Temperature state and estimation of deviation in the shape of the spherical shell of the calibration spacecraft in the shadow section of the near-Earth orbit

A complex mathematical model describing alteration in a shape of a spherical shell of a calibration spacecraft is presented. The alteration is caused by the uneven temperature distribution over the shell surface when it is in the shadow section of the near-earth orbit. The thermal part of the model takes into account influence upon the shell of the own Earth radiation and the radiation heat transfer in the shell cavity. Unevenness of the shell surface radiation leads to the unevenness of the temperature distribution over the shell surface and thus to the alteration in shape of the spherical shell, that can affect the device functional characteristics. To determine the distortion in shape of the spherical shell, the fundamentals of the membrane theory of rotational shells were used. The quantitative analysis of the discussed model was carried out for cases of the steady non-uniform temperature distribution along the shell surface arising at different heights of the spacecraft above the Earth's surface. Obtained estimations of the distortion in shape of the shell of the calibration spacecraft can be compared with the permissible deviations that do not violate the spacecraft functional characteristics in the shadow section of the near-Earth orbit.