Marinada '24

[lang=hr] Zvijezde $A$ i $B$ gibaju se oko središta masa po kružnim stazama polumjera $r_A$ i $r_B$. Opažanjem je ustanovljeno da je razdoblje ophoda zvijezda oko zajedničkoga središta masa $50$ godina dok je uzajamna udaljenost zvijezda $25 a.j.$. Također, zvijezda $B$ je 5 puta udaljenija od središta masa sustava nego zvijezda $A$. Masa svijezde $B$ može se zapisati u obliku $x \cdot 10^{30} kg$. Odredite $x$ i zaokružite na dvije decimale. ($1 a.j. = 149.6 \cdot 10^9 m$, $G = 6.67 \cdot 10^{-11} m^3kg^{-1}s^{-2}$, $1 god. = 365.25 dana$) [/lang] [lang=en] Stars $A$ and $B$ move in circular orbits around their center of mass with radii $r_A$ and $r_B$. Observations have shown that the orbital period of the stars around the common center of mass is $50$ years, while the mutual distance between the stars is $25 \text{ AU}$. Additionally, star $B$ is 5 times farther from the center of mass of the system than star $A$. The mass of star $B$ can be written in the form $x \cdot 10^{30} \text{ kg}$. Determine $x$ and round it to two decimals. ($1 \text{ AU} = 149.6 \cdot 10^9 \text{ m}$, $G = 6.67 \cdot 10^{-11} \text{ m}^3\text{kg}^{-1}\text{s}^{-2}$, $1 \text{ year} = 365.25 \text{ days}$) [/lang]