Question

Derive the "Clarke radius", the altitude above the surface of the Earth where a satellite in a circular orbit has an orbital period of exactly one day. Assume a spherical Earth, and use the following constants (taken from Vallado, David A., Fundamentals of Astrodynamics and Applications, 2nd ed. 2001) Gravitational constant: G 6.673 x 10-20 km Radius of the Earth: Re = 6378.137 km 1024 kg Mass of the Earth: Me = 5.9733328 x Round your final answer to four significant digits.

Answer 1

Speced a Satallite asound objet an Gm is the radius or +!9&O t 2TY Now, 0bital Speed PT 257 is the period a Whre Tis the 20 eaxth. Circumtorenca 0f 275 Gm So, 2 27 86400 Seconds Them T: 24 h When T2 m 3 Y 4 T Pu tHing the valius (6.63 x10 Nmlg') (S a 4x(3.14)2 (5.98x10 K 2 8.64 X10 7.5497 x lo 6378.137km 6378 X10m Liven Earth radius Surtace ot the earth, Satallites .2258-06378)X 10* Distamce trom the needs to 03bit,R(4. 3.5880 X10 m R =