De-Orbit Burn
Mission 

-Han Solo on the Millennium Falcon (Star Wars)

Mission

Part One: Spinoff Essay

Write a one-page detailed summary (at least 500 words) of one of the Spinoffs techonolgies that have impacted your life.  Explain how the technology is used and how it has impacted your life.  List all your sources.  You can review the list of spinoffs here.

Part Two :Shuttle Math

Free Fall!

On the Space Shuttle the gravitational status of astronauts is often describing as a "Zero-G" environment.  This implies that the force of gravity does not apply to the Shuttle in orbit. This is not true!

Gravity is the attractive force between bodies related to their masses and distances. Every object in the universe with mass exerts a gravitational pull on every other massive object. The more massive the object, the stronger the gravitational attraction, and the closer the objects are to each other, the more strongly the attraction will be felt.

Sir Isaac Newton realized that the same force that caused apples to fall from trees was responsible for holding the Moon in orbit around Earth (and the planets around the Sun). He also realized that as the distance grows between two objects the attraction drops, but most importantly.. it never reaches zero!

So how does the gravity of Earth affect a spacecraft in orbit? The gravitational pull of Earth on the Shuttle astronauts is almost exactly the same as the gravitational force holding you in chair. "But wait", you say, "the astronauts are floating, and I'm not!" 

True, the astronauts are experiencing weightlessness, but they are not experiencing a true zero-g environment. The astronauts are experiencing weightlessness because they are in free fall. Isaac Newton realized that gravity's effects on objects could also be described in terms of falling. Click here to read the story of Newton and the apple.

Check out NASA's Liftoff to Learning videos about freefall, Newton in Space, Microgravity, and Space Basics!

So apples fall from trees and the Moon (and the Shuttle) falls around the Earth.

If you threw a baseball directly towards the horizon it would travel forever if it were not being acted upon by gravity and friction (produced by the resistance of the air molecules). Gravity causes the ball to fall back to Earth in an arc. If you throw the ball harder it will travel farther, but will still fall in an arc.

If you throw it really hard or launch it via a cannon, the ball could travel so far that as it arcs towards the surface the curvature of the Earth matches the curvature of the arc.

The ball would be continually arcing towards a surface that is continually arcing out of its way. For an interactive animated version of Newton's cannon on a mountain, click here!

Newton's illustration from his book, Principia.

The speed necessary to reach this situation is about 28,200 kilometers per hour (17,500 miles per hour) and this is the speed that the Space Shuttle must attain to continue to fall around Earth (remain in orbit) at an altitude of 300 kilometers (186 miles).  (To go farther than that, or "escape" the Earth's gravitational force, if you wanted to go to the moon for example, you have to go even faster than that. The "escape velocity" for the Earth is about 40,300 kilometers per hour, or about 25,000 miles per hour).

Therefore the shuttle astronauts are in free fall but still affected by the gravitational pull of Earth. If Earth's gravity were to disappear, the Shuttle would fly off in a straight line!

So, how much weaker is the force of gravity at 500 kilometers above Earth's surface? Calculate how much of a g force the astronauts are actually experiencing. This equation can be modified for any other planet by replacing using the planet's radius and its surface gravity (how many g's).

You can figure it out using the equation below that uses simple multiplication and division:

gr = R²/r² x g

R =  the radius of the planet

r =  the distance from the center of mass of the planet to the center of mass of the object in orbit

g = the gravitational attraction of the planet on objects on its surface

gr = the gravitational attraction of the planet as felt on the less massive object

Hints: To find the radius of the Earth in kilometers, use http://roland.grc.nasa.gov/~dglover/dictionary/tables/table2.html. The gravitational attraction of the Earth on the surface is 1g.

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

• Ask Dr. Math
• The Math Forum
• Quick Math
• The Math Help Desk
• Interactive Algebra!

Rubric Assignment 3

Your assignment will be graded on your essay, 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)