Knowing that the mass of the galactic center of a galaxy is MGC 3.57 × 106 M. Deter- mine the orbital period of a star orbiting it whose orbit semi-major axis is 900 AU. NOTE: you can assume that the orbit is almost circular and that the mass of the star is too small to contribute to the period calculation.
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- Problem Set on Binary Systems: 1.Consider two stars in orbit about a mutual center of mass. If a1 is the semimajor axis of the orbit of star of mass m, and a, is the semimajor axis of the orbit of star of mass m2, prove that the semimajor axis of the orbit of the reduced mass is given by a = a, + a2. points)A supernova in a distant galaxy is observed to be having an absolute magnitude of -19 and an apparent magnitude of 17. Estimate the distance to the galaxy.What is the orbital period of a bit of matter in an accretion disk 5 ✕ 105 km from a 69-solar-mass black hole?
- (Astronomy) Black Hole Gravity I. If the gravitational acceleration is g=GM/r^2, what gravitational acceleration does a particle feel at the Schwarzshild radius of a 12-solar-mass black hole star? Express your answer in units of m/s2. Please round your answer to three significant digits.The Tully-Fischer method relies on being able to relate the mass of a galaxy to its rotation velocity. Stars in the outer-most regions of the Milky Way galaxy, located at a distance of 50 kpc from the galactic centre, are observed to orbit at a speed vrot determine the mass in the Milky Way that lies interior to 50 kpc. Express your answer in units of the Solar mass. 250 km s-1. Using Kepler's 3rd Law,For a circular velocity profile of the type (r) = αν ar³/6, where a is a constant and is the radial distance from the centre of a spiral galaxy, find the ratio (r)/(r), where (r) is the epicyclic frequency and 2(r) is the angular velocity. Enter your answer to 2 decimal places.
- (Astronomy) Neutron Star Escape Velocity. What is the escape velocity at the surface of a 2.80-solar-mass neutron star that has a typical radius for this type of star? Express your answer in units of km/s.A galaxy's rotation curve is a measure of the orbital speed of stars as a function of distance from the galaxy's centre. The fact that rotation curves are primarily flat at large galactocen- tric distances (vrot(r) ~ constant) is the most common example of why astronomer's believe dark matter exists. Let's work out why! Assuming that each star in a given galaxy has a circular orbit, we know that the accelera- tion due to gravity felt by each star is due to the mass enclosed within its orbital radius r and equal to v?/r. Here, ve is the circular orbit velocity of the star. (a) Show that the expected relationship between ve and r due to the stellar halo (p(r) xr-3.5) does not produce a flat rotation curve. (b) Show that a p(r) ∞ r¯² density profile successfully produces a flat ro- tation curve and must therefore be the general profile that dark matter follows in our galaxy.Figure 2 shows the "rotation curve" of NGC 2742. It plots the “radial velocity (V)" (how fast material is moving either toward or away from us) that is measured for objects at different distances (R = radius") from the center of the galaxy. The center of the galaxy is at 0 kpc (kiloparsecs) with a speed of 9 km/sec away from us. (These velocities have been corrected for the observed tilt of the galaxy and represent true orbital velocities of the stars and gas.) 200 100 U4779 -100 As you can see, one side of the galaxy is moving with a negative velocity (spinning toward us), while the other side has a positive velocity (spinning away from us). Using Newton's gravity equation, we will be able to determine the gravitational mass of the entire galaxy and how the mass varies versus distance from the galaxy's center. -200 -8 8 -4 Radius (kpc) Read the following text carefully and follow the instructions: Select five radii spaced evenly from 0-10 kpc across the galaxy. Your selections should…