# Homework Help: Yet another problem from classical mechanics

1. Nov 4, 2008

### haplo

1. The problem statement, all variables and given/known data

THis time it is rather 3 problems, you are required to solve two of them before tackling third.

So, in the first problem is about hoffman transfe. YOu are asked to calculate the velocity of the spaceship when it leaves the earth and at it's encounter with juputer. It was easily done through conservation f angular momentum and energy equations. Velocity of spaceship is 7.7km/s at jupiters orbit and juputer is 13.1 So the velocity relative to jupiter is 5.4.

The second problem is about slingshot manuever :

the problems states: ON reaching the vicinity of jupiter the spaaroundcecraft is swung around the planet by it's gravitational attraction. Consider the encounter in a frame of reference in which jupiter is at rest. What is magnitude and direction of the spacecrafts velocity before scattering and magnitude after scattering. If scattering angle in this frame is 90 degress what is it's impact parameter and distance of closest approach.

THis one was also easy to solve. From previous problem we know that velocity relative to jupiter is 7.4 in sun refference amd direction is the same as juputers. So in juputers frame it is 5.4 towards juputer. After scattering the velocity should be the same 5.4. For second part impact paramter is easily calculated from b=a*cot(1/2*theta), where a=(Rjupiter+Rearth)/2. And distance of closest approach from radial energy equation by setting Vr=0 and calculating R.

And here comes the last problem.
If the manuever described in previos problem is in orbital plane so that final velocity of the spacecraft is radially away from the sun. What is it's magnitude and direction relative to the sun. Use radial energy equation to determine spacecrafts furthers distance from the sun. FInd new orbital period.

Any hints on how to complete the first part. It looks difficult to understand what impact paramter should be as well as scattering angel? What values from previous problems should you use?

2. Relevant equations

3. The attempt at a solution