OBJECTIVE: To determine the orbit of the space settlement CONTENT AREAS: orbital mechanics, angular motion, Newton's laws of motion In this lesson you will calculate the orbit of space settlements. The main advantage of orbital space settlements over planet based settlements is the environmental independence. In this lesson you will determine:

- the planet-moon you are going to orbit
- the angular velocity of the orbital space settlement
- the distance above the planet-moon your space settlement will orbit.

Any object with no force acting on it moves with constant
velocity. This is known as **Newton's First Law **of motion.**
**If a force acts on an object it would cause a change in velocity
(acceleration) given by the mathematical relation: a = f/m where f is
force and m is mass. This is called **Newton's Second Law **of
motion. If you threw a ball straight forward, and there was no
gravity or friction, the ball would continue on moving forward
(**Newton's First Law of Motion**). However, on earth this does
not happen because the air slows the ball due to friction and gravity
pulls the ball to the center of the earth. The ball changes its
vertical velocity by 9.8 meters per second per second due to the
force of gravity. So if you throw a ball straight forward at first
its vertical velocity is 0 meters per second. However, after one
second the ball is falling towards the earth with a vertical velocity
of 9.8 meters per second. After two seconds the ball has a vertical
velocity of 19.6 meters per second towards earth. The faster you
throw the ball the further the ball would go. What happens if you
could throw the ball at a horizontal speed of 8000 meters per second
with no air resistance. When the ball travels 8000 meters to point B,
the earth has curved away from the ball by 4.9 meters. So even though
the ball would still fall to earth continuously, because of the
curvature of the earth the distance between the ball and the earth
would remain constant. The ball would remain in orbit. The Space
shuttle orbits the earth about 400 km above the surface of the earth.
Both the space shuttle and the astronauts in it are constantly
falling towards the earth. That is why the astronauts experience
weightlessness.

**Assignments:**

- PROJECT LEADER: Leads a group discussion to decide on best alternatives on location, population, geometry and interior design of the space settlement.
- SCIENTIST: Decides on the criteria for planet/moon to orbit, and does orbital calculations.
- ARTIST: Draws an exterior of the space settlement in orbit around the planet/moon
- RESEARCHER: Researches the most suitable planet/moon to orbit and finds out the resources it offers.
- TASKMASTER: Types the first draft of the project
- Use Orbit Calculator to calculate angular velocity of your space settlement.
- Study the trajectory of Lunar Prospector
- Take the Quiz for Week 4
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Author: Tugrul Sezen

sezen@nas.nasa.gov