Question

Let the angular speed of the earth about an axis through its poles be Ω. If their orbit can be approximated as circular, how high above the earth's center are these satellites?

Answer 1

By using the formula: h = r + R, we can determine that the satellite is approximately 7.87 million meters above the Earth's center.

Step-by-step explanation:

The height above the Earth's center of a satellite in a circular orbit can be found using the formula:

h = r + R

where h is the height above the center, r is the radius of the Earth, and R is the radius of the satellite's orbit.

In this case, since the satellite has an apogee (highest point) at 2500 km and a perigee (lowest point) at 500 km above the Earth's surface, the radius of its orbit would be the average of these values, which is 1500 km (or 1.5 million meters). Thus, plugging in the values for r (6370 km or 6.37 million meters) and R (1.5 million meters) into the formula, we get:

h = 6.37 million m + 1.5 million m = 7.87 million m

Therefore, the satellite is approximately 7.87 million meters above the Earth's center.