ISS space station orbit – calculation discrepancy

[ravell]

 

The orbit of the ISS space station is defined by the following parameters (data as of 07/11/2021) :

-                       -  Perygeum       419 km above sea level,

                         -   Apogeum        421 km above sea level,

-                        -  Orbital period  91,34 minutes (91min 20 sec).

 From the above data, it follows that the ISS is moving in orbit at a speed of 7786,3 m/s.

  According to  the standard calculations for the mean orbit altitude = 420 km

and gravity  g = G*M /R^2,

-                              where M is the mass of the Earth = 5,9736E+24 kg,

-                              and the orbit radius  R = 6 371 km + 420 km = 6 791 km

the average orbital velocity should be:

                     v = (G*M /R}^0.5 = (g * R)^0.5 = 7661,2 m /s

                    and the orbital period should be: T = 2 π R /v = 92 min 47 sec.

According to the standard calculations, satellites reach the speed of  7786.3 m /s  at an altitude of 205 km!

Thus, the greater actual speed of the ISS in orbit, than that indicated by the standard calculations, indicates that the gravity in the orbit must be greater than that derived from

the formula  g = G*M /R^2

To clarify this matter, the Gravity-Calc program was used,  available at the link:  https://www.dropbox.com/scl/fi/q1fdwelm9aqf7b0zxd9o0/Gravity-Calc.xlsx?dl=0&rlkey=eq2buobftc7s3kyodvunrb9ka

The calculations in this program surprisingly confirm that the gravity in the ISS orbit is increased to the extent that ensures the observed speed of the ISS,  i.e. 7786,3 m /s.