=========================preview======================
(PHYS002)Additional_Past_Papers.pdf
Back to PHYS002 Login to download
======================================================
(From 2002 Fall Midterm 2)
Problem 2 (20 marks)
The upper figure (i) shows the relative orbit of a binary system as viewed from Earths direction, drawn to scale. The lower figure (ii) shows its light curve.
(a)
What is the period of the light curve? [2]
(b)
If the star at the front of the configuration in figure (i) is hotter than that at the back, what is the possible time that this configuration is observed? Refer your answer to the time axis of figure (ii). [2]
(c)
What is the ratio of the luminosity of the stars at its brightest and faintest moments? [4]
(d)
Measure the orbital size. Give your answer in AU. (1 AU = 215 solar radii) [2]
(e)
What is the total mass of the binary system? Give your answer in solar masses. [4]
(f)
Measure the radii of the two stars. Give your answer in solar radii. [2]
(g)
Assuming that the orbit is almost edge on, what should be the time duration of the deeper depression in luminosity (including the setting on and off of the eclipse)? What is the percentage difference between your calculated answer and the time duration measured from figure (ii)? [4]
Time (days) StarA
Size of sun StarB
0P
1Q
2654.3
3654.5
3.2654.7
3.0654.9
Solution
a)
period = 2.5 days Ans. [2] (0 marks for 1.25 days)
b)
The time is at 1.25 days Ans.[2] (2 marks for 1.3 or 1.2, 1 mark for 1.5, no marks for ans outside this range)
c)
Ratio = 2.512m = 2.512 (3.06-2.24) = 2.13 Ans.[4] (2 marks for step, 1 mark for plugging in correct values, 1 for ans)
(full marks for 1/2.13=0.469, 2 marks if the calculation is only for2.512 (2.36-2.24) = 1.12 or 2.512 (3.06-2.36) = 1.91)
d) The orbital size (diameter 2R) = (74mm/2mm) solar radius = 37 solar radius = 37/215 AU = 0.172 AU.[2] (1 mark for step, 1 for ans)
e) Total mass = Ma + Mb = a3/P2 = (0.172/2)3/(2.5/365)2 = 13.58 solar mass. [4] (3 marks for step, 1 for ans)
Note: if you use the diameter (0.172AU) as a, you will get 2 marks for step only.
f) Radius of the larger star, rl = 17mm/(22mm) solar radius = 4.25 solar radius.[1]
Radius of the smaller star, rs= 15mm/(22mm) solar radius = 3.75 solar radius.[1]
g)
Speed of rotation of the star is 2R/period; duration of the deeper depression is 2(rl+rs) /speed = 2(rl+rs)/(2R/period) = 2(4.25+3.75)x(2.5 days)/(2x37/2) = 0.34days.[2] (1 mark for step, 1 for ans)
The measured time duration for the depression is about 0.5 days.
Hence the percentage difference between the calculated answer and the measured value is
32% ans [2] (1 mark for step, 1 for ans)
----------------------------------------------------------------------------------------------
(From 2002 Spring Midterm 2)
Problem 2 (20 marks)
The figure in the following page shows the spectra of a binary