Soal Latihan Astrofisika

Bagi yang berminat, silakan mencoba beberapa soal latihan yang akan melatih pemahaman Anda dalam hal Astrofisika.
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Soal Latihan Astrofisika 1 _ 2009

Brown Dwarfs Could Be More Common Than We Thought

In 2007, something strange happened to a distant star near the centre of our galaxy; it underwent what is known as a ‘microlensing’ event. This transient brightening didn’t have anything to do with the star itself, it had something to do with what passed in front of it. 1,700 light years away between us and the distant star, a brown dwarf crossed our line of sight with the starlight. Although one would think that the star would have been blocked by the brown dwarf, its light was actually amplified, generating a flash. This flash was created via a space-time phenomenon known as gravitational lensing.

Although lensing isn’t rare in itself (although this particular event is considered the “most extreme” ever observed), the fact that astronomers had the opportunity to witness a brown dwarf causing it means that either they were very lucky, or we have to think about re-writing the stellar physics textbooks.

“By several measures OGLE-2007-BLG-224 was the most extreme microlensing event (EME) ever observed,” says Andrew Gould of Ohio State University in Columbus in a publication released earlier this month, “having a substantially higher magnification, shorter-duration peak, and faster angular speed across the sky than any previous well-observed event.”

OGLE-2007-BLG-224 revealed the passage of a brown dwarf passing in front of a distant star. The gravity of this small “failed star” deflected the starlight path slightly, creating a gravitational lens very briefly. Fortunately there were a number of astronomers prepared for the event and captured the transient flash of starlight as the brown dwarf focused the light for observers here on Earth.

From these observations, Gould and his team of 65 international collaborators managed to calculate some characteristics of the brown dwarf “lens” itself. The brown dwarf has a mass of 0.056 (+/- 0.004) solar masses, with a distance of 525 (+/- 40) parsecs (~1,700 light years) and a transverse velocity of 113 (+/- 21) km/s.

Although getting the chance to see this happen is a noteworthy in itself, the fact that it was a brown dwarf that acted as the lens is extremely rare; so rare in fact, that Gould believes something is awry.

“In this light, we note that two other sets of investigators have concluded that they must have been ‘lucky’ unless old-population brown-dwarfs are more common than generally assumed,” Gould said.

Either serendipity had a huge role to play, or there are far more brown dwarfs out there than we thought. If there are more brown dwarfs, something isn’t right with our understanding of stellar evolution. Brown dwarfs may be a more common feature in our galaxy than we previously calculate.

Sources: “The Extreme Microlensing Event OGLE-2007-BLG-224: Terrestrial Parallax Observation of a Thick-Disk Brown Dwarf,” Gould et al., 2009.
arXiv:0904.0249v1 [astro-ph.GA], New Scientist, Astroengine.com

Cited from : Universe Today

The Anatomy of a Solar Explosion

Wouldn’t it be great if solar physicists could predict sun storms just like meteorologist predict hurricanes? Well, now perhaps they can. NASA’s twin STEREO observatories have made the first 3-D measurements of solar explosions, known as coronal mass ejections (CMEs), allowing scientists to see their size and shape, and image them as they travel approximately 93 million miles from the sun to Earth. With STEREO, scientists can now capture images of solar storms and make real-time measurements of their magnetic fields, much the same way that satellites allow forecasters to see the development of a hurricane. Eruptions from the sun’s outer atmosphere, or corona, can wreak havoc on satellites (and astronauts) in orbit or induce large currents in power grids on Earth, which can cause power disruptions or black outs.

“We can now see a CME from the time it leaves the solar surface until it reaches Earth, and we can reconstruct the event in 3D directly from the images,” said Angelos Vourlidas, a solar physicist at the Naval Research Laboratory, Washington, and project scientist for the Sun Earth Connection Coronal and Heliospheric Investigation aboard STEREO. In the video above, see some of the 3-D imagery, and hear Vourlidas talk about about the new findings.

CMEs spew billions of tons of plasma into space at thousands of miles per hour and carry some of the sun’s magnetic field with it. These solar storm clouds create a shock wave and a large, moving disturbance in the solar system. The shock can accelerate some of the particles in space to high energies, a form of “solar cosmic rays” that can be hazardous to spacecraft and astronauts. The CME material, which arrives days later, can disrupt Earth’s magnetic field, or magnetosphere, and upper atmosphere.

STEREO consists of two nearly identical observatories that make simultaneous observations of CMEs from two different vantage points. One observatory ‘leads’ Earth in its orbit around the sun, while the other observatory ‘trails’ the planet. STEREO’s two vantage points provide a unique view of the anatomy of a solar storm as it evolves and travels toward Earth. Once the CME arrives at the orbit of Earth, sensors on the satellites take in situ measurements of the solar storm cloud, providing a “ground truth” between what was seen at a distance and what is real inside the CME.

The combination is providing solar physicists with the most complete understanding to date of the inner workings of these storms. It also represents a big step toward predicting when and how the impact will be felt at Earth. The separation angle between the satellites affords researchers to track a CME in three dimensions, something they have done several times in the past few years as they have learned to use this new space weather tool.

“The in situ measurements from STEREO and other near-Earth spacecraft link the physical properties of the escaping CME to the remote images,” said Antoinette “Toni” Galvin, a solar physicist at the University of New Hampshire, and the principal investigator on STEREO’s Plasma and Suprathermal Ion Composition (PLASTIC) instrument. “This helps us to understand how the internal structure of the CME was formed and to better predict its impact on Earth.”

Until now, CMEs could be imaged near the sun but the next measurements had to wait until the CME cloud arrived at Earth three to seven days later. STEREO’s real-time images and measurements give scientists a slew of information—speed, direction, and velocity—of a CME days sooner than with previous methods. As a result, more time is available for power companies and satellite operators to prepare for potentially damaging solar storms.

Much like a hurricane’s destructive force depends on its direction, size, and speed, the seriousness of a CME’s effects depends on its size and speed, as well as whether it makes a direct or oblique hit across Earth’s orbit.

CMEs disturb the space dominated by Earth’s magnetic field. Disruptions to the magnetosphere can trigger the brightly colored, dancing lights known as auroras, or Northern and Southern Lights. While these displays are harmless, they indicate that Earth’s upper atmosphere and ionosphere are in turmoil.

Sun storms can interfere with communications between ground stations and satellites, airplane pilots, and astronauts. Radio noise from a storm can also disrupt cell phone service. Disturbances in the ionosphere caused by CMEs can distort the accuracy of Global Positioning System (GPS) navigation and, in extreme cases, induce stray electrical currents in long cables and power transformers on the ground.

The twin STEREO spacecraft were launched October 25, 2006, into Earth’s orbit around the sun.

Sources: NASA, APL

Cited from : Universe Today

Jawaban Soal Latihan Fotometri

Beberapa hari yang lalu, saya pernah menge-post-kan beberapa soal latihan fotometri. Jika Anda sudah mencobanya, coba bandingkan dengan jawaban yang bisa di download dari link di bawah ini.

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Jawaban Soal Latihan Soal Fotometri

Soal Latihan 2 : Spektroskopi

Karena tahap seleksi peserta olimpiade sains nasional Astronomi 2009 semakin dekat, saya mencoba membantu dengan memberikan beberapa soal latihan lagi. Kali ini, soal-soal ini bertema spektroskopi. Silakan dicoba dan didiskusikan dengan guru/tutor/teman.

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Soal Latihan Spektroskopi_2009

Refraksi Atmosfer

Posisi benda langit yang tampak di langit sebenarnya berbeda dengan posisi fisiknya, salah satu sebab adalah karena efek refraksi.

Efek refraksi pada saat Matahari atau Bulan terbenam
Saat Matahari atau Bulan terbit/terbenam, jarak zenit dari pusat kedua benda tersebut adalah 90^o. Refraksi yang terjadi saat itu disebut sebagai refraksi horisontal.

Refraksi horisontal saat benda langit terbit/terbenam adalah 35‟. Jika jarak zenit = 90^o, maka jarak zenit benar adalah 90^o35‟.

Efek refraksi pada asensiorekta dan deklinasi
- α’ – α = R sec δ’ sin η
- δ’ – δ = R cos η
dengan η adalah sudut paralaktik

Koreksi semi diameter
Pada saat Matahari terbenam, z = 90^o, h’ = 0^o, maka :
- jarak zenit piringan Matahari adalah : z = 90^o + R_{z = 90 deg}
- tinggi pusat Matahari adalah : h = 0^o - R_{z = 90 deg}

Matahari dikatakan terbit jika batas atas piringan mulai muncul di horison, dan terbenam jika batas piringan sudah terbenam di horison, maka z dan h harus dikoreksi oleh semidiameter piringan Matahari, S, sehingga :
z = 90^o + R_{z = 90 deg} + S
h = 0^o - R_{z = 90 deg} - S

Jadi, saat Matahari atau Bulan terbit atau terbenam :
h<sub>sun = - 0^o50’
hmoon = + 0^o08

Koreksi ketinggian di atas muka laut
Bidang horison pengamat di Bumi bergantung kepada ketinggian pengamat. Jika pengamat berada pada ketinggian l (meter) dari muka laut, maka sudut kedalaman (angle of dip), θ, adalah:
θ = 1’.93√l (dalam satuan menit busur).

Jika efek refraksi diperhitungkan, maka :
θ = 1’.78√l (dalam satuan menit busur)

Jarak ke horison-laut, dituliskan dengan :
d = 3.57√l (dalam km)

Jika efek refraksi diperhitungkan, maka :
d = 3.87√l (dalam km)

Soal Latihan
The White Bear from the previous International Astronomy Olympiad is still sitting at the North Pole. But this year a follower is appeared – a Penguin is sitting at the South Pole. Recently, after the ending of polar night, the Penguin observed the sunrise. What did the Bear observe this time? Draw what the White Bear saw at the moment when the Penguin observed exactly half of the solar disk on the horizon. Assume that the Earth is spherical. The answer should be explained by drawing a figure with an image of the Bear on North Pole; necessary sizes or angular sizes should be in the picture. Recollect for yourself the necessary information about the animals. (taken from IAO)</sub>

Soal Latihan Fotometri

Karena sudah semakin dekat dengan seleksi peserta olimpiade astronomi 2009, saya berikan beberapa soal sebagai latihan tentang fotometri.
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Soal Latihan 2009 - Fotometri

Waktu Sideris dan Waktu Sinodis

Sidereal time is a measure of the position of the Earth in its rotation around its axis, or time measured by the apparent diurnal motion of the vernal equinox, which is very close to, but not identical to, the motion of stars. They differ by the precession of the vernal equinox in right ascension relative to the stars.

Earth's sidereal day also differs from its rotation period relative to the background stars by the amount of precession in right ascension during one day (8.4 ms). Its J2000 mean value is 23h56m4.090530833s. Etymology of sidereal is from Latin "sidereus" from sidus, sider- = star. Therefore, its meaning relates to a measurement of time relative to the position of the stars.

Definition

Local Sidereal Time (LST) = RA + HA
Greenwich Sidereal Time (GST) is the LST at the Greenwich Meridian

Sidereal time is defined as the hour angle of the vernal equinox. When the meridian of the vernal equinox is directly overhead, local sidereal time is 00:00. Greenwich Sidereal Time is the hour angle of the vernal equinox at the prime meridian at Greenwich, England; local values differ according to longitude. When one moves eastward 15° in longitude, sidereal time is larger by one hour (note that it wraps around at 24 hours). Unlike computing local solar time, differences are counted to the accuracy of measurement, not just in whole hours. Greenwich Sidereal Time and UT1 differ from each other by a constant rate (GST = 1.00273790935 × UT1). Sidereal time is used at astronomical observatories because sidereal time makes it very easy to work out which astronomical objects will be observable at a given time. Objects are located in the night sky using right ascension and declination relative to the celestial equator (analogous to longitude and latitude on Earth), and when sidereal time is equal to an object's right ascension, the object will be at its highest point in the sky, or culmination, at which time it is best placed for observation, as atmospheric extinction is minimized.

Sidereal time and solar time
Solar time is measured by the apparent diurnal motion of the sun, and local noon in solar time is defined as the moment when the sun is at its highest point in the sky (exactly due south or north depending on the observer's latitude and the season). The average time taken for the sun to return to its highest point is 24 hours.

During the time needed by the Earth to complete a rotation around its axis (a sidereal day), the Earth moves a short distance (approximately 1°) along its orbit around the sun. Therefore, after a sidereal day, the Earth still needs to rotate a small extra angular distance before the sun reaches its highest point. A solar day is, therefore, nearly 4 minutes longer than a sidereal day.

The stars, however, are so far away that the Earth's movement along its orbit makes a generally negligible difference to their apparent direction (see, however, parallax), and so they return to their highest point in a sidereal day. A sidereal day is almost 4 minutes shorter than a mean solar day.

Another way to see this difference is to notice that, relative to the stars, the Sun appears to move around the Earth once per year. Therefore, there is one less solar day per year than there are sidereal days. This makes a sidereal day approximately ^365.24⁄_366.24 times the length of the 24-hour solar day, giving approximately 23 hours, 56 minutes, 4.1 seconds (86,164.1 seconds).

Sidereal time vs solar time. Above left: a distant star (the small red circle) and the Sun are at culmination, on the local meridian. Centre: only the distant star is at culmination (a mean sidereal day). Right: few minutes later the Sun is on the local meridian again. A solar day is complete.

Precession effects
The Earth's rotation is not simply a simple rotation around an axis that would always remain parallel to itself. The Earth's rotational axis itself rotates about a second axis, orthogonal to the Earth's orbit, taking about 25,800 years to perform a complete rotation. This phenomenon is called the precession of the equinoxes. Because of this precession, the stars appear to move around the Earth in a manner more complicated than a simple constant rotation.

For this reason, to simplify the description of Earth's orientation in astronomy and geodesy, it is conventional to describe Earth's rotation relative to a frame which is itself precessing slowly. In this reference frame, Earth's rotation is close to constant, but the stars appear to rotate slowly with a period of about 25,800 years. It is also in this reference frame that the tropical year, the year related to the Earth's seasons, represents one orbit of the Earth around the sun. The precise definition of a sidereal day is the time taken for one rotation of the Earth in this precessing reference frame.

Exact duration and its variation

A mean sidereal day is about 23 h 56 m 4.1 s in length. However, due to variations in the rotation rate of the Earth the rate of an ideal sidereal clock deviates from any simple multiple of a civil clock. In practice, the difference is kept track of by the difference UTC–UT1, which is measured by radio telescopes and kept on file and available to the public at the IERS and at the United States Naval Observatory.

Given a tropical year of 365.242190402 days from Simon et al. this gives a sidereal day of 86,400 × ^{365.242190402}⁄_{366.242190402}, or 86,164.09053 seconds.

According to Aoki et al., an accurate value for the sidereal day at the beginning of 2000 is ¹⁄_{1.002737909350795} times a mean solar day of 86,400 seconds, which gives 86,164.090530833 seconds. For times within a century of 1984, the ratio only alters in its 11th decimal place. This web-based sidereal time calculator uses a truncated ratio of ¹⁄_{1.00273790935}.

Because this is the period of rotation in a precessing reference frame, it is not directly related to the mean rotation rate of the Earth in an inertial frame, which is given by ω=2π/T where T is the slightly longer stellar day given by Aoki et al. as 86,164.09890369732 seconds. This can be calculated by noting that ω is the magnitude of the vector sum of the rotations leading to the sidereal day and the precession of that rotation vector. In fact, the period of the Earth's rotation varies on hourly to interannual timescales by around a millisecond, together with a secular increase in length of day of about 2.3 milliseconds per century which mostly results from slowing of the Earth's rotation by tidal friction.

Source : wikipedia, Polaris Project,Positional Astronomy

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