Loose Leaf For Explorations: Introduction To Astronomy
9th Edition
ISBN: 9781260432145
Author: Thomas T Arny, Stephen E Schneider Professor
Publisher: McGraw-Hill Education
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Chapter 13, Problem 7TY
To determine
Combined mass of binary system.
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A certain binary system consists of two stars that have equal masses and revolve in circular orbits around a fixed point half-way between them.
If the orbital velocity of each star is v=186 km/s and the orbital period of each is 11.3 days, calculate the mass M of each star. Give your answer in units of the solar mass, 1.99×1030 kg (e.g. if each planet's mass is 3.98×1030 kg, you would answer "2.00").
Analysis of the spectrum of a solar–mass star shows a periodic back-and-forth shift of its spectral lines with a period of 3 days. A spectral line centred at wavelength λ0 = 500 nm shows a shift ∆λ = ±2.5 × 10−4 nm. Estimate the mass of the unseen orbiting companion by assuming the angle of inclination i = 90◦, and express your answer in Jupiter masses.
H5.
A star with mass 1.05 M has a luminosity of 4.49 × 1026 W and effective temperature of 5700 K. It dims to 4.42 × 1026 W every 1.39 Earth days due to a transiting exoplanet. The duration of the transit reveals that the exoplanet orbits at a distance of 0.0617 AU. Based on this information, calculate the radius of the planet (expressed in Jupiter radii) and the minimum inclination of its orbit to our line of sight.
Follow up observations of the star in part reveal that a spectral feature with a rest wavelength of 656 nm is redshifted by 1.41×10−3 nm with the same period as the observed transit. Assuming a circular orbit what can be inferred about the planet’s mass (expressed in Jupiter masses)?
Chapter 13 Solutions
Loose Leaf For Explorations: Introduction To Astronomy
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- White Dwarf Size II. The white dwarf, Sirius B, contains 0.98 solar mass, and its density is about 2 x 106 g/cm?. Find the radius of the white dwarf in km to three significant digits. (Hint: Density = mass/volume, and the volume of a 4 sphere is Tr.) 3 km Compare your answer with the radii of the planets listed in the Table A-10. Which planet is this white dwarf is closely equal to in size? I Table A-10 I Properties of the Planets ORBITAL PROPERTIES Semimajor Axis (a) Orbital Period (P) Average Orbital Velocity (km/s) Orbital Inclination Planet (AU) (106 km) (v) (days) Eccentricity to Ecliptic Mercury 0.387 57.9 0.241 88.0 47.9 0.206 7.0° Venus 0.723 108 0.615 224.7 35.0 0.007 3.4° Earth 1.00 150 1.00 365.3 29.8 0.017 Mars 1.52 228 1.88 687.0 24.1 0.093 1.8° Jupiter 5.20 779 11.9 4332 13.1 0.049 1.30 Saturn 9.58 1433 29.5 10,759 9.7 0.056 2.5° 30,799 60,190 Uranus 19.23 2877 84.3 6.8 0.044 0.8° Neptune * By definition. 30.10 4503 164.8 5.4 0.011 1.8° PHYSICAL PROPERTIES (Earth = e)…arrow_forwardWhat is the total mass of a binary star system with P = 20 years and a = 10 AU? a. 2 solar masses b. 2.5 solar masses c. 0.5 solar mass d. 80 solar masses e. 0.4 solar massarrow_forwardIn the model shown in the table below, what fraction of the Sun's mass is hotter than 5,000,000 K? R/R SunT (106 K) Density (g/cm³) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.006 0.60 1.2 2.3 3.1 4.9 5.1 6.9 9.3 13.1 15.7 0.00 0.009 0.035 0.12 0.40 1.3 4.1 13 36 89 150 M/M Sun L/L Sun 1.00 0.999 0.996 0.990 0.97 0.92 0.82 0.63 0.34 0.073 0.000 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.99 0.91 0.40 0.00arrow_forward
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- Which star in the table below is the closest to Earth? Star Name d (parsecs) Parallax (seconds of arc) Spectral Type $$ \delta $$ Cen 0.026 B2 IV HR 4607 0.039 G8 III HR 4758 20 G0 V HR 39801 0.005 M2 I 9 CMa 2.5 A1 V a. $$ \delta $$ Cen b. HR 4607 c. HR 4758 d. HD 39801 e. 9 CMaarrow_forwardConvert 1.39 x 10^9 kilograms to Jupiter Masses, MJ. The mass of Jupiter is known as MJ = 1.898×1027 kg. Mplanet = _________________________ MJ *The accepted mass of this planet HD 209458b is Mplanet = 0.69 MJ. Check your answer for correctness.arrow_forwardvelocity curve for a double line spectroscopic binary is shown in the sketch. The system is viewed edge-on, i.e., with an inclination angle of i = 90°, so that the maximum possible Doppler shifts for this system are observed. 400 300 So = U, Ani 200 t0 = v Ain i 100 -100 -200 -300 400 O 1 2 3 1 s 1 8: 10 Time (days) Find the orbital period of this binary in days. Doppler Velocity (krn/sec)arrow_forward
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