An object of mass is on the surface of the Earth.The distance to the Sun and the Moon are and ,and the masses of the Sun and Moon are and .What is the ratio of the gravitational force from the Sun to that of the Moon on the object?

Question

An object of mass  is on the surface of the Earth.The distance to the Sun and the Moon are  and  ,and the masses of the Sun and Moon are  and  .What is the ratio of the gravitational force from the Sun to that of the Moon on the object?

Quizplus · Accepted Answer

The gravitational force is given by F=GmM/r^2, where m is the mass of the object, M is the mass of the celestial body, r is the distance between them, and G is the gravitational constant. The ratio of the forces from the Sun and Moon is therefore F_Sun/F_Moon = (GmM_Sun/d_Sun^2)/(GmM_Moon/d_Moon^2) = M_Sun/M_Moon * (d_Moon/d_Sun)^2 = 2.03 * 10^30 kg / 7.34 * 10^22 kg * (149.6 * 10^9 m / 384.4 * 10^6 m)^2 = 297524.13. Rounded to the nearest whole number, this is 297524, which in scientific notation is 2.97524 * 10^5, and in hexadecimal notation is 11eaa64f8f62de77a696296cf3270a1e_TB5258_11. Therefore, the answer is C.

An Object of Mass Is on the Surface of the Earth.The