Orbiting the Earth Worksheet Answer Key

1. 4 + 24/60)/3 = 1.47 hours or 88 minutes.

2. 4/24 x 88 minutes = 14.67 minutes.

3. 2,700 miles/17,544 mph = 0.15 hours or 0.15 x 60 = 9 minutes.

4. To get the time in terms of hours add 4 + (24/60)) to get 4.4 hours. 17,544 miles/hour x 4.4 hours = 77,193 miles. John Glenn traveled approximately 77,193 miles.

5. 77193 miles/3 orbits = 25,731 miles/orbit. 25,731 represents the circumference of his orbit. Since circumference = 2 x (pi) x radius, the radius of his orbit = 25,731/(2 x (pi)) = 4095 miles. 4095 represents the distance from the center of the earth. His distance above the earth would be 4095 miles - radius of the earth = 4095 miles - (7928/2) miles = 131 miles. The actual elliptical orbit ranged from 99 miles to 165 miles.

6. The semi major axis a = (265 + 159)/2 + 6382 = 6594 kilometers. Period = 2 (pi) x square root (6594³/398601) = 5328 seconds = 88.8 minutes.

7. The semi major axis a = 482 + 6382 = 6864 kilometers. Period = 2 (pi) x square root (6864³/398601) = 5659 seconds = 94.3 minutes.

8. The period is 24 hours = 24 x 60 x 60 = 86400 seconds. Plugging this into the equation gives 86400 = 2 (pi) x square root(a³/398601). Solving for a gives you a = cube root ((86400/(2 x pi))² x 398601) = 42241 kilometers. So the altitude above earth = 42241 - 6382 = 35,859 kilometers above earth. 35,859 kilometers x 0.6215 = 22,286 miles above earth.