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II. Short Answer Questions · Q11

Q.Why is the energy of a satellite (or any other planet) negative?

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Step 1. A satellite's potential energy is U=−GMsMe/(Re+h)U=-GM_sM_e/(R_e+h), and its kinetic energy (using the orbital speed) works out to K.E.=12GMsMe/(Re+h)K.E.=\tfrac12 GM_sM_e/(R_e+h) -- exactly half of ∣U∣|U|.

Step 2. Adding them, E=K.E.+U=12∣U∣−∣U∣=−12∣U∣E=K.E.+U=\tfrac12|U|-|U|=-\tfrac12|U|, which is negative since ∣U∣>0|U|>0. …

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