text: i wonder how have the scientists measured the distance between earth and the moon ? surely they have used mathematics. but which branch of mathematics? maybe could you explain please? when the apollo astronauts went to the moon, they left there a parabolic reflector facing earth directly, on that side of the moon that looks at us always (remember the moon is tidally locked, implying, period of rotation and revolution are the same).  back on earth, light from lasers was bounced off these reflectors and the time interval between transmission and reception was detected using suitable sensing devices.  if d is the distance between moon and the earth and t the above time interval, then  d = ct/2, where c = speed of light in vaccum= 3 x 10^8 m/s  as you probably know, the measured distance is around 384000 km.  there is no special branch of mathematics involved (if you discount multiplication and division). rather it involves precise optics - reflection.  ***  the above talks about measurement - what you question sought. if you are interested in "calculation" of the distance, follow this  the phases of the moon as seen from earth repeat after around 29.53 days. this we may take approximately as the period of the moon (actually it is 27.3 days; so accuracy is lost). assuming you know the mass of the moon and earth, you can use newton's law of gravitation for the gravitational force and equate it to the centripetal force to get the approximate distance.  p.s: i wanted to answer first. but because of the detail i have provided, two of them overtook me.