A near miss

Classical Mechanics Level 3

Recently, Asteroid 2012 DA14 came within 34,200 km from the center of the earth at its point of closest approach. If the moon goes around the earth once every 27.5 days, what is the ratio of the distance of closest approach of DA14 to the radius of the orbit of the moon?

Details and assumptions

  • The mass of the earth is \(6 \times 10^{24}~\mbox{kg}\).
  • One day is 24 hours.
  • Assume the moon orbits the earth in a circle.
  • Newton's constant is \(G=6.67 \times 10^{-11}~\mbox{N}~\mbox{m}^2/\mbox{kg}^2\).

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