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A spacecraft is in a 500-km by 900-km leo. how long (in minutes) does it take to coast from perigee to the apogee?

Sagot :

Spacecraft will take around 49 minute and 92 second to coast from perigee to the apogee.

We use Kepler's third law for which the time period is defined as

[tex]T = 2 \pi \sqrt[]{\frac{a^{3} }{GM} }[/tex]

The Prague's altitude is the shortest distance between the earth's surface and satellite.

The average distance of the perigee and  apogee of satellite can be defined as

a = R + [tex]\frac{r_{1} +r_{2} }{2}[/tex]

R is the radius of earth (6374.1km)

r1 is the lower orbit. (500km)

r2 is the higher orbit.(900km)

Using the values in above equation we get:

6374.1+ (500+ 900)/2

a = 7078.1 km

Time taken to fly from perigee to apogee equals to the half of the orbital speed so

t = T/2

[tex]t = \pi \sqrt[]{\frac{a^{3} }{GM} }[/tex]

by using the values we get-

=  √[(7078.1)³/6.67 ×10⁻¹¹ × 6×10²⁴]

= 295573.94 * 10⁻²

= 2995.73s

t = 49 mint 92 sec

It will take around 49 minute and 92 second to coast from perigee to the apogee.

To know more about perigee ang apogee :

https://brainly.com/question/28538480

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