Consider a binary star system consisting of t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For a binary star system, the sum of masses is given by Kepler's Third Law in units of solar masses, astronomical units, and years: $M_1 + M_2 = \

Vedclass · Accepted Answer

$25, 5$

Vedclass · Answer

(B) For a binary star system, the sum of masses is given by Kepler's Third Law in units of solar masses, astronomical units, and years: $M_1 + M_2 = \frac{r^3}{T^2}$.Given $r = 30 	ext{ AU}$ and $T = 30 	ext{ years}$, we have $M_1 + M_2 = \frac{30^3}{30^2} = 30 	ext{ solar masses}$ .....$(i)$.By the definition of the centre of mass, $M_1 r_1 = M_2 r_2$. Given that one star is $5$ times farther from the centre of mass than the other, let $r_2 = 5r_1$. Thus, $M_1 r_1 = M_2 (5r_1)$, which implies $M_1 = 5M_2$ .....$(ii)$.Substituting $(ii)$ into $(i)$: $5M_2 + M_2 = 30 \Rightarrow 6M_2 = 30 \Rightarrow M_2 = 5 	ext{ solar masses}$.Then $M_1 = 5(5) = 25 	ext{ solar masses}$.Therefore, the masses are $25$ and $5$ solar masses.

Similar Questions

$A$ planet of mass $M$ has a satellite of mass $m$,revolving around the planet in a circular orbit of radius $r$ and time period $T$. The mass $(M)$ of the planet is

The distances of two planets $A$ and $B$ from the sun are $r_A$ and $r_B$ respectively, such that $r_B = 100 r_A$. The ratio of the orbital speed of planet $A$ to that of planet $B$ is (both planets are revolving around the sun in circular orbits).

The orbital angular momentum of a satellite revolving at a distance $r$ from the centre is $L$. If the distance is increased to $16r$,then the new angular momentum will be

$A$ satellite $S$ is moving in an elliptical orbit around the Earth. The mass of the satellite is very small compared to the mass of the Earth.

The time period of an artificial satellite in a circular orbit of radius $R$ is $2 \, days$ and its orbital velocity is $v_0$. If the time period of another satellite in a circular orbit is $16 \, days$,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module