A satellite is put into an elliptical orbit around the Earth. When the satellite is at its perigee, its nearest point to the Earth, its height above the ground is hp = 229.0 km,…

Question

asked Feb 23, 2020 205k views

1 Answer

Gladwin · Answer 1 · 2020-02-28T11:06:40+0000

Answer:

The height above the ground is 1279.51 km

Solution:

As per the question:

Height above the ground,
$h_(p) = 229.0\ km$

Speed of the satellite,
$v_(p) = 8.050\ km/s = 8050\ m/s$

Gravitational constant,
$G = 6.67* 10^(- 11)\ m.kg$

Mass of the Earth, m =
$5.972* 10^(24)\ kg$

Now,

The distance of the earth from the perigee is given by:

R_(p) = h_(p) + R_(E)

where

$R_(E) = 6371\ km$

$R_(p) = 229.0 + 6371 = 6600\ km$

Now,

To calculate the distance of the earth from the earth from the apogee:

R_(A) = (R_(p))/((2Gm)/(v_(p)^(2)R_(p) - 1))

R_(A) = (6600* 1000)/((2* 6.67* 10^(- 11)* 5.972* 10^(24))/(8050^(2)6600* 1000 ) - 1)}

$R_(A) = 7650.51\ km$

Height above the ground,
$h_(A) = R_(A) - R_(E) = 7650.51 - 6371 = 1279.51\ km$