Question

(a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an initial speed of 4.98 104 m/s relative to the Sun. What would its speed be when it is very far from the Earth (in m/s)? Ignore atmospheric friction, the effects of other planets, and the rotation of the Earth. (Consider the mass of the Sun in your calculations.)

(b)

What If? The speed provided in part (a) is very difficult to achieve technologically. Often, Jupiter is used as a "gravitational slingshot" to increase the speed of a probe to the escape speed from the solar system, which is 1.85 ✕ 10⁴ m/s from a point on Jupiter's orbit around the Sun (if Jupiter is not nearby). If the probe is launched from the Earth's surface at a speed of 4.10 ✕ 10⁴ m/s relative to the Sun, what is the increase in speed needed from the gravitational slingshot at Jupiter for the space probe to escape the solar system (in m/s)? (Assume that the Earth and the point on Jupiter's orbit lie along the same radial line from the Sun.)

Answer 1

AK+OP = O v -m GMM O r 2 Yt os [v-x] &M 2 2-O O.5 Lv(4.98 KIo = 2 0.5 V2= 51121.81 m ls SEREDX S.11X10 m/s V2