#1 b, c #1فيفашаеConsider a binary system in which both stars have circular orbits. For star 1, the radius of thisorbit is 0.500 AU. For star 2, it is 0.125 AU. The period of revolution of both stars is 96 days and11 hours. (Recall that there are about 365.25 days in a year on average. The days given here are"mean solar days" that last exactly 24.00 hours)моa) Determine the mass of each star (expressed in solar masses).b) Sketch the two orbits, showing the position of each star at a given moment.c) Determine the speed that star 1 has along its orbit (express this speed in km/s).d) Do the same as in part c) but this time for star 2.Now consider a slightly different situation in which the circular orbits are replaced by ellipsesthat have an eccentricity of 0.550. The value of the semimajor axes a, and a2 are simply equalto the values you had for the radii R₁ and R₂.e) Use the following URL (https://ccnmtl.github.io/astro-simulations/eclipsing-binary-simulator/) tovisualize the two elliptical orbits. Note that you cannot enter the exact values of M₁ and M₂but you can still visualize the two orbits by using the same ratio M₁/M₂. Make a sketch of thetwo orbits showing the position of each star at a given moment.Determine the distance of closest approach between the stars, using the values of a1, a2 and e.Similarly, determine the distance of largest separation between the stars.h) If this binary system is located at a distance of 40.0 1.y. from us, is it possible for the HubbleSpace Telescope (aperture = 2.40 m) to "resolve" this system (that is to see the two stars asstars froom leles cropedistinct objects)?double stars froom6to seef)g)

Question

#1 b, c #1فيفашаеConsider a binary system in which both stars have circular orbits. For star 1, the radius of thisorbit is 0.500 AU. For star 2, it is 0.125 AU. The period of revolution of both stars is 96 days and11 hours. (Recall that there are about 365.25 days in a year on average. The days given here are&#34;mean solar days&#34; that last exactly 24.00 hours)моa) Determine the mass of each star (expressed in solar masses).b) Sketch the two orbits, showing the position of each star at a given moment.c) Determine the speed that star 1 has along its orbit (express this speed in km/s).d) Do the same as in part c) but this time for star 2.Now consider a slightly different situation in which the circular orbits are replaced by ellipsesthat have an eccentricity of 0.550. The value of the semimajor axes a, and a2 are simply equalto the values you had for the radii R₁ and R₂.e) Use the following URL (https://ccnmtl.github.io/astro-simulations/eclipsing-binary-simulator/) tovisualize the two elliptical orbits. Note that you cannot enter the exact values of M₁ and M₂but you can still visualize the two orbits by using the same ratio M₁/M₂. Make a sketch of thetwo orbits showing the position of each star at a given moment.Determine the distance of closest approach between the stars, using the values of a1, a2 and e.Similarly, determine the distance of largest separation between the stars.h) If this binary system is located at a distance of 40.0 1.y. from us, is it possible for the HubbleSpace Telescope (aperture = 2.40 m) to &#34;resolve&#34; this system (that is to see the two stars asstars froom leles cropedistinct objects)?double stars froom6to seef)g)

Accepted Answer

Solution 1:
b). The circular orbit of the binary star system is shown in the figure given below.

b) Sketch the two orbits, showing the position of each star at a given moment. c) Determine the speed that star 1 has along its orbit (express this speed in km/s).