Armageddon

Classical Mechanics Level 3

If the Earth were suddenly stopped in its orbit, how long in days would it take for it to collide with the Sun?

Details and Assumptions

Regard the Sun and Earth as fixed point masses.
Mass of the Sun, \(M=1.989\times 10^{30} \text{kg}\).
Mass of Earth, \(m=5.972\times 10^{24} \text{kg}\).
Distance Earth to the Sun, \(R=1.496\times 10^{8} \text{km}\).
The gravitational constant, \(G=6.674\times 10^{-11} \text{m}^3\text{kg}^{-1}\text{s}^{-2}\).

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