Consider a GTO orbit (see Wikipedia article on GTO) with the perigee just outside the Earth's atmosphere at an altitude of 622km and apogee near the GEO orbit at an altitudeof 35,786km. Assume that the Earth's radius is RE = 6378km. All orbits around a single large body are elliptical (it is called a two-body problem and you will learn about it inorbital mechanics). Furthermore, the center of the large body is at one of the foci of the ellipse. The semi-major axis can be calculated by averaging the distance of the perigeeand apogee from the center of the Earth. What is the semi-minor axis (in km)?2b2c2a

Answered: Consider a GTO orbit (see Wikipedia…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Consider a GTO orbit (see Wikipedia article on GTO) with the perigee just outside the Earth's atmosphere at an altitude of 622km and apogee near the GEO orbit at an altitude
of 35,786km. Assume that the Earth's radius is RE = 6378km. All orbits around a single large body are elliptical (it is called a two-body problem and you will learn about it in
orbital mechanics). Furthermore, the center of the large body is at one of the foci of the ellipse. The semi-major axis can be calculated by averaging the distance of the perigee
and apogee from the center of the Earth. What is the semi-minor axis (in km)?
2b
2c
2a

Expert Solution

Step 1

From the figure,

$2 a = d i s \tan c e b e t w e e n t h e p e r i g e e a n d a p o g e e 2 a = 622 + R_{E} + R_{E} + 35786 a = 24582 k m$

Now, the distance between the two foci can be obtained by subtracting the distance between perigee and center of the earth from the distance between the apogee and the center of the earth.

$2 c = 35786 + R_{E} - (622 + R_{E}) 2 c = 35164 c = 17582 k m$

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