0

Guest

Courses New

Spacecraft Voyager 2 (mass m and speed l' relative to the Sun) approaches the planet Jupiter (mass M and speed V relative to the Sun) as shown in Fig. The spacecraft rounds the planet and departs in the opposite direction. What is its speed, relative to the Sun, after this "slingshot" encounter? Assume that v = 12 km/s and V = 13 km/s (the orbital speed of Jupiter), and that this is an elastic collision. The mass of Jupiter is very much greater than the mass of the spacecraft, M >> m. (See "The Slingshot Effect: Explanation and Analogies," by Albert A. Bartlett and Charles W. Hord, The Physics Teacher; November 1985, p. 466.)

Spacecraft Voyager 2 (mass m and speed l' relative to the Sun) approaches the planet Jupiter (mass M and speed V relative to the Sun) as shown in Fig. The spacecraft rounds the
planet and departs in the opposite direction. What is its speed, relative to the Sun, after this "slingshot" encounter? Assume that v = 12 km/s and V = 13 km/s (the orbital speed of Jupiter), and that this is an elastic collision. The mass of Jupiter is very much greater than the mass of the spacecraft, M >> m. (See "The Slingshot Effect: Explanation and Analogies," by Albert A. Bartlett and Charles W. Hord, The Physics Teacher; November 1985, p. 466.)

Grade:11

2 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago
234-144_1.PNG
Kozerone
11 Points
6 years ago
Kevin Nash was right.
$v_{2f}\approx2v_{1i}-v_{2i}
But how do we get there?
Well, we have to use conservation of momentum and conservation of kinetic energy to get there, because this is an inelastic collision (KE is conserved). You will get two equations from the two conservation laws. The information $M \gg m$ is useful when you try to solve for $v_{2f}$ using these two equations, because it will allow you to make this expression: $(m/M)^2(v_{2f}+v_{2i})^2$ go to zero.  So you will not need to know what the value of $M$ is, to solve for $v_{2f}$.
 
 

Think You Can Provide A Better Answer ?

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More