Question

La Observatorul Astronomic , Luna a fost observata in faza de Luna Plina cu ajutorul unei lunete cu distanta focala de 500 cm . Daca Luna se afla la o distanta de 380000 km fata de Pamant si are diametrul de 3500 km , afla dimensiunea discului lunar in planul focal al lunetei .

Answer 1

[tex]\displaystyle Se~da:\\ \\ F=500cm=5m\\ \\ d=380000km=3,8\times 10^8m\\ \\ h_0=3500km=3,5\times 10^6m\\ \\ h=?cm\\ \\ \\ [/tex]


$\displaystyle Formule:\\ \\ \Gamma=\frac h{h_0}=\frac fd\\ \\ h=\frac{h_0\times f}{d}\\ \\ \\ \frac 1F=\frac 1d+\frac 1f\\ \\ \frac 1f=\frac 1F-\frac 1d\\ \\ \frac 1f=\frac {d-F}{d\times F}\\ \\ f=\frac{d\times F}{d-F}\\ \\ \\ h=\frac{h_0\times d\times F}{d\times(d-F)}\\ \\ h=\frac{h_0\times F}{d-F}$


[tex]\displaystyle Calcule:\\ \\ h=\frac{3,5\times 10^6\times 5}{3,8\times 10^8-5}\approx 0,046m=4,6cm[/tex]