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CH 12: Gravitation

CH 12: Gravitation. We have used the gravitational acceleration of an object to determine the weight of that object relative to the Earth. Where does this acceleration come from?.

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CH 12: Gravitation

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  1. CH 12: Gravitation

  2. We have used the gravitational acceleration of an object to determine the weight of that object relative to the Earth. Where does this acceleration come from? The gravitational acceleration is due to the gravitational force, an attractive force that exists between the two masses. M1 and M2 – Masses of the two objects [kg] G – Universal gravitational constant G = 6.67x10-11 N m2/kg2 r – distance separating the center of mass of the two objects [m] Fg – Gravitational force between the two objects [N] This force is often very small unless you are using at least one very large mass! Dog Boy FDB Example: What is the force a 40 kg boy exerts on his 20 kg dog if they are separated by a distance of 2 m? FBD This is an example of Newton’s 3rd Law. The force on each object is equal, but they have opposite directions. 2 m

  3. Now that we know how to determine the magnitude of the gravitational force, how can we determine the magnitude of the gravitational acceleration? If we look specifically at an object on the surface of the Earth. If neither the mass of the Earth nor the radius of the Earth change this acceleration would be constant. This is only valid for an object at the surface of the Earth! Notice that the acceleration would depend on the distance away from the surface of the Earth. When we are looking at an object at some altitude we must modify the expression for the acceleration in the following way: The gravitational acceleration depends on the altitude of the mass above the Earth.We can use g as an approximation of the gravitational acceleration for objects that are close to the surface of the Earth.

  4. Kepler’s Laws of Planetary Motion Kepler’s laws are all derived from the law of universal gravitation and angular motion. 1) All planets move in elliptical orbits. Using the law of gravitation it is possible to prove that the orbital path of plants is elliptical. 2) The radius vector from the sun to the planet sweeps out equal areas in equal time intervals. Fg Fg dr v Perigee (Perihelion) – Closest Apogee (Aphelion) – Furthest r dA dr dA r v L is constant constant

  5. 3) The square of the orbital period of any planet is proportional to the cube of the semimajor axis of the elliptical orbit. Semiminor axis Semimajor axis 2b 2a Average velocity of an object in a circular orbit c Foci Assuming a circular orbit: For an elliptical path we substitute a for r

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