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 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?27 kg as proton mass.

2. Because you are moving with an enormous speed, your mission from the previous problem A.1
will be influenced by the e_ects of time dilation described by special relativity: Your spaceship
launches in June 2020 and returns back to Earth directly a_er 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?
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3. The 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.

4. 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.
5. 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 H_ line peak is clearly visible:
(a) Mark the first four spectral lines of hydrogen (H_, H_, H, H_) 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?

Question

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 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?27 kg as proton mass.

2. Because you are moving with an enormous speed, your mission from the previous problem A.1
will be influenced by the e_ects of time dilation described by special relativity: Your spaceship
launches in June 2020 and returns back to Earth directly a_er 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?
www.

3. The 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.

4. 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.
5. 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 H_ line peak is clearly visible:
(a) Mark the first four spectral lines of hydrogen (H_, H_, H, H_) 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?

Accepted Answer

“Since you have asked multiple question, we will solve the first question for you. If you want any…