Orbiting the Earth Worksheet

Show the calculations on a separate sheet of paper to be turned in as a group.

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.