A long fall

Classical Mechanics Level pending

The Earth orbits around the Sun because it has angular momentum. If we stopped the Earth in orbit and then let it fall straight towards the Sun, how long would it take to reach the sun in seconds?

Details and assumptions

  • The mass of the Sun is 2×1030 kg2 \times 10^{30}~\mbox{kg}.
  • The mass of the Earth is 6×1024 kg6 \times 10^{24}~\mbox{kg}.
  • Newton's constant is 6.67×1011 Nm2/kg26.67 \times 10^{-11}~\mbox{Nm}^2/\mbox{kg}^2.
  • The Earth is 149,600,000 km149,600,000~\mbox{km} from the Sun.
  • You may treat the Earth and Sun as point masses.
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