![(1) 1. (10 points] In a simple model for a spherically symmetric dark matter halo, the dark matter density is given by M PDM](http://img.homeworklib.com/questions/be9e7de0-7791-11eb-8afb-d7bd6efddea0.png?x-oss-process=image/resize,w_560)
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cosmology
(1) 1. (10 points] In a simple model for a spherically symmetric dark matter halo,...
The Navarro Frenk & White (NFW) model describes the (spherically symmetric) haloes of dark matter that...
The Navarro Frenk & White (NFW) model describes the
(spherically symmetric) haloes of dark matter that form in
cosmological simulations. It says that the density of dark matter
follows the distribution
, where is the distance from
the center of the halo, and is an arbitrary length.
Show (using Poisson’s formula) that the potential consistent with
this density distribution is
, where
.
+- p(r) = p(-) *-8
3. The Milky Way's Dark Matter Halo The Milky Way's rotation curve is approximately a constant, v...
3. The Milky Way's Dark Matter Halo The Milky Way's rotation curve is approximately a constant, v(r) ~220 km/s, for 5 20 kpc, This constant circular velocity cannot be explained by the observed distribution of luminous mass Instead, we propose that the Milky Way is embedded in a roughly spherical dark matter halo. (a) Calculate M(r), the enclosed mass of the spherical dark matter halo as a function of r in the range 5< T < 20 kpc, assuming the...
Galaxies contain both stars and dark matter. The mass M of a galaxy that is located...
Galaxies contain both stars and dark matter. The mass M of a galaxy that is located within a certain star's orbit is given by where v is the velocity of the star, r is the distance from the galaxy's center to the star, and G is Newton's gravitational constant, 6.673 x 10- N m/kg Stars near the edge of a particular galaxy have velocities of 259 km/s. The radius of the galaxy is 53 kpc. How much mass is in...
Question 1 (10 marks) (a) (4 marks) Recall that the gravitational potential energy for two masses...
Question 1 (10 marks) (a) (4 marks) Recall that the gravitational potential energy for two masses is Ug-GMm Use this fact to show that the virial theorem holds for a mass m, executing uniform circular motion about a much larger mass M (b) (3 marks) The potential energy of a collection of N particles each of mass m in a region with radius R can be written as Use this expression to derive a mass estimate for the virialized system...
1).In a uniform circular motion, instantaneous velocity is tangent to the circle a) True b) False...
1).In a uniform circular motion, instantaneous velocity is tangent to the circle a) True b) False c) Can's say 2).In a uniform circular motion, acceleration is normal to the velocity and directed toward the center a) True b) False c) Unknown 3). For a particle of mass 'm' moving with a uniform velocity 'v' in a circle of radius 'r', write the expression for centripetal force (Fc)? 4). If a particle rotates in a circle of radius r= 10 cm...
1). In a uniform circular motion, instantaneous velocity is tangent to the circle a) True b)...
1). In a uniform circular motion, instantaneous velocity is tangent to the circle a) True b) False c) Can's say 2).In a uniform circular motion, acceleration is normal to the velocity and directed toward the center a) True b) False c) Unknown 3). For a particle of mass 'm' moving with a uniform velocity 'v'in a circle of radius 'r', write the expression for centripetal force (Fc)? 4). If a particle rotates in a circle of radius r = 10...
PLEASE SHOW ALL WORK. THANKS. III, SIMPLE HARMONIC HECK (30 pts: 10 pts each piece), The...
PLEASE SHOW ALL WORK. THANKS.
III, SIMPLE HARMONIC HECK (30 pts: 10 pts each piece), The statements immediately to follow (even when long and complicated) are considered in this context) GIVEN You may assume and rely on them for the problem/proof to follow a bit further down. Note: In some cases, "GIVEN' might mean 'self-evident' or 'obvious', but in other cases, it might not. GIVEN might not mean "obvious"; it can simply mean 'somehow established prior to this discussion'. GIVEN...
could you please solve a and b? Chapier 2i. Note: you needn't derive Kepler's laws-but do...
could you please solve a and b?
Chapier 2i. Note: you needn't derive Kepler's laws-but do mention when you are using them, an describe the physical concepts involved and the meanings behind the variables. u) Consider two stars Mi and M; bound together by their mutual gravitational force (and isolated from other forces) moving in elliptical orbits (of eccentricity e and semi-major axes ai and az) at distances 11 in n and r from their center of mass located at...
Need by 12 pm July 30, 2020 with answers shown and explanation. Thank you. R 1)...
Need by 12 pm July 30, 2020 with answers shown and explanation.
Thank you.
R 1) Two resistors are connected to each other in parallel, one resistor has a known value of R, the resistance of the second one is unknown. If the equivalent of two resistors in parallel is equal to what is the resistance of the second one? A) R B) 2R E) 4R 2) Which one of the following sentences is correct about the velocity selector? A)...
b. For the above to be true, the constant term e must be related HOW to...
b. For the above to be true, the constant term e must be related HOW to the constants 0 and K ? (Write down an equation that includes all four constants.) (3 pts.) c. Show how v, the speed at which one pulse (or crest or trough, etc.) of the wave propagates, can be expressed in terms of your finding in (b). Show reasoning, not just a final answer (3 pts). w = angular frequency = number of cycles per...
The Navarro Frenk & White (NFW) model describes the
(spherically symmetric) haloes of dark matter that form in
cosmological simulations. It says that the density of dark matter
follows the distribution
, where is the distance from
the center of the halo, and is an arbitrary length.
Show (using Poisson’s formula) that the potential consistent with
this density distribution is
, where
.
+- p(r) = p(-) *-8
3. The Milky Way's Dark Matter Halo The Milky Way's rotation curve is approximately a constant, v(r) ~220 km/s, for 5 20 kpc, This constant circular velocity cannot be explained by the observed distribution of luminous mass Instead, we propose that the Milky Way is embedded in a roughly spherical dark matter halo. (a) Calculate M(r), the enclosed mass of the spherical dark matter halo as a function of r in the range 5< T < 20 kpc, assuming the...
Galaxies contain both stars and dark matter. The mass M of a galaxy that is located within a certain star's orbit is given by where v is the velocity of the star, r is the distance from the galaxy's center to the star, and G is Newton's gravitational constant, 6.673 x 10- N m/kg Stars near the edge of a particular galaxy have velocities of 259 km/s. The radius of the galaxy is 53 kpc. How much mass is in...
Question 1 (10 marks) (a) (4 marks) Recall that the gravitational potential energy for two masses is Ug-GMm Use this fact to show that the virial theorem holds for a mass m, executing uniform circular motion about a much larger mass M (b) (3 marks) The potential energy of a collection of N particles each of mass m in a region with radius R can be written as Use this expression to derive a mass estimate for the virialized system...
1).In a uniform circular motion, instantaneous velocity is tangent to the circle a) True b) False c) Can's say 2).In a uniform circular motion, acceleration is normal to the velocity and directed toward the center a) True b) False c) Unknown 3). For a particle of mass 'm' moving with a uniform velocity 'v' in a circle of radius 'r', write the expression for centripetal force (Fc)? 4). If a particle rotates in a circle of radius r= 10 cm...
1). In a uniform circular motion, instantaneous velocity is tangent to the circle a) True b) False c) Can's say 2).In a uniform circular motion, acceleration is normal to the velocity and directed toward the center a) True b) False c) Unknown 3). For a particle of mass 'm' moving with a uniform velocity 'v'in a circle of radius 'r', write the expression for centripetal force (Fc)? 4). If a particle rotates in a circle of radius r = 10...
PLEASE SHOW ALL WORK. THANKS.
III, SIMPLE HARMONIC HECK (30 pts: 10 pts each piece), The statements immediately to follow (even when long and complicated) are considered in this context) GIVEN You may assume and rely on them for the problem/proof to follow a bit further down. Note: In some cases, "GIVEN' might mean 'self-evident' or 'obvious', but in other cases, it might not. GIVEN might not mean "obvious"; it can simply mean 'somehow established prior to this discussion'. GIVEN...
could you please solve a and b?
Chapier 2i. Note: you needn't derive Kepler's laws-but do mention when you are using them, an describe the physical concepts involved and the meanings behind the variables. u) Consider two stars Mi and M; bound together by their mutual gravitational force (and isolated from other forces) moving in elliptical orbits (of eccentricity e and semi-major axes ai and az) at distances 11 in n and r from their center of mass located at...
Need by 12 pm July 30, 2020 with answers shown and explanation.
Thank you.
R 1) Two resistors are connected to each other in parallel, one resistor has a known value of R, the resistance of the second one is unknown. If the equivalent of two resistors in parallel is equal to what is the resistance of the second one? A) R B) 2R E) 4R 2) Which one of the following sentences is correct about the velocity selector? A)...
b. For the above to be true, the constant term e must be related HOW to the constants 0 and K ? (Write down an equation that includes all four constants.) (3 pts.) c. Show how v, the speed at which one pulse (or crest or trough, etc.) of the wave propagates, can be expressed in terms of your finding in (b). Show reasoning, not just a final answer (3 pts). w = angular frequency = number of cycles per...
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