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Next, we will continue our 'what if' game by considering what would happen if Newton's Law of Gravity were not inverse square in nature (that
Next, we will continue our 'what if' game by considering what would happen if Newton's Law of Gravity were not inverse square in nature (that is, the force did NOT depend on r^-2 [or 1/r 2]). Instead we will consider the situation that would exist if the force of gravity depended on r -1.8 instead! We first consider the strength of the new force. Since the radius is to the negative power (that is, it is in the denominator), and since r^1.8 is less than r 2, we see that r^-1.8 is greater than r*-2 ! Thus the new force will be greater than the real force of gravity. Next we consider whether we can still have circular motion with this stronger force of gravity. As long as Newton's Second Law of Motion holds true, and as long as the definitions of velocity and acceleration hold true so that a = v 2/r, we CAN still have circular motion. Question #7 : Enter in the circular speed for the Earth in m/s: 2 . 36882e14 ( Recall M-sun = 2830 kg ; R = 1. 5ell m) Your answer was NOT correct. Try again. HINT #2: F = ma with F = G*Mc*m*r^-1. 8 and a = v^2/r leads to: V = SQR ( G*Mc*r - .8) HINT: use the y x button on your calculator to find r^0.8
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