Question

The height of a satellite at perigee is 300 km above the Earth's surface, and it is 3000 km at apogee. Find the orbit's eccentricity.

Answer 1

To find the orbit's eccentricity, subtract the distance from the center of Earth to perigee from the distance from the center of Earth to apogee, and divide by the distance from the center of Earth to apogee. The result is approximately 0.718.

Step-by-step explanation:

To find the orbit's eccentricity, we can use the formula:

Eccentricity (e) = (a - b)/a

where 'a' is the distance from the center of the ellipse to one of the foci (apogee) and 'b' is the distance from the center of the ellipse to one of the vertices (perigee).

In this case, 'a' is the distance from the center of Earth to apogee (3000 km + 6370 km) and 'b' is the distance from the center of Earth to perigee (300 km + 6370 km).

Plugging these values into the formula:

e = (3000 km + 6370 km - 300 km - 6370 km)/(3000 km + 6370 km)

Simplifying:

e = 0.718

Therefore, the orbit's eccentricity is approximately 0.718.