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-Astronomers need to identify the position of objects in the sky with very high precision. For that,

it is essential to have coordinate systems that specify the position of an object at a given time.

One of them is the equatorial coordinate system that is widely used in astronomy.


(a) Explain how the equatorial coordinate system works.

(b) What is the meaning of J2000 that often occurs together with equatorial coordinates?


-The object NGC 4440 is a galaxy located in the Virgo Cluster at the following equatorial coordinates

(J2000): 12h 27m 53.6s (right ascension), 12o 17' 36'' (declination). The Calar Alto Observatory

is located in Spain at the geographical coordinates 37.23oN and 2.55oW.


(c) Is the NGC 4440 galaxy observable from the Calar Alto Observatory?


This problem requires you to read the following recently published scientific article:

Measuring the ionisation fraction in a jet from a massive protostar.

Fedriani, R., Caratti o Garatti, A., Purser, S.J.D. et al. Nat Commun 10, 3630 (2019).

Link: https://www.nature.com/articles/s41467-019-11595-x.pdf

Answer the following questions related to this article:

(a) Why are massive stars important for the development of the universe?

(b) How can the ionised part of jets be observed?

(c) What kind of region is G35.2N? Describe how it is structured.

(d) What is the ionisation fraction χe and how do the authors calculate its value?

(e) How is the mass-loss rate being determined for knots K3 and K4? Why not for K1 and K2?

(f) Why is the ionisation fraction so small for G35.2N?


Astronomers need to identify the position of objects in the sky with very high precision. For that, it is essential to have coordinate systems that specify the position of an object at a given time. One of them is the equatorial coordinate system that is widely used in astronomy. (a) Explain how the equatorial coordinate system works. (b) What is the meaning of J2000 that oen occurs together with equatorial coordinates? The object NGC 4440 is a galaxy located in the Virgo Cluster at the following equatorial coordinates (J2000): 12h 27m 53.6s (right ascension), 12◦ 170 3600 (declination). The Calar Alto Observatory is located in Spain at the geographical coordinates 37.23◦N and 2.55◦W. (c) Is the NGC 4440 galaxy observable from the Calar Alto Observatory?


The most common isotope of gold is gold-197 with a measured mass of 196.966569u.

  1. Determine the mass defect;
  2. Determine the binding energy;
  3. Determine the binding energy per nucleon.

Problem A.3: Total Solar Eclipse (4 Points) A total solar eclipse occurs when the Moon moves between the Earth and the Sun and completely blocks out the Sun. This phenomenon is very spectacular and attracts people from all cultures. However, total solar eclipses can also take place on other planets of the Solar System. Determine for each of the following moons if they can create a total solar eclipse on their planet. Moon Radius Distance to Planet Planet Distance to the Sun Phobos 11 km 9376 km Mars 228 × 106 km Callisto 2410 km 1.883 × 106 km Jupiter 779 × 106 km Titan 2574 km 1.222 × 106 km Saturn 1433 × 106 km Oberon 761 km 0.584 × 106 km Uranus 2875 × 106 km Note: The radius of the Sun is 696 × 103 km. 


A space probe is about to launch with the objective to explore the planets Mars and Jupiter. To

use the lowest amount of energy, the rocket starts from the Earth’s orbit (A) and flies in an elliptical orbit to Mars (B), such that the ellipse has its perihelion at Earth’s orbit and its aphelion at

Mars’ orbit. The space probe explores Mars for some time until Mars has completed 1/4 of its orbit

(C). After that, the space probe uses the same ellipse to get from Mars (C) to Jupiter (D). There the

mission is completed, and the space probe will stay around Jupiter.

The drawing below shows the trajectory of the space probe (not drawn to scale):


Below you find the orbital period and the semi-major axis of the three planets:


planet orbital period Semi-major axis

Earth 365 days 1.00 AU

Mars 687 days 1.52 AU

Jupiter 4333 days 5.20 AU


How many years after its launch from the Earth (A) will the space probe arrive at Jupiter (D)?


State and explain the two traditional postulates from which special relativity originates.


Problem A.3: Total Solar Eclipse (4 Points)

A total solar eclipse occurs when the Moon moves between the Earth and the Sun and completely

blocks out the Sun. This phenomenon is very spectacular and attracts people from all cultures.

However, total solar eclipses can also take place on other planets of the Solar System.

Determine for each of the following moons if they can create a total solar eclipse on their planet.

Moon Radius Distance to Planet Planet Distance to the Sun

Phobos 11 km 9376 km Mars 228 × 106 km

Callisto 2410 km 1.883 × 106 km Jupiter 779 × 106 km

Titan 2574 km 1.222 × 106 km Saturn 1433 × 106 km

Oberon 761 km 0.584 × 106 km Uranus 2875 × 106 km

Note: The radius of the Sun is 696 × 103 km


Stationary flow


Shock wave


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