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Because the mass outside this inner region is almost constant, the density distribution can be
written as following (assume a flat Milky Way with height z0):
ρ(r) = (
ρ0, r ≤ R0
0, r > R0
(a) Derive an expression for the mass M(r) enclosed within the radius r.
(b) Derive the expected rotational velocity of the Milky Way v(r) at a radius r.
(c) Derive the dark matter mass Mdm(r) enclosed in r and explain its distributed.
spaceship can travel with 70% the speed of light and has a cylindrical shape with a diameter of
6 m at the front surface and a length of 25 m. You have to cross the interstellar medium with an
approximated density of 1 hydrogen atom/m3.
(a) Calculate the time it takes your spaceship to reach Sirius.
(b) Determine the mass of interstellar gas that collides with your spaceship during the mission.
Note: Use 1.673 10
Our Sun shines bright with a luminosity of 3.828 x 10 Watt. Her energy is responsible for many processes and the habitable temperatures on the Earth that make our life possible.
(a) Calculate the amount of energy arriving on the Earth in a single day.
litres of heating oil (energy density: 37.3 x 10 J/litre) is this equivalent?
(b) To how many (c) The Earth reflects 30% of this energy: Determine the temperature on Earth's surface.
(d) What other factors should be considered to get an even more precise temperature estimate?
Note: The Earth's radius is
6370 km, the Sun's radius is 696 x 10 km; 1 AU is 1.495 x 10 km.
approximated density of
(a) Calculate the (b)
1
You are on an interstellar mission from the Earth to the 8.7 light-years distant star Sirius. Your spaceship can travel with 70% the speed of light and has a cylindrical shape with a diameter of 6 m at the front surface and a length of 25 m. You have to cross the interstellar medium with an hydrogen atom/m
time it takes
your spaceship to reach Sirius.
Determine the mass of interstellar gas that collides with your spaceship during the mission.
Note: Use 1.673 x 10-27 kg as proton mass.
Because the mass outside this inner region is almost constant, the density distribution can be
written as following (assume a flat Milky Way with height z0):
ρ(r) = (
ρ0, r ≤ R0
0, r > R0
(a) Derive an expression for the mass M(r) enclosed within the radius r.
(b) Derive the expected rotational velocity of the Milky Way v(r) at a radius r.
(c) Astronomical observations indicate that the rotational velocity follows a dierent behaviour:
vobs(r) = p
Gπρ0z0R0
5/2
1 + e
−4r/R0
−
5
4
Draw the expected and observed rotational velocity into the plot below:
(d) Scientists believe the reasons for the dierence to be dark matter: Determine the rotational
velocity due to dark matter vDM (r) from R0 and draw it into the plot above.
(e) Derive the dark matter mass MDM (r) enclosed in r and explain its distributed.
(f) Explain briefly three theories that provide explanations for dark matter.
you can observe the following spectrum of the object. The Hα line peak is clearly visible:
(a) Mark the first four spectral lines of hydrogen (Hα, Hβ, Hγ, Hδ) in the spectrum.
(b) Determine the radial velocity and the direction of the object’s movement.
(c) Calculate the distance to the observed object.
(d) What possible type of object is your team observing?
The e star Sirius has an apparent magnitude of -1.46 and appears 95-times brighter compared to
the more distant star Tau Ceti, which has an absolute magnitude of 5.69.
(a) Explain the terms apparent magnitude, absolute magnitude and bolometric magnitude.
(b) Calculate the apparent magnitude of the star Tau Ceti.
(c) Find the distance between the Earth and Tau Ceti.
Distance Orbital Period
Mercury 0.39 AU 88 days
Venus 0.72 AU 225 days
Earth 1.00 AU 365 days
Mars 1.52 AU 687 days
(a) Calculate the average distance of Mercury, Venus and Mars to the Earth.
Which one of these planets is the closest to Earth on average?
(b) Calculate the average distance of Mercury, Venus and Earth to Mars.
Which one of these planets is the closest to Mars on average?
(c) What do you expect for the other planets?
Because the mass outside this inner region is almost constant, the density distribution can be
written as following (assume a flat Milky Way with height z0):
ρ(r) = (
ρ0, r ≤ R0
0, r > R0
(a) Derive an expression for the mass M(r) enclosed within the radius r.
(b) Derive the expected rotational velocity of the Milky Way v(r) at a radius r.
(c) Astronomical observations indicate that the rotational velocity follows a dierent behaviour:
vobs(r) = p
Gπρ0z0R0
5/2
1 + e
−4r/R0
5
4
Draw the expected and observed rotational velocity into the plot below:
(d) Scientists believe the reasons for the dierence to be dark matter: Determine the rotational
velocity due to dark matter vDM (r) from R0 and draw it into the plot above.
(e) Derive the dark matter mass MDM (r) enclosed in r and explain its distributed.
(f) Explain briefly three theories that provide explanations for dark matter.
spaceship can travel with 70% the speed of light and has a cylindrical shape with a diameter of
6 m at the front surface and a length of 25 m. You have to cross the interstellar medium with an
approximated density of 1 hydrogen atom/m3
.
(a) Calculate the time it takes your spaceship to reach Sirius.
(b) Determine the mass of interstellar gas that collides with your spaceship during the mission.
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#340153 on Dec 2023