Using the Text book Understanding Space Chapter 6&7

1. Why does a spacecraft transferringfrom an initial circular orbit to a larger circular orbit perform two maneuvers, both of which increase it's speed, but end up with a slower orbitalvelocity in the final orbit than it started with in the original orbit?

2 .Why do we take the absolute value of the difference between the two orbital velocities when we compute total V?

3. Suppose you want to move a spacecraft from a circular orbit at 500 km altitude to a circular orbit at 150 km altitude to ensurethat its orbit will naturally decay over a few years.

What velocity change (V₁) isneeded to go from the initial circular orbit into the transfer orbit?

What velocity change (V₂) is needed to go from the transfer orbit to the final circular orbit?

What is the time (TOF) required for the transfer?

5. A spacecraft deployed into a circular orbit, inclined 57 at 200 km altitude, needs to change to a polar orbit at the same altitude. What V does this maneuver require?

6. Now that the spacecraft from the previous problem is in a polar orbit, what V will change the right ascension of the ascending node by 35?

7. Imagine you are in charge of a rescue mission. The spacecraft in distress is in a circular orbit at 400 km altitude. The rescue vehicle is in a coplanar circular orbit at 350 km altitude. The rescue vehicle is 135 behind the target spacecraft.

• What is the TOF of the rescue vehicle's transfer orbit to rendezvous with the target spacecraft?

• What is the rescue vehicle's angular velocity?

• What is the target spacecraft's angular velocity?

• What is the lead angle?

• What is the final phase angle?

8. NASA is sending a remote-sensing spacecraft to Mars.

Given:

Earth parking orbit altitude=1000 km

Mars Parking orbit altitude= 500 km

_Earth= 3.99x10⁵ km³/s²

_Mars= 4.280x10⁴ km³/s²

_Sun= 1.33x10¹¹ km³/s²

^{Earth's orbital radius =1.50 x108km (assume Earth has a circular orbit for this problem)}

Mars' orbital radius =2.28 x10⁸km (assume Mars has a circular orbit for this problem)

^{Find the semi majoraxis of the transferorbit (enter your answer as a number which will be assumed to be in km)}