Question

What would become of the Earth's orbit if half of the Sun's mass were suddenly to disappear, considering the Earth's kinetic energy (KE) and potential energy (PE)? Would the Earth remain bound to the Sun?

A) The Earth's orbit would expand, and the Earth would remain bound
B) The Earth's orbit would shrink, and the Earth would remain bound
C) The Earth's orbit would expand, and the Earth would not remain bound
D) The Earth's orbit would shrink, and the Earth would not remain bound

Answer 1

If half of the Sun's mass were to suddenly vanish, Earth's orbit would expand due to the decrease in gravitational pull, but it would remain bound to the Sun. This is due to the conservation of angular momentum and Kepler's third law relating to orbital dynamics.

Step-by-step explanation:

If half of the Sun's mass were to disappear suddenly, the gravitational force that it exerts on Earth would also decrease suddenly. Since Earth's kinetic energy and potential energy with respect to the Sun are proportional to the mass of the Sun, a sudden decrease in the Sun's mass would mean that Earth's orbital speed would be too great for the reduced gravitational pull. This mismatch would result in Earth moving to a higher orbit around the Sun to conserve angular momentum. Furthermore, according to Kepler's third law, if the mass of the Sun decreases, the diameter of Earth's orbit would indeed expand. In summary, Earth would remain bound but in an expanded orbit, following a path that is affected by the reduced gravitational attraction. The correct answer to this question is A) The Earth's orbit would expand, and the Earth would remain bound.