Astronomy | Astrophysics Answers

Because your spaceship has an engine failure, you crash-land with an emergency capsule at the equator of a nearby planet. The planet is very small and the surface is a desert with some stones and small rocks laying around. You needwater to survive. However,water is only available at the poles of the planet. You find the following items in your emergency capsule:
 Stopwatch
 Electronic scale
 2m yardstick
 1 Litre oil
 Measuring cup
Describe an experiment to determine your distance to the poles by using the available items.
Hint: As the planet is very small, you can assume the same density everywhere.

2. (a) A particle P moves along the x-axis with constant acceleration a in the positive x-direction. Initially
P is at the origin and is moving with velocity u in the positive x-direction. Show that the velocity v
and displacement x of P at time t are given by
v = u + at, x = ut +
1
2
at2
,
and deduce that
v
2 = u
2 + 2ax.
(b) The trajectory of a charged particle moving in a magnetic field is given by
r = b cos (Ωt)i + b sin (Ωt)j + ctk,
where b, Ω and c are positive constants. Show that the particle moves with constant speed and find the
magnitude of its acceleration.

This problem requires you to read the following recently published scientific article:
Observation of GravitationalWaves from a Binary Black Hole Merger.
B. P. Abbott et al., LIGO Scientific Collaboration and Virgo Collaboration
arXiv:1602.03837, (2016). Link: https://arxiv.org/pdf/1602.03837.pdf
Answer following questions related to this article:
(a) How was the existence of gravitational waves first shown?
(b) Which detectors exist around the world? Why did only LIGO detect GW150914?
(c) Explain the components of the LIGO detectors.
(d) Describe the dierent sources of noise. How was their impact reduced?
(e) What indicates that the gravitational wave originated from the merger of a black hole?
(f) Which are the methods used to search for gravitational wave signals in the detector data?
(g) How were the source parameters (mass, distance, etc.) determined from the data?

The table below lists the average distance R to the Sun and orbital period T of the first planets:
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 you are moving with an enormous speed, your mission from the previous problem A.1 will be influenced by the eects of time dilation described by special relativity: Your spaceship launches in June2020andreturnsbacktoEarthdirectly aer arriving at Sirius.
a) How many years will have passed from your prespwctive
b) At what Earth date (year and month) will you arrive back to Earth?

Because your spaceship has an engine failure, you crash-land with an emergency capsule at the
equator of a nearby planet. The planet is very small and the surface is a desert with some stones
and small rocks laying around. You needwater to survive. However,water is only available at the
poles of the planet. You find the following items in your emergency capsule:
 Stopwatch
 Electronic scale
 2m yardstick
 1 Litre oil
 Measuring cup
Describe an experiment to determine your distance to the poles by using the available items.

The table below lists the average distance R to the Sun and orbital period T of the first planets:
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 you are moving with an enormous speed, your mission from the previous problem A.1
will be influenced by the eects of time dilation described by special relativity: Your spaceship
launches in June 2020 and returns back to Earth directly aer arriving at Sirius.
(a) How many years will have passed from your perspective?
(b) At which Earth date (year and month) will you arrive back to Earth?

Your research team analysis the light of a mysterious object in space. By using a spectrometer,
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?

Problem B.3: Mysterious Object (6 Points)
Your research team analysis the light of a mysterious object in space. By using a spectrometer,
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?