Answer :
The orbital height of the satellite is 630 km and its velocity is 7.76 km/s. The apogee height of the satellite is 7350 km and the perigee height of the satellite is 6650 km.
(a)
The orbital height of the satellite can be found using the following formula:
h = a - R
where:
h is the orbital height
a is the semi-major axis of the orbit
R is the radius of the Earth
Substituting the values, we get:
h = 7000 km - 6370 km = 630 km
The velocity of the satellite can be found using the following formula:
v = √(GMa) / (a - R)
where:
v is the velocity of the satellite
G is the gravitational constant
M is the mass of the Earth
a is the semi-major axis of the orbit
R is the radius of the Earth
Substituting the values, we get:
v = √(6.674 × 10^-11 N m^2 / kg^2 * 5.972 × 10^24 kg * 7000 km) / (7000 km - 6370 km) = 7.76 km/s
Therefore, the orbital height of the satellite is 630 km and its velocity is 7.76 km/s.
(b)
The apogee height of the satellite is the distance between the satellite and the Earth at the farthest point of its orbit. The perigee height of the satellite is the distance between the satellite and the Earth at the closest point of its orbit.
The apogee height can be found using the following formula:
h_apogee = a + ea
where:
h_apogee is the apogee height
a is the semi-major axis of the orbit
e is the eccentricity of the orbit
Substituting the values, we get:
h_apogee = 7000 km + 0.05 * 7000 km = 7350 km
The perigee height can be found using the following formula:
h_perigee = a - ea
Substituting the values, we get:
h_perigee = 7000 km - 0.05 * 7000 km = 6650 km
Therefore, the apogee height of the satellite is 7350 km and the perigee height of the satellite is 6650 km.
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