Respuesta :
Answer:
The height above the ground is 1279.51 km
Solution:
As per the question:
Height above the ground, [tex]h_{p} = 229.0\ km[/tex]
Speed of the satellite, [tex]v_{p} = 8.050\ km/s = 8050\ m/s[/tex]
Gravitational constant, [tex]G = 6.67\times 10^{- 11}\ m.kg[/tex]
Mass of the Earth, m = [tex]5.972\times 10^{24}\ kg[/tex]
Now,
The distance of the earth from the perigee is given by:
[tex]R_{p} = h_{p} + R_{E}[/tex]
where
[tex]R_{E} = 6371\ km[/tex]
[tex]R_{p} = 229.0 + 6371 = 6600\ km[/tex]
Now,
To calculate the distance of the earth from the earth from the apogee:
[tex]R_{A} = \frac{R_{p}}{\frac{2Gm}{v_{p}^{2}R_{p} - 1}}[/tex]
[tex]R_{A} = \frac{6600\times 1000}{\frac{2\times 6.67\times 10^{- 11}\times 5.972\times 10^{24}}{8050^{2}6600\times 1000 } - 1}}[/tex]
[tex]R_{A} = 7650.51\ km[/tex]
Height above the ground, [tex]h_{A} = R_{A} - R_{E} = 7650.51 - 6371 = 1279.51\ km[/tex]
