ASTR 303 Assignment 1 Spring 2025 PDF

ASTR 303 | Assignment 1 Dr. H. Boyce Spring 2025 ASTR 303 - Assignment 1 Due: Thur January 23 in class at CLE C108 Please make sure you include your name and/or student number on each page you submit and...

ASTR 303 | Assignment 1 Dr. H. Boyce Spring 2025 ASTR 303 - Assignment 1 Due: Thur January 23 in class at CLE C108 Please make sure you include your name and/or student number on each page you submit and make sure sheets are fastened together well. 1.​ Assuming that both an average human and the Sun emit thermal radiation as blackbodies, which of the two emits more radiation per unit mass? By what factor, approximately? Assume standard values for the Sun’s radius, effective temperature, mass, and luminosity, and approximate a human by a cylinder of height 1.8m, radius 30cm, temperature 300K, and weight 70kg. (5 points) 2.​ If three stars of equal luminosity form a tightly bound system, how much brighter than a single star is the resulting system, in magnitudes? (5 points) 3.​ If we approximate the Milky Way as a sphere of radius 5 kpc and luminosity 2e10 Lsun, what would be its effective temperature? (5 points) 4.​ The proper motion ν is the angular velocity of a star across the sky, and it depends on the star’s tangential velocity, vT, and its distance, d. Writing this in the form ν=k*vT /d: what is the numerical value of the proportionality constant k if ν is measured in arcsec/yr, vT in km/s and d in kpc? (5 points) 5.​ The Sun “lights up” the daytime sky to an average surface brightness of µV=+4 mag/ arcsec2. The apparent brightness of the Sun is mV=-26.75 and that of the full Moon is mV=-12.5. a.​ What is the total daytime sky brightness? Express the result in magnitudes. How much brighter/fainter is this than the Sun? (10 points) b.​ Use this result to work out the surface brightness of the night time moonlit sky. Assume full Moon and express the result in magnitudes per square arcsec. (5 points) c.​ Compare the result in (b) with the surface brightness of the night sky when the Moon is below the horizon: 22.5 mag/arcsec2. Comment. (5 points) 6.​ Barnard’s star has a proper motion of 10.3 arcsec/yr, parallax 0.545 arcsec, and radial velocity -108 km/s. a.​ What is the speed of this star? Express the result in km/s. (5 points) b.​ Assuming that its velocity remains constant, what would be the proper motion of Barnard’s star 100yrs from now? Express the result in arcsec/yr. (5 points) ASTR 303 | Assignment 1 Dr. H. Boyce Spring 2025 7.​ A star like the Sun is observed to have a radial velocity “wobble” of +-10 m/s, with a period of 10 days. a.​ What is the mass of a planet that could produce this effect? (Assume the planet’s circular orbit is seen edge-on by us.) (10 points) b.​ If the star is 100pc away, what is the maximum angular separation between the planet and its central star? (5 points) 8.​ The central surface brightness of a globular cluster projected onto the bulge of M31 is measured to be 19 mag per arcsec2. Considering that similar globular clusters have central surface brightness of 20 mag per arcsec2, what is the surface brightness of M31’s bulge at that point? (10 points) 9.​ IB is the B-band surface brightness of a galactic disk measured in LSun/pc2. Show that, when viewed face-on, the B-band surface brightness of the disk will be measured to be µB magnitudes per square arcsecond, where µB=27.05-2.5 log(IB). (The Sun’s absolute magnitude in the B-band is 5.48.) (10 points)