Neptune has a radius of 2.48 × 10⁷ m and an escape velocity of 23,300 m/s. What is the mass of Neptune? G = 6.67 x 10^-11 N·m²/kg². A) 1.01 × 10²⁶ kg B) 2.02 × 10²⁶ kg C) 3.03 × 10²⁶ kg D) 4.04 × 10²⁶ kg E) 5.05 × 10²⁶ kg

Question

Quizplus · Accepted Answer

We can start by using the formula for escape velocity:

Ve = sqrt(2GM/R)

where Ve is the escape velocity, G is the gravitational constant, M is the mass of Neptune, and R is the radius of Neptune.

Rearranging the formula gives:

M = Ve^2R/2G

Plugging in the values gives:

M = (23300 m/s)^2(2.48 x 10^7 m)/(2 x 6.67 x 10^-11 Nm^2/kg^2)

M = 1.02 x 10^26 kg

Since this answer is closest to choice A, that is the best choice.

Neptune Has a Radius of 2