Concept #1: Escape Velocity

Example #1: Escaping An Orbit Around Mars

A space probe is launched from the Earth at a speed of 16 km/s. Is this speed large enough for the probe to leave the Solar System, considering only the effects of the Earth and the Sun? Note that the Solar System is 122 AU from the Sun, the Earth is 6400 km is radius, the Sun is 1 AU from the Earth, the mass of the Earth is 5.94x1024 kg, and the mass of the Sun is 1.99x1030 kg. Hint: at the edge of the solar system, the effect of the Earth is negligible compared to the effect of the Sun.

Suppose that the Sun were to collapse under its own gravitational pull. To what radius would it have to be reduced in order for the escape velocity to be equal the speed of light, 3.00 x 108 m/s? The mass of the Sun is 2.00 x 1030 kg and G = 6.67 x 10-11 N•m2/kg2.
(A) 1.48 km
(B) 2.96 km
(C) 1.52 km
(D) 2.10 km
(E) None of these

What is the escape speed from the sun, beginning (from rest relative to the sun) at the orbit of Earth, R = 1.50 × 108 km. (Given: G = 6.67 × 10–11 N · m2/kg2; mass of the sun = 2.0 × 10 30 kg.)A. 1.3 × 106 m/sB. 2.1 × 104 m/sC. 9.4 ×105 m/sD. 4.2 × 104 m/sE. 3.0 × 104 m/s

Suppose that the Sun were to collapse under its own gravitational force. To what radius would it have to be reduced in order to become a black hole? The mass of the Sun is 2.00 x 1030 kg, G = 6.67 x 10-11 Nm2/kg2 and c = 3.00 x 108 m/s.
a) 2.96 km
b) 1.48 km
c) 1.52 km
d) 2.10 km
e) None of the others