Another commonly calculated velocity in galactic dynamics is the escape velocity vesc, that is the minimum velocity a star must have in order to escape the gravitational field of the galaxy. (a) Starting from the work required to move a body over a distance dr against f show that the escape velocity from a point mass galaxy is vsc = 2GM/r where r is your initial distance. (b) Since we know galaxies aren't actually point-masses, also show that vesc from r for a galaxy with a p(r) x r-² density profile is vese = 2v?(1+ ln(R/r)). Here you must assume that R is a cutoff radius at which the mass density is zero. (c) The largest velocity measured for any star in the solar neighbourhood, at r=8 kpc, is 440 km/s. Assuming that this star is still bound to the galaxy, find the lower limit (in kiloparsecs), to the cutoff radius R and a lower limit (in solar units) to the mass of the galaxy. Note the solar rotation velocity is 220 km/s.

Another commonly calculated velocity in galactic dynamics is the escape velocity vesc, that is the minimum velocity a star must have in order to escape the gravitational field of the galaxy. (a) Starting from the work required to move a body over a distance dr against f show that the escape velocity from a point mass galaxy is vsc = 2GM/r where r is your initial distance. (b) Since we know galaxies aren't actually point-masses, also show that vesc from r for a galaxy with a p(r) x r-² density profile is vese = 2v?(1+ ln(R/r)). Here you must assume that R is a cutoff radius at which the mass density is zero. (c) The largest velocity measured for any star in the solar neighbourhood, at r=8 kpc, is 440 km/s. Assuming that this star is still bound to the galaxy, find the lower limit (in kiloparsecs), to the cutoff radius R and a lower limit (in solar units) to the mass of the galaxy. Note the solar rotation velocity is 220 km/s.

Similar questions

The expanding universe is carrying distant objects away from each other at a rate proportional to their separations. We use the Doppler effect observed in spectra of distant galaxies and quasars to calculate recession speeds. For the most distant objects recession speeds approach c, and therefore, the relativistic Doppler shift expression must be used. We define the redshift, z, as the fractional change in wavelength. a) The most distant quasar currently known is ULAS J1120+0641, discovered with the UK Infrared Telescope on Mauna Kea. It has a redshift of 7.1. Calculate its radial velocity in terms of v/c. b) Determine the distance to this quasar. c) At what wavelength would the Ha line (656.28 nm) be observed for this quasar?
Certain spiral galaxy is 9.7 Mpc away from us. How fast in km/s is this galaxy moving away from us?
What is the orbital period of a bit of matter in an accretion disk that is located 4 ✕ 105 km from a 87 M black hole? Use the circular orbit velocity formula.
When two spiral galaxies collide, the stars generally do not run into each other, but the gas clouds do collide, triggering a burst of new star formation. (a) Estimate the probability that our Sun would collide with another star in the Andromeda Galaxy, if a collision between the Milky Way and Andromeda were happening at the present time. To simplify the problem, assume that each galaxy has 100 billion stars exactly like the Sun spread evenly over a circular disk with a radius of 100,000 light-years. (Hint: First calculate the total area of 100 billion circles with the radius of the Sun and then compare that total area to the area of the galactic disk.) (b) Estimate the probability that a gas cloud in our galaxy could collide with another gas cloud in the Andromeda Galaxy. To simplify the problem, assume that each galaxy contains 100,000 gas clouds of warm hydrogen gas, that each cloud has a radius of 300 light-years, and that these clouds are spread evenly over a circular disk with a…
Near the center of our galaxy, hydrogen gas is moving directly away from us in its orbit about a black hole. We receive electromagnetic radiation of wavelength 1888 nm and know that it was 1875 nm when emitted by the hydrogen gas. Randomized Variablesλ = 1888 nm What is the ratio of the speed of the gas to the speed of light?
a) Briefly explain what is meant by "particle horizon" and "event horizon" in cosmology. b) Calculate the physical particle horizon, RH (t), at time t. Assume a flat FRW universe which is dominated by a fluid that gives rise to scale factor evolution a(t) = ao ()*, to where n is a constant with 0
True or false The escape speed from a black hole would be greater than the speed of light. If the impact time of a collision is increased, the force of impact will decrease. A size of a Kelvin degree (oK) is larger than a Celsius degree (oC).
(a) Let L be the diameter of our galaxy.Suppose that a person in a spaceship of massm wants to travel across the galaxy at constantspeed, taking proper time τ. Find the kineticenergy of the spaceship. (b) Your friend is impa-tient, and wants to make the voyage in an hour.For L = 105 light years, estimate the energy inunits of megatons of TNT (1 megaton=4×109 J).
A 50 g tennis ball revolves around a 2-kg bowling ball in a universe that is otherwise empty. If the orbit is circular with radius of 10 m, calculate: a) The speed of the tennis ball b) The period of its motion Take the tennis ball and the bowling ball as particles.
Suppose a galaxy is moving away from Earth at a speed of 0.78c. It emits radio waves of 0.680 m. What wavelength would we detect on Earth? with a wavelength
The most distant quasar is "J0313-1806". Its redshift is z = 7.64. [ z = (femitted - fobserved)/ fobserved] Assume that the redshift is due to relative motion. Then how fast is the quasar moving away from Earth? (speed as the fraction of c = ) | .704 According to Hubble's Law, the distance (r) depends on the speed of recession (v) according to v = Hor where Ho~ 20km/s Mly How many years are required for light to travel from the quasar to Earth? (years = )
In the red shift of radiation from a distant galaxy, a certain radiation, known to have a wavelength of 434 nm when observed in the laboratory, has a wavelength of 462 nm. (a)What is the radial speed of the galaxy relative to Earth? (b) Is the galaxy approaching or receding from Earth?