Question Number 226115 by fantastic2 last updated on 20/Nov/25
$${can}\:{we}\:{find}\:{the}\:{black}\:{area} \\ $$$$\left({the}\:{shadow}\:{of}\:{earth}\right){on}\:{the}\:{moon}\:{during} \\ $$$${moon}\:{eclipse}\:{after}\:{time}\:{t}\:{of} \\ $$$${its}\:{starting}? \\ $$$${Given}: \\ $$$${Moon}\:{radius}={R}_{{m}} \\ $$$${Earth}\:{rafius}={R}_{{e}} \\ $$$${Sun}\:{radius}={R}_{{s}} \\ $$$$\omega_{{e}} \:{and}\:\omega_{{m}} \:{given}\left({both}\:{anticlockwise}\right) \\ $$$$\omega_{{m}} \Rightarrow{Earth}\:{is}\:{center} \\ $$$$\omega_{{e}} \Rightarrow{Sun}\:{is}\:{center} \\ $$$${Sun}\:{Earth}\:{distance}\left({center}\right)={L}_{{S}−{E}} \\ $$$${Earth}\:{Moon}\:{distance}\left({center}\right)={L}_{{E}−{M}} \\ $$
Commented by mr W last updated on 20/Nov/25
$${yes},\:{it}\:{is}\:{already}\:{very}\:{difficult}\:{even}\: \\ $$$${when}\:{we}\:{treat}\:{the}\:{earth}\:{as}\:{a}\:{sphere}. \\ $$
Commented by mr W last updated on 20/Nov/25
$${at}\:{first}\:{i}'{m}\:{interested}\:{why}\:{you}\:{in}\: \\ $$$${such}\:{a}\:{question}\:{don}'{t}\:{treat}\:{the} \\ $$$${earth}\:{as}\:{a}\:{sphere},\:{but}\:{as}\:{an}\:{oblate} \\ $$$${sphere}.\:{do}\:{you}\:{think}\:{the}\:{question}\: \\ $$$${were}\:{too}\:{easy}\:{if}\:{the}\:{earth}\:{is}\:{seen} \\ $$$${as}\:{a}\:{sphere}? \\ $$$${do}\:{you}\:{have}\:{the}\:{solution}\:{even}\:{for}\: \\ $$$${the}\:{easy}\:{case}\:{that}\:{the}\:{earth}\:{is}\:{a}\: \\ $$$${sphere}? \\ $$
Commented by fantastic2 last updated on 20/Nov/25
$${to}\:{be}\:{honest}\:{i}\:{didnt}\:{think}\:{about}\:{it}\: \\ $$$${but}\:{now}\:{i}\:{realize}\:{that}\:{it}\:{is}\: \\ $$$${indeed}\:{difficult}\:{if}\:{we}\:{take} \\ $$$${earth}\:{as}\:{a}\:{sphere}\: \\ $$