Please help Astronomy or physics. I posted 5 times and nobody answered. I will s
ID: 3307864 • Letter: P
Question
Please help Astronomy or physics. I posted 5 times and nobody answered.
I will seperate the question by two.
Please do 3 and 4.
An eclipsing-spectroscopic binary consisting of two main sequence stars is located 50.0 parsecs from Earth, and has an orbit, velocity curve, and light curve with the following properties: (a) Orbit: P. 100 days, inclination i = 90.0°. The orbits are perfectly circular. (b) Velocity curve: Brighter (and hotter) star: Vmax = +57.1 km s-1, vmin = +2.90 km s-1 Fainter (and cooler) star: Vmax = +68.3 km s-1, Vmin = -8.30 km s-1 (C) Light curve: The brighter star is the one being eclipsed at the time of primary eclipse. Full duration of each eclipse: 0.812 days Duration of the flat part of each eclipse: 0.172 days combined light: mbol = 5.545 (apparent bolometric magnitude) apparent bolometric magnitude at primary eclipse minimum: mbol = 5.990 apparent bolometric magnitude at secondary eclipse minimum: mbol = 5.790 1. From the information given above, determine the amplitude of the velocity curve for each star (make sure to subtract out the center of mass velocity of the system with respect to Earth). 2. Use that information to calculate the semi-major axis of each star's orbit about the center of mass in astronomical units. 3. Use the periods and semi-major axes to get the mass of each star in solar masses. 4. Now use the eclipse times to get the radius of each star in solar radii. 5. Using the magnitude information given above, determine the luminosity (in solar luminosities) and bolometric absolute magnitude of each star (assume the bolometric absolute magnitude of the Sun is exactly 4.74) 6. Use the information to calculate the effective blackbody surface temperature of each star in K. 7. Sketch the light and velocity curves for the system, labelling the axes with tick marks and appropriate units. Use two graphs, one directly above the other, with identical x-axes (rep- resenting time), so that the corresponding events and times in the two curves can be easily identified, as well as the relationship between the light variations and velocity variations. Show at least one full period of the system in your graphs. When plotting, don't worry that the length of the eclipses are so much shorter than the orbital period - indicate the time and depth of the eclipses as best as you can. 8. Summarize the properties you found for each star (in solar units) in a table.Explanation / Answer
3. By Kepler's third law, for a circular orbit,
T = 2pi x (a3 / u)1/2 , where T is the period which is 100 days, a is the semi major axis, u is the gravitational parameter u = GM, therefore
T2 = 4(pi)2 x (a3/GM)
(100)2 = 4 x 9.869 x ((50)3 /6.67 x 10-11 M)
104 = 39.476 x [125 x 103 / 6.67 x 10-11 M)
104 = 39.476 x [ 18.740 x 1014/M]
104 = 739.78024 x 1014/M
M = 739.78024 x 1014/104 = 739.78024 x 1010 kg , since 1Ms = 1.989 x 1030 kg, therefore, M = 739.78024 x 1010 x 1.989 x 1030 = 739.78024 x 1010Ms .
4. Since the orbit is circular, the radius or the distance from the the center to the circumference of the orbit is constant and maximum, therefore, r = vmax + vmin/vmax - vmin = 5.71 + 2.90 / 5.71 - 2.90 = 3.0640 km , since 1Rs = 695700 km , therefore, r = 3.0640 x 695700 km = 3.0640 Rs.