Mission

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"To know the world one must construct it."
-Cesare Pavese

Mission

Part One: Mars Colony Essay and Graphic

Your assignment is to design a colony of 30 people for the planet Mars and submit a labeled drawing and a one-page description of how it works via the Comm Link.

First, make a list of the people and their jobs, then add the facilities and transportation (or other special requirements) each of those positions would need. 

Choose a location on the planet, and lay out where each of your buildings will go. Draw the colony as you would a bird's-eye map and submit the map (labeled) with the written text (one-page or at least 500 words) describing the colony's components via the Comm Link.

Make sure you include the following:

• Colony location on Mars 
• Living quarters 
• Working facilities (shops, factories, laboratories) 
• Recreation facilities 
• Transportation systems 
• Energy source (power plants) 
• Recycling systems for air, water, and waste 
• Food production systems 
• Colony structure (constitution, government, laws, flag) 

Feel free to use the resources at Reaching for the Red Planet to start!  This is a very good example of a Martian colony developed by students that you can use as a reference, and here is another one.  List all your sources.

Part Two: Mars Math  

Determine the orbital velocity of our Mars spacecraft at the point of departure, when it leaves Earth orbit, and at the point of arrival at Mars. You can do this using an equation that gives the velocity of an object at various points on an elliptical orbit. It is the vis-viva equation determined by the German scientist Gottfried Leibniz in the 17th century.  This equation will allow you to predict the orbital velocity of the spacecraft at the point of departure (Point A on the diagram) and the point of arrival (Point B on the diagram). You will need to use your answer from the last Mars Math problem for the semi-major axis to complete this equation.

The term, "vis viva," derives from the Latin, vis = force or power, and viva = living. In the older writings, it was associated with the ability of a body to do work on its environment. Now it usually refers to the principle of energy conservation.

One derives the velocity of a planet or spacecraft in its orbit by writing out the vis viva equation:

kinetic energy + gravitational potential energy = a constant (K)

The constant is calculated from the mass of the primary (the Sun, in the case of our solar system) and the semi-major axis of the orbit.  The kinetic energy term contains the square of the velocity.

The terms used in the vis-viva Equation are defined below.

K =  energy constant (K=  -GMm/2a)
M = Mass of the primary object (sun) in kilograms
m = mass of the secondary object (spacecraft) in kilograms
G = Gravitational constant (unit is in meters/kilogram seconds) More about the Gravitational constant!
r = the distance from the Earth (for Point A), or Mars (for Point B), to the Sun
a = semi-major axis of the ellipse

The vis-viva equation is written

v= {2(K+GMm/r)/m} ^1/2

where

K=  -GMm/2a

Therefore, 

v= {2GM (1/r - 1/[2a])} ^1/2

Or, finally for your use (we have worked out the gravitational constant times the mass of the sun for you). You will need to use the semi-major axis of the ellipse to complete the problem.

v= 1.6 x 10¹⁰  (1/r - 1/[2a]) ^1/2

Use the equation above to determine the velocity at point A (the point of departure) and at point B (the point of arrival) on the diagram below in kilometers/sec and in miles per hour. 

Your units are meters/second. (If you trace the sequence of the three equations and balance them you will see how this occurs).

Remember: Both terms, r and a, need to be converted to meters...use exponents!   You will need to convert your answer from meters/second to kilometers/second, and then to miles per hour.

1.  The distance from the Earth to the Sun is 150 million km 
2.  The distance from Mars to the Sun is 230 million km 

r = the distance from the Earth (for Point A), or Mars (for Point B), to the Sun

a - semi-major axis of the ellipse

v= 1.6 x 10¹⁰  (1/r - 1/[2a])^1/2

Hint:

1 million kilometers can be expressed as 1(10⁹)

v= 1.6 x 10¹⁰  (1/r - 1/[2a])^1/2

Here are some more links about the Vis-Via equation you can check out.

http://www.treasure-troves.com/bios/Leibniz.html
http://www.execpc.com/~berrestr/hel-con.html
http://www.newadvent.org/cathen/05422a.htm

Thank you to Joe Kolecki and NASA's Learning Technology Project at the Glenn Research Center for use of these questions and activities.

Here are a few on-line Math sites that might help you!

Ask Dr. Math

The Math Forum

Quick Math

Spark Notes: Math

The Math Help Desk

and check out, Interactive Algebra!

Rubric Assignment 10

Your assignment will be graded on your essay, graphic, answer to the math problem and quiz score using the following rubric. If your assignment is late, points will be deducted as follows:

•  If assignment is one day late, 1 point will be deducted.

•  If assignment is two or three days late, 2 points will be deducted.

•  If assignment is four or five days late, 3 points will be deducted.

•  If assignment is six or more days late, 4 points will be deducted.

Next... Extended Mission (optional)