ch13-p087 - 87. (a) The total energy is conserved, so there...

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87. (a) The total energy is conserved, so there is no difference between its values at aphelion and perihelion. (b) Since the change is small, we use differentials: () ( ) ( ) 11 30 24 9 2 2 11 6.67 10 1.99 10 5.98 10 51 0 1.5 10 ES GM M dU dr r §· ×× × ¨¸ =≈ × ©¹ × which yields Δ U 1.8 × 10 32 J. A more direct subtraction of the values of the potential energies leads to the same result. (c) From the previous two parts, we see that the variation in the kinetic energy
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