# Unit 6: End of Unit Exam

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Brief summary of Unit Six:

In this unit we reviewed the basics of the ellipse. We moved on to discuss the Hohmann transfer orbit between Earth and Jupiter. We ended with a discussion of launch windows.

Before you go to the quiz, see how you do on these two questions. If you have trouble, you might want to review the unit, send a question to the discussion group, or seek help from the instructor.

Practice Question One

Why can't a Hohmann transfer orbit between Earth and Jupiter be a circle? After all, the orbits of Earth and Jupiter are nearly circular.

Practice Question Two

To get to Mars via a Hohmann transfer orbit, you would have to launch the rocket from Earth when Mars and the Earth are closest in their orbits. True or false? Explain.

You will get instant feedback on your score on Quiz Six (and your instructor will also be informed of your score). If your score is OK, you may proceed directly to the Essay Question Four on BLackboard. Otherwise, you might want to look at what you missed, ask your instructor about questions you missed, or review relevant parts of the unit.

Essay Question

Imagine that a spaceship to Mars is first assembled in low Earth orbit, where it has an orbital speed around Earth of about 7 km/s, while Earth is moving around the Sun at about 30 km/s. Here are some statements about what would need to happen next to get it on its way to Mars. Some of these statements are false. Identify which ones and explain what is wrong with them:

A. To leave the vicinity of Earth this will need to be given a speed of about 11 km/s. This could be in any direction (except directions that would make it crash into Earth or the Moon) but the cheapest boost would be to add 4 km/s in the direction it is already moving.

B. To get the spacecraft to Mars we should wait until Mars and Earth are as close as they get and then blast off in the direction of Mars.

C. If Earth's gravity were somehow magically turned off, the spaceship would immediately leave Earth's vicinity along a straight line that passes through the center of the Earth.

D. If two parts of the ship are not attached to each other, then because each piece only has half the mass of the complete ship, the two parts will go into a very different orbit than was intended.

E. To leave Earth's orbit and follow the hohmann orbit to Mars requires the spacecraft to travel at least ____ km/s. To leave the solar system entirely the spacecraft would need to be traveling at ____ km/s. If you knew only these two facts about the planets, and that Jupiter is farther from the Sun than Mars, what could you say about how fast it would have to move to go to Jupiter? Explain!.

Alternative Essay Question

Imagine that someone discovers an alien spaceship in a perfectly circular orbit at exactly 4 AU from our Sun.
a. How long does it take this spaceship to go around the Sun once?
b. How long would it take us to get to this spaceship if we followed a Hohmann transfer orbit from Earth?
c. Assuming for simplicity that Earth's orbit is also circular:
Describe how you would figure out when to launch the spaceship -- that is, what would be the geometrical arrangement of the three bodies, Earth, Sun, and spaceship at the time of the launch of our probe?

Don't forget to contribute to the discussion on Blackboard on one of the topics in this unit!