Newton S Second Law Of Motion In Vector Form Is F Ma 1 Where F Is The Force Vector In N Newtons And A Is The Accel 1 (49.82 KiB) Viewed 25 times
Newton S Second Law Of Motion In Vector Form Is F Ma 1 Where F Is The Force Vector In N Newtons And A Is The Accel 2 (49.82 KiB) Viewed 25 times
Newton's second law of motion in vector form is: F=ma (1) where F is the force vector in N (Newtons), and a is the acceleration vector in m/s2 , and m is the mass in kg. 2 m! Newton's law of gravitation in vector form is: GMm (2) FP FI where G=6,67x10-1 is the universal gravitational constant, M is the mass of s² - kg the larger object (the Sun), and is 2x10 kg. and m is the mass the smaller one (the planets or the spacecraft). The vector is the vector connecting the Sun to the orbiting objects. Note that in (1) and (2), the variables F. a and F are all functions of time, and ä(t) = F"() 2) The motion force in Equation (1) and the gravitational force in Equation (2) are equal. Equate the right hand sides of equations (1) and (2), and cancel the common factor on the left and right sides. 3) Using ä(t)= F"(t), and F(t)= x(t)i + y(t)j, convert the equation in step 2 above to an equation involving x(i), y(t) and their second derivatives. Note that these are the xy- coordinates of each orbiting object.
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