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In the article the heat transfer in packages of multilayer shield-vacuum thermal insulation plates of spacecrafts is modeling to define the optimal characteristics of the thermal protection which are depending on the sun heat flow.

The shield-vacuum thermal insulation protection consists of multilayer package of thin plates having low emissitivity factor and separated by airless layer.

The heat transfer between plates realizes by means of radiation with reradiation and absorption by heat capacity in the plates.

The optimal choice of the shield-vacuum thermal insulation characteristics is in the exactly amount plates calculation, thickness of the plates, emissitivity factors providing given temperature inside a spacecraft for comfortable human presence.

In the article a new stable method for numerical solving of heat transfer problems that are described by systems of nonlinear ordinary differential equations without involving iteration procedures is proposed.

Simulation allowed to construct nomograms of dependences of temperatures at the internal shield-vacuum thermal insulation surface on amount of plates, their thickness, emissitivity factor.

Such nomograms allow to define shield-vacuum thermal insulation characteristics using given temperature on the internal border.

It was determined the temperature distribution by shield-vacuum thermal insulation thickness becomes stable after approximately 10 minutes.

The stabilization essentially depends on time of being exposed to heat sun flow, thickness of plates and their amount in the shield-vacuum thermal insulation.

It was also determined the shield-vacuum thermal insulation has low heat lag, i.e. the number plates changing from optimal amount by 1 results to temperature changing by 10-15 ̊ C from the given temperature.

To eliminate this effect it is necessary to put a lag heat insulation at the internal shield-vacuum thermal insulation surface.