What is the escape velocity of a rocket launched from position A,the center of the three planet system depicted in the figure.Each planet has mass M = 10²⁴ kg,radius R = 10⁶ m,and the center-to-center distance between any two planets is 10 R.

Question

Quizplus · Accepted Answer

The escape velocity, ve, is given by the formula: ve = sqrt(2GM/r), where G is the gravitational constant, M is the mass of the planet, and r is the distance from the center of the planet.

Since the rocket is launched from position A, which is at the center of the system, the distance to the nearest planet is 2R (from the center of the rocket to the surface of the planet), and the total mass acting on the rocket is the sum of the masses of all three planets: 
M_total = 3M = 3 x 10^24 kg

Substituting these values into the formula, we get: 
ve = sqrt(2 x 6.674 x 10^-11 x 3 x 10^24 / (2 x 10R)) 
= sqrt(2.004 x 10^14) 
= 1.417 x 10^7 m/s 
= 14,170 km/s

Therefore, the correct answer is B) 8.33 km/s.

What Is the Escape Velocity of a Rocket Launched from Position