▁mod elling ▁of ▁the ▁stell ar ▁structure ▁equations ▁ ▁The ▁differential ▁equations ▁of ▁stell ar ▁structure , ▁such ▁as ▁the ▁equation ▁of ▁hydro static ▁equilibrium , ▁are ▁integrated ▁numer ically . ▁The ▁differential ▁equations ▁are ▁approxim ated ▁by ▁difference ▁equations . ▁The ▁star ▁is ▁imag ined ▁to ▁be ▁made ▁up ▁of ▁spher ically ▁symmetric ▁shell s ▁and ▁the ▁numerical ▁integration ▁carried ▁out ▁in ▁finite ▁steps ▁making ▁use ▁of ▁the ▁equations ▁of ▁state , ▁giving ▁relationships ▁for ▁the ▁pressure , ▁the ▁opacity ▁and ▁the ▁energy ▁generation ▁rate ▁in ▁terms ▁of ▁the ▁density , ▁temperature ▁and ▁composition . ▁ ▁E volution ▁of ▁the ▁Sun ▁ ▁N uc lear ▁re actions ▁in ▁the ▁core ▁of ▁the ▁Sun ▁change ▁its ▁composition , ▁by ▁converting ▁hydro gen ▁nuc lei ▁into ▁hel ium ▁nuc lei ▁by ▁the ▁pro ton - pro ton ▁chain ▁and ▁( to ▁a ▁less er ▁extent ▁in ▁the ▁Sun ▁than ▁in ▁more ▁massive ▁stars ) ▁the ▁C NO ▁cycle . ▁This ▁increases ▁the ▁mean ▁mole cular ▁weight ▁in ▁the ▁core ▁of ▁the ▁Sun , ▁which ▁should ▁lead ▁to ▁a ▁decrease ▁in ▁pressure . ▁This ▁does ▁not ▁happen ▁as ▁instead ▁the ▁core ▁contract s . ▁By ▁the ▁vi rial ▁theorem ▁half ▁of ▁the ▁gravit ational ▁potential ▁energy ▁released ▁by ▁this ▁contra ction ▁goes ▁towards ▁raising ▁the ▁temperature ▁of ▁the ▁core , ▁and ▁the ▁other ▁half ▁is ▁radi ated ▁away . ▁This ▁increase ▁in ▁temperature ▁also ▁increases ▁the ▁pressure ▁and ▁rest ores ▁the ▁balance ▁of ▁hydro static ▁equilibrium . ▁The ▁lum inos ity ▁of ▁the ▁Sun ▁is