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Transcript
Gravitation Gravitation vs. Gravity All objects near the surface of Earth accelerate toward Earth at a rate of 9.8m/s2 regardless of their mass and assuming there is no air resistance. The force of gravity can be found two different ways depending on the location of the object relative to Earth. Near the surface F=mg where rearranging for g, we get g=F/m. Therefore a m/s2 is equivalent to a N/kg. In addition to acceleration, this is the gravitational field strength. Just like electric field is a N/C. g is the amount of force felt per kg of mass. Alternate Calculations This holds true at the surface of Earth and at any distance away from Earth. r is the distance between the centers of mass of each object. At very large distances, the radius of Earth itself is negligible. Combining the two Substituting mg for F gives us mg=(GMm)/r2 g = (GM)/ r2 Use this to solve for the acceleration due to gravity on any planet where M is the mass of the planet and r is the radius of the planet. Orbiting objects Any object orbiting another object is NOT weightless. Gravitational fields are everywhere in space due to masses in space. Therefore objects in space have weight. These objects are in freefall. But as they fall toward a planet, the surface of the planet curves away from them so they can never reach the surface. Orbiting objects are undergoing UCM where Fc=mv2/r Centripetal force has to be caused by something and in this case it is gravity. mv2/r = (GMm)/r2 v = √(GM/r) This is the orbital velocity of an object in in a geosynchronous orbit. Gravitational Forces These are vectors and should following the same rules for vectors when investigating multiple masses interacting. Solve for components and find the resultant.