Question 3

If the solar system was embedded in a uniform dust cloud of density $\rho$, what would be the law of force on a planet at a distance $r$from the centre of the Sun. (Such a force law was once suggested as the cause of the anomalous advance in the perihelion of Mercury.)

Treating the Earth's orbit as circular, estimate what density of dust would be needed to change the length of the year by one day. (Assume that the radius of the Earth's orbit remains at approximately $1.5\times 10^8$ km.)

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