The spacecraft

The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point.
Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered a sphere with a radius of 6378km.

Correct result:

x =  368.3833 km

Solution:

α=34+3760=207760=34376034.6167  u=615 km R=6378 km β=90+α=90+34.6167=747760=1243760124.6167  (x+R)2=u2+R22 u R cosα  x=u2+R22 u R cosβR=u2+R22 u R cos124.616666667 R=6152+637822 615 6378 cos124.616666667 6378=6152+637822 615 6378 (0.568083)6378=368.383=368.3833 km



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