Question

A comet s moving in its orbit toward the Sun. As it approaches the Sun, part of the comet evaporates due to the Sun’s heat. The comet and Sun exert a gravitational force, F, on each other. After six weeks, the comet and Sun are one-eighth of their original distance apart, and the comet is one-fourth of its original mass. Which of the following is the force on the comet at the final distance?

Answer 1

After the comet becomes one-fourth of its original mass and one-eighth its original distance from the Sun, the gravitational force it experiences is 16 times the original force due to the inverse-square law of gravitation.

Step-by-step explanation:

To answer the question of what the force on the comet at the final distance is, we can invoke Newton's law of universal gravitation. The force of gravity between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

With the comet being one-eighth of its original distance from the sun and one-fourth of its original mass, the reduced mass results in a reduction of the gravitational force. However, the much smaller distance increases the force greatly since force varies inversely with the square of the distance. Specifically, if the original force was F, the new force is (1/4)/(1/8)^2 = (1/4)/(1/64) = 16 times the original force. Formally, F_{new} = (1/4 * M_comet * M_sun) / (1/64 * r^2), which simplifies to F_{new} = 16 * F, where M_comet and M_sun are the masses of the comet and the Sun, respectively, and r is the initial distance between them.