Orbital Energy

Estimate the total energy of Earth’s orbit in \(\si{\joule}\).

Details and Assumptions:

  • \(G = \SI[per-mode=symbol]{6.6e-11}{\newton\per\kilo\gram\squared\meter\squared}\)
  • \(M_\textrm{Earth} = \SI{6e24}{\kilogram}\)
  • \(M_\textrm{Sun} = \SI{2e30}{\kilogram}\)
  • \(\SI{1}{\astronomicalunit} = \SI{1.5e11}{\meter}\) (This is the mean distance from the Earth to the Sun.)

I created this problem for the 2013 UBC Physics Olympics (Problem 2).
Answers to a \( 2 \% \) margin of error will be accepted.

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