Milky Way galaxy has a halo filled with dark matter. The total mass of the dark...

Milky Way galaxy has a halo filled with dark matter. The total mass of the dark matter
halo is about 1012 MSun, or 2×1042 kg. To simplify things, let’s assume this dark matter halo
is spherical with a radius of about 100,000 light years, and that it is uniformly filled with
whatever is responsible for dark matter. The following calculations will help you to com-
pare different dark matter hypotheses to see if they are reasonable. You will need to use
the formula for the volume of a sphere and the definition of density as mass per volume.
A. Consider the hypothesis that black holes with a mass of the sun are responsible for
dark matter. If this is true, what is the volume of space in our galaxy within which we
would expect to find one such black hole?
B. Take the cubed root of this volume, which gives you an estimate of approximately how
close we would expect such a black hole to be to our own solar system on average.
Given that the closest black holes that we know of are several thousand light years
away, does this dark matter hypothesis seem possible?
C. What if the dark matter were due to planet-sized black holes, about 10 Earth masses
each? Following the same steps as in part A and B to estimate about how close we
would expect such a black hole to be to Earth. If Planet X is found to be a black hole
about 600 AU from the Sun, would this support this theory explaining dark matter

Solutions

Expert Solution

Given that:

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

The mass of dark matter in the Milky Way is measured to be about 2×1042 kg....

The mass of dark matter in the Milky Way is measured to be about 2×1042 kg. Black holes emit no light, so perhaps they may be responsible for the unseen dark matter? To evalu- ate this possibility, determine how many black holes must exist to explain the dark matter and what process created them. As far as we know, every black hole was formed as a re- sult of a supernova explosion (though not every supernova creates a black hole)....

The mass of dark matter in the Milky Way is measured to be about 2×1042 kg....

The mass of dark matter in the Milky Way is measured to be about 2×1042 kg. Black holes emit no light, so perhaps they may be responsible for the unseen dark matter? To evaluate this possibility, determine how many black holes must exist to explain the dark matter and what process created them. As far as we know, every black hole was formed as a result of a supernova explosion A. Find the number of black holes in the Galaxy...

The total mass of the dark matter halo is about 1012 MSun, or 2×1042 kg. To...

The total mass of the dark matter halo is about 1012 MSun, or 2×1042 kg. To simplify things, let’s assume this dark matter halo is spherical with a radius of about 100,000 light years, and that it is uniformly filled with whatever is responsible for dark matter. The following calculations will help you to com- pare different dark matter hypotheses to see if they are reasonable. You will need to use the formula for the volume of a sphere and...

1. The Milky Way stellar mass is 1e11 M_sun. The total mass of the Milky Way...

1. The Milky Way stellar mass is 1e11 M_sun. The total mass of the Milky Way is 1e12 M_sun. How many 0.05 M_sun Brown Dwarfs would be required to account for the Dark Matter in the Milky Way? Give your answer in terms of billions. 2. The BAO length scale is 150 Mpc. How many light years is this? Please give your answer to 1 significant figure. 3. Observations of distant galaxies reveal how they looked in the past, akin...

Calculate the gravity Mass of Andromeda galaxy 1.5 × 10^42 kg Mass of Milky Way galaxy 8.0...

Calculate the gravity Mass of Andromeda galaxy 1.5 × 10^42 kg Mass of Milky Way galaxy 8.0 × 10^1 % of Andromeda's mass Distance between the galaxies 2.9 *10^6 light years 1) Even though it is not quite right for this situation, use Newton's Law of Gravitation to calculate the force of gravity (in Newtons) between the Milky Way galaxy and the Andromeda galaxy today. 2) In the future, will the force of gravity between the two galaxies increase, decrease or stay...

Dark matter; C&O 24.22. (a) Assume that the density of dark matter in our Galaxy is...

Dark matter; C&O 24.22. (a) Assume that the density of dark matter in our Galaxy is given by ρ(r) = ρ0/(1+(r/a) ^2) . Show that the amount of dark matter interior to a radius r is given by: Mr = 4πρ0a^2 [ r − a tan^−1 ( r/a )]. (b) If 5.4 × 10^11 M⊙ of dark matter is located within 50 kpc of the Galactic centre, determine ρ0 in units of M⊙ kpc−1 . Repeat your calculation if 1.9...

Our Sun, with mass 2.00×1030 kg, revolves about the center of the Milky Way galaxy, which...

Our Sun, with mass 2.00×1030 kg, revolves about the center of the Milky Way galaxy, which is 2.20×1020 m away, once every 2.50×108 years. Assuming that each of the stars in the galaxy has a mass equal to that of our Sun, that the stars are distributed uniformly in a sphere about the galactic center, and that our Sun is essentially at the edge of that sphere, estimate roughly the number of stars in the galaxy.

According to current theory of galaxy disk formation, galaxy disks are embedded in extended dark matter...

According to current theory of galaxy disk formation, galaxy disks are embedded in extended dark matter halos whose density profiles can roughly be written as ρ(r) = V_vir 2 /(4πGr2), where V_vir is a constant. (1) What is the total mass of the halo within a radius R, M(< R)? (2) What is the rotation curve, Vc(R), of the disk embedded in such a halo (assuming disk mass can be neglected)? (3) What is the mean mass density of the...

The galaxy that contains our solar system, the milky way, is approximately a uniform disc of...

The galaxy that contains our solar system, the milky way, is approximately a uniform disc of mass 10^12Msun and diameter 175×10^3 light years. Assuming that the center of mass of the galaxy is at rest, estimate the time that it takes the sun to complete one orbit around the galaxy center. A few useful numbers: the mass of the sun Msun = 2 × 10^30kg, 1 light year = 9.46 × 10^15m, and the distance between the sun and the...

The supermassive black hole in the center of the Milky Way has a mass of roughly...

The supermassive black hole in the center of the Milky Way has a mass of roughly 3 million M⊙and the Milky Way is approximately10 billion years old. Estimate the average amount of matter accreted by the black hole per year since that time and use that information to propose modes by which the black hole has grown. That is, make some simple models which describe what the black hole might have eaten, and how much it has eaten as a...

Subjects