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Orbiting the Earth (Grade Levels 8-10)
We Have Liftoff
| Orbiting The Earth
| Solar System
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1.
John Glenn’s first ride into space was aboard a Mercury-Atlas rocket,
and the time of the trip was a total of 4 hours, 55 minutes, and 23 seconds.
This included the launching of Glenn into space, three orbits of earth,
and the reentry back to earth. Assume that the three orbits of the earth
lasted 4 hours and 24 minutes. How long did it take him to make one orbit
of the earth?
2.
The continental United States covers approximately four
time zones, or very roughly 4/24 of the earth’s circumference.
How long would it take Glenn to pass over the United
States?
3.
Glenn’s average orbital velocity was 17,544 mph. Suppose
rather than being up in space, Glenn was traveling this
fast on the surface of the earth. At this speed, how
long would it take him to travel from Portland, OR to
Miami, FL--a distance of 2,700 miles?
4.
Estimate how many miles John Glenn traveled during his
orbiting of the earth.
5.
Assume for a moment that John Glenn’s orbit was circular.
You should know that circular orbits are rather special.
Most orbits are elliptical. How high above the earth
must John Glenn have been to cover this distance in
three orbits? The diameter of the earth is 12,756 kilometers
or 7,928 miles.
For
a spacecraft, satellite, or other body (such as the
moon) that orbits the earth, an equation links 1) how
high above the earth the object is, and 2) the period
or time it takes the object to complete one orbit. This
equation is
Period
= 2 (pi) x square root (a3/mu)
The
Period is the time in seconds it takes to complete one
orbit.
a
is called the "semi major axis." Calculate this by taking
the average of the altitude when the object is closest
to the earth with the altitude when it is farthest from
the earth and then add the radius of the earth. Do this
calculation in kilometers.
Mu
is the gravitational constant of the earth. This number
is 398,601 km3/sec2.
For
your information:
Miles x 1.609 gives you kilometers.
Kilometers x 0.6215 gives you miles.
Perigee: for an object orbiting the earth, this is the
point closest to the center of the earth.
Apogee: for an object orbiting the earth, this is the
point farthest from the center of the earth.
6.
John Glenn’s actual orbit in the Mercury spacecraft
ranged from 159 km (perigee) to 265 km (apogee) above
the earth. Calculate the time it took Glenn to complete
one orbit using this method. The radius of the earth
is approximately 6382 kilometers.
7.
On the space shuttle mission, John Glenn and the rest
of the crew will be about 300 miles or 482 kilometers
above the earth. Assuming a circular orbit, how long
will it take them to complete on orbit?
Have
you heard of people who have dishes in their yard or
on their houses to receive TV channels? These dishes
work off of satellites that are in Geosynchronous orbits.
Geosynchronous means that from our vantage point on
earth, the satellite seems to remain in the same place
in the sky. These are circular orbits in which the time
it takes to complete one orbit is the same as the 24
hours it takes the earth to complete one revolution.
So people who use these dishes don’t have to go out
and adjust the dish.
8.
Using the formula above, figure out how high a satellite
would need to be for a geosynchronous orbit. Remember
that a includes the radius of the earth. Convert
your answer to miles when you are done.
Photo
from NASA
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