the angle between the z axis and the radius vector connecting the origin to the point in question, while is the angle between the projection of the radius vector onto the x-y plane and the x axis. Several other definitions are in use, and so care must be taken ...
The speed (or the magnitude of velocity) relative to the centre of mass is constant: [1]: 30 = = where: , is the gravitational constant, is the mass of both orbiting bodies (+), although in common practice, if the greater mass is significantly larger, the lesser mass is often neglected, with minimal change in the result.
Next Newton proves his "Theorema II" which shows that if Kepler's second law results, then the force involved must be along the line between the two bodies. In other words, Newton proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.
At the equator, the velocity of Earth's surface is about 465 metres per second (1,674 km/h; 1,040 mph). The amount of centripetal force required to cause an object to move along a circular path with a radius of 6378 kilometres (the Earth's equatorial radius), at 465 m/s, is about 0.034 newtons per kilogram of mass. For a 10,000-gram internal ...
Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Both are inverse-square laws, where force is inversely proportional to the square of the distance between the bodies. Coulomb's law has charge in place of mass and a ...
Here Newton finds the centripetal force to produce motion in this configuration would be inversely proportional to the square of the radius vector. (Translation: 'Therefore, the centripetal force is reciprocally as L X SP², that is, (reciprocally) in the doubled ratio [i.e., square] of the distance ... .')