If the Earth suddenly stopped in its orbit around the Sun,it would fall into the Sun.Find the speed of the Earth as it impacted the Sun. Radius of the Sun: 6.96 * 10⁸ m
Radius of the Earth: 6.38 *10⁶ m
Initial distance between the Earth and the Sun: 1.50 * 10¹¹ m
Mass of the Earth: 5.98 * 10²⁴ kg
Mass of the Sun: 1.99 *10³⁰ kg

Question

Quizplus · Accepted Answer

When the Earth stops in its orbit, it will start falling towards the Sun due to the gravitational attraction between the two. Using conservation of energy, we can find the speed of the Earth just before impact:

Gravitational potential energy at initial position = Kinetic energy just before impact + Gravitational potential energy at impact

(-GMm/R) = 0.5mv^2 + (-GMm/2R)

where G is the universal gravitational constant, M is the mass of the Sun, m is the mass of the Earth, R is the initial distance between them, and v is the speed of the Earth just before impact.

Solving for v, we get:

v = sqrt(2GM/R) = sqrt(2(6.67e-11)(1.99e30)/(6.96e8)) = 6.13e5 m/s ≈ 6.13 x 10^10 m/s

Therefore, the best choice is C, 6.13 x 10^10 m/s.

If the Earth Suddenly Stopped in Its Orbit Around the Sun,it