Chapter 56, The Masses of Orbiting Star Video Solutions, Pathways to Astronomy

Problem 1

Two stars are in a binary system. Find their combined mass if they have
a. an orbital period, $P$, of 5 years and an orbital separation, $a$, of $10 \mathrm{AU}$.
b. an orbital period, $P$, of 2 years and an orbital separation, $a$, of $4 \mathrm{AU}$.

Andy Chen

Numerade Educator

02:19

Problem 2

Mizar A and B are about 400 AU apart, currently. Their orbital period is estimated to be between 2000 and 4000 years. What range of masses does this suggest for the pair?

Narayan Hari

Numerade Educator

07:44

Problem 3

Two stars are orbiting each other, and the sum of their masses is $6 M_{\odot} .$ It is found that star $A$ of the pair is orbiting 3 arcsec from the center of mass, while star $B$ is orbiting 6 arcsec from the center of mass. What are the two stars' masses?

Eduard Sanchez

Numerade Educator

04:15

Problem 4

Find the distance from the center of the Sun of the center of mass between the $\operatorname{Sun}\left(M_{\odot}=1.99 \times 10^{30} \mathrm{kg}\right)$ and the following planets:
a. Earth $\left(M=5.97 \times 10^{24} \mathrm{kg} ; a=1.50 \times 10^{8} \mathrm{km}\right)$
b. Jupiter $\left(M=1.90 \times 10^{27} \mathrm{kg} ; a=7.78 \times 10^{8} \mathrm{km}\right)$
c. Saturn $\left(M=5.68 \times 10^{26} \mathrm{kg} ; a=1.43 \times 10^{9} \mathrm{km}\right)$

Ajay Singhal

Numerade Educator

02:37

Problem 5

When Jupiter and Saturn are on the same side of the Sun, is the center of mass inside or outside the Sun's radius $\left(R_{\odot}=6.96 \times\right.$ $\left.10^{5} \mathrm{km}\right) ?$

Arun Bana

Numerade Educator

06:36

Problem 6

Two stars are orbiting each other, both 4.2 arcsec from their center of mass. Their orbital period is 420.3 years and their distance from the Earth is 104.1 ly. Find their masses.

Matthew Miranda

Numerade Educator

06:36

Problem 7

Using Kepler's third law, we find that the combined mass of a binary system is $55.5 \mathrm{M}_{\odot} .$ The stars have separations of 6.3 arcsec and 2.5 arcsec from the center of mass, and the system is at a distance of 64 ly from the Earth. Find their distances from the center of mass of the system, and their individual masses.

Matthew Miranda

Numerade Educator