Astronomy | Astrophysics Answers

Problem A.2: Resolution of Telescopes (4 Points)

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?

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 coordi￾nates (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?

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 I Radius I Distance to Planet I Planet I Distance to the Sun

Phobos I11 km I 9376 km I Mars I 228 × 10^6 km

Callisto I 2410 km I1.883 × 10^6 km | Jupiter 779 × 10^6 km

Titan | 2574 km |1.222 × 10^6 km | Saturn |1433 × 10^6 km

Oberon | 761 km | 0.584 × 10^6 km | Uranus | 2875 × 10^6 km

Note: The radius of the Sun is 696 × 10^3 km.

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?

Problem A.1: Equatorial Coordinate System (4 Points) 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?

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?

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 coordi-

nates (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?

We are planning to build our

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

300 nm. The farthest distance between the Earth and Jupiter is 766 × 10^5 km and the Great Red

Spot has currently a diameter of 17,540 km.

(i) By the help of the Rayleigh criterion,try to determine the diameter of the lens’ aperture of our telescope

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

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

craters with our new telescope. The distance between Moon and Earth is 355,340 km.

(ii) Find out the smallest possible size of the craters that our telescope can resolve.

Is Exploring Space Really Important? Write about this in about 350 words

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?