Final answer:
The apogee altitude of the satellite is 5,630 km, and the perigee altitude is 1,630 km above Earth's surface. The satellite's velocity will be higher at perigee and lower at apogee due to the conservation of angular momentum; precise calculations for velocity would require additional data and Kepler's laws.
Step-by-step explanation:
To estimate the apogee and perigee altitudes of a satellite with a given eccentricity of 0.2 and a semi-major axis of 10,000 km, you can use the formulae for elliptical orbits.
The apogee (A) is the farthest point from Earth, and the perigee (P) is the closest point to Earth.
The formulae for these distances, measured from the center of Earth, are A = a(1+e) and P = a(1-e), where a is the semi-major axis and e is the eccentricity.
For the given semi-major axis (a) of 10,000 km and eccentricity (e) of 0.2, the apogee is A = 10,000 km x (1 + 0.2) = 12,000 km and the perigee is P = 10,000 km x (1 - 0.2) = 8,000 km. To convert these to altitudes above Earth's surface, we subtract Earth's mean radius (approximately 6,370 km) from these distances.
Therefore, the apogee altitude above Earth's surface is A - 6,370 km = 5,630 km
and the perigee altitude is P - 6,370 km = 1,630 km.
To estimate the satellite velocity at apogee and perigee, we need to use Kepler's laws and the conservation of angular momentum, which imply that the satellite's velocity will be greater at perigee than at apogee due to its closer proximity to Earth.
The calculation for these velocities depends on the mass of Earth and requires a more complex analysis.