Astronomy | Astrophysics Answers

The average density of a white dwarf of radius 10⁹ cm is 10⁶ gm/cm³ . Is general theory of relativity needed to study the dynamics of this star? What happens if the star shrinks to a radius thousand times smaller? 

The latitude and longitude (in degrees) of Mumbai and Shillong are as follows:

Mumbai: latitude 19 N longitude 73 E

Shillong: latitude 26 N longitude 92 E.

When it is 12:00 O’clock local time at Shillong, what is the local time in Mumbai?

Telescopes are an essential tool for astronomers to study the universe. You plan to build your

own telescope that can resolve the Great Red Spot on the surface of Jupiter at a wavelength of

600 nm. The farthest distance between the Earth and Jupiter is 968 × 106 km and the Great Red

Spot has currently a diameter of 16,500 km.

(a) Use the Rayleigh criterion to determine the diameter of the lens’ aperture of your telescope

that is needed to resolve the Great Red Spot on Jupiter.

Impacts have formed many craters on the Moon’s surface. You would like to study some of the

craters with your new telescope. The distance between Moon and Earth is 384,400 km.

(b) What is the smallest possible size of the craters that your telescope can resolve?

What is meant by the apparent magnitude of a star? How is it related to the brightness of the star? An object A has an apparent magnitude of –5. Another object B has an apparent magnitude of –10. Calculate the ratio of their brightness.

Express the distances of the stars Sirius A and Antares from the Earth in light years.

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

Special relativity has become a fundamental theory in the 20th century and is crucial for explaining many astrophysical phenomena. A central aspect of special relativity is the transformation from one reference frame to another. The following Lorentz transformation matrix gives the transformation from a frame at rest to a moving frame with velocity v along the z-axis: where β = v/c with c being the speed of light in a vacuum, and γ is the Lorentz factor: γ = 1 p 1 − β 2 (a) State and explain the two traditional postulates from which special relativity originates. (b) Draw a plot of the Lorentz factor for 0 ≤ β ≤ 0.9 to see how its value changes. One of the many exciting phenomena of special relativity is time dilation. Imagine astronauts in a spaceship that is passing by the Earth with a high velocity. (c) Are clocks ticking slower for the people on Earth or for the astronauts on the spaceship? (d) How fast must the spaceship travel such that the clocks go twice as slow?

Telescopes are an essential tool for astronomers to study the universe. You plan to build your own telescope that can resolve the Great Red Spot on the surface of Jupiter at a wavelength of 600 nm. The farthest distance between the Earth and Jupiter is 968 × 106 km and the Great Red Spot has currently a diameter of 16,500 km. (a) Use the Rayleigh criterion to determine the diameter of the lens’ aperture of your telescope that is needed to resolve the Great Red Spot on Jupiter. Impacts have formed many craters on the Moon’s surface. You would like to study some of the craters with your new telescope. The distance between Moon and Earth is 384,400 km. (b) What is the smallest possible size of the craters that your telescope can resolve?

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). Aer 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): Sun Earth Mars Jupiter A B D C Below you find the obrital period and the semi-major axis of the three planets: 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 aer its launch from the Earth (A) will the space probe arrive at Jupiter (D)?

Problem C.2 : Massive Protostar Jet (10 Points)

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?