Mayo 2010
Examen Final de Astronomia Observacional. Para presentar el 25 de mayo en el tiempo de clase.
Presente una solicitud de tiempo de telescopio para dos de los objetos abajo indicados en la columna de sus nombres.
Es importante destacar en la solicitud: la localizacion del observatorio en donde observara, las fechas de observacion, el numero de noches solicitadas, las fases de la luna, la instrumentacion que se utilizara (telescopio, equipo periferico y detector) y, por supuesto, las justificaciones cientificas para tal seleccion.
Es indispensable enfatizar brevemente que resultados cientificos se esperan obtener, que fisica hay detras, que aportaciones daran sus datos al conocimiento universal y la metodologia que se seguira para la reduccion e interpretacion de los datos.
Sigan los formatos de solicitud del OAN (anexo a la presente) pero NO RESTRINJAN la instrumentacion a la de nuestro observatorio. Hagan su solicitud pensando en un observatorio ideal con la mejor instrumentacion posible.
La fecha de entrega del examen es el martes 2 de diciembre a las 16 hrs. No hay extension al plazo. Se les pide no consultar con ningun investigador, ni estudiante avanzado, y solo entre si para asesorarse o discutir. Se puede consultar libremente la biblioteca y los bancos de datos. Estoy en la mejor disposición de responder preguntas y dudas y proponer ideas y referencias.
Favor de entregar en esa fecha todo el material de su temporada de observacion asi como los mapas de identificación que fueran a utilizar. Este material, recuerden, tambien se evalua. Asimismo traigan en esa fecha todas sus practicas evaluadas. Se hara un breve examen oral individual sobre su presentacion.
Buen trabajo y mejor suerte.
angel andrea erika rocio jared david linda laura
TVBoo AE Boo AC And RU Psc Y Lac Z Lac BG Lac SZ Tau
Ngc6882 Ngc104 Ngc4147 Ngc5272 Ngc6121 IC 1613 M31 M32
Ngc6618 Ngc3918 Ngc7662 Ngc6853 Ngc2392 LZ Her ER Ori YY Eri
ALGUNAS DIRECCIONES ELECTRÓNICAS QUE PUDIERAN SERLES UTILES.
http://obswww.unige.ch/webda/cgi-bin/ocl_page.cgi?dirname=ngc6913
http://adsabs.harvard.edu/abstract_service.html
http://simbad.u-strasbg.fr/Simbad
http://nedwww.ipac.caltech.edu/
SOLICITUD DE TIEMPO DE TELESCOPIO OBSERVATORIO ASTRONOMICO NACIONAL
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I)- INVESTIGADOR PRINCIPAL:
FECHA:
INSTITUCION:
E-MAIL:
FAX:
TELEFONO:
________________________________________________________________________________
II)- TITULO DEL PROYECTO (max. 12 palabras):
________________________________________________________________________________
III)- DESCRIPCION RESUMIDA DEL PROYECTO (max. 5 lineas):
________________________________________________________________________________
IV)- PERIODOS DE OBSERVACION
________________________________________________________________________________
TELESCOPIO INSTRUMENTO, DETECTOR, OTROS ACCESORIOS
________________________________________________________________________________
1-
________________________________________________________________________________
V)- # DE NOCHES LUNA(O,G,B,C) PERIODOS FECHAS ________________________________________________________________________________
1-
________________________________________________________________________________
VI)- FECHAS INACEPTABLES Y RAZONES :
________________________________________________________________________________
VII)- JUSTIFICACION DEL EQUIPO Y NOCHES SOLICITADAS. ESPECIFIQUE EL PORQUE DEL EQUIPO SOLICITADOS, NUMERO DE NOCHES Y FASES LUNARES (max. 10 lineas):
________________________________________________________________________________
VIII)- LISTE LOS OBJETOS A OBSERVAR, COORDENADAS Y MAGNITUDES
________________________________________________________________________________
IX)- JUSTIFICACION CIENTIFICA. Esta debe ser autocontenida, no incluya pretiros, sobretiros, etc. Mencione de una manera concisa los antecedentes de su programa y los objetivos que se buscan en la temporada solicitada (max. 1 pagina)
jueves, 6 de mayo de 2010
miércoles, 30 de septiembre de 2009
Recetario fotometrico
Recetario fotometrico
Struve
Stellar Parallaxes.
The determination of the trigonometric parallaxes of stars is of fundamental importance in stellar astronomy, for without knowledge of the stellar distances very little information concerning their brightnesses, sizes and distribution in space could be obtained.
The linear distance (in kilometers) of a star whose parallax is known can easily be found, since the parallax of a star is the angle subtended by the radius of the earth’s orbit as seen from the star.
The parallax of the nearest star, α Centauri, is 0”.751. Since one astronomical unit = 1.5 x 10*8 km, the distance to α Centauri may be found from the ratio
p” α Cen / (360x60’x60”) = 1.5 x 10*8 /(2pi d α cen)
Or, since p” α Cen = 0”.751
d (α Cen) = 4.1 x 10*13 km
Units of Distance.
Since stellar distances are large, to new units of length are used. The parsec is defined as the distance from which the radius of the earth’s orbit subtends an angle of one second of arc:
1 parsec distance of a star whose parallax is one second of arc
in kilometers, this distance is given by the ratio
1/(360x60’x60”) = 1.5 x 10*8 km/ (2 pi dpc)
or 1 parsec = 3.1 x 10*13 kilometers
Thus, the distance to α Centauri is
d(α Centauri) = (4.1 x 10*13)/(3.1 x 10*13) = 1.3 pc
By definition, a star whose parallax is 1 second of arc is at a distance of one parsec. If it has a parallax of ½”, or 0.5”, it is at a distance of two parsecs. In general,
d (in parsecs) = 1/p”
For α Centauri dα Centauri = 1/0”751 = 1.3 parsecs
The other unit of distance is the light year:
1 light year = distance traveled by light in one year.
1 light year = 3 x 10*5 x 3.16 x 10*7 kilometers, 1 ly = 9.5 x 10*12 km.
The distance to Centauri in light years is, then:
d(α Centauri) = 4.1 x 10*13 light years
Extensive programs of parallax rneasurements are being carried out at many observatories. Several thousand stars have been found to have measurable parallaxes, but because of the technical difficulties in measuring very small relative displacements of star images on photographic plates, the lower limit of an observable parallax is about 0”.01; that is, the trigonometric parallax method of determining stellar distances is useful only up to distances of the order of 100 parsecs. Subsequent chapters of this book will describe other methods of estimating stellar distances. All of them, however, are based ultimately upon trigonometric parallax determinations of the nearest stars.
Motz, essentials of astronomy
The brightness ratio for stars of different magnitudes
We shall see how to assign magnitudes to stars that are not exactly 100 times fainter than (that is 1/100 as bright as) the standard first-magnitude star. W can do this by determining how much two stars differ in brightness if they differ by one magnitude. To ascertain this from our scale let b1 be the apparent brightness of a star of the first-magnitude, b2 the apparent brightness of a star of the second magnitude, etc., so that bm is the apparent brightness of a star of the mth magnitude. The factor bm/bm +1 is then the number of times an mth magnitude star is brighter than a star of magnitude m + 1. Let us call this factor, a, so that a star of the first magnitude is a times as bright as one of the second magnitude; a star of the second magnitude is a times as bright as one of the third magnitude, etc. In other words we have
(b1/b2) x( b2/b3)x(b3/b4)x(b4/b5)x(b5/b6)=b1/b6=100
a x a x a x a x a = a*5 = 100.
We see from this that a is equal to the fifth root of 100 or, what is the same thing,
a = 10*2/5 ,
which is very nearly equal to 2.512. Thus a star of any magnitude is somewhat more than 2 1/2 times brighter than the star of the next higher magnitude. Note that the larger magnitudes are associated with the fainter stars.
Let us now consider two stars, one of which is of the mth apparent magnitude, and the other of the nth apparent magnitude, and let bm and bn be their apparent brightnesses respectively. What is the ratio of these brightnesses? We know that for each magnitude step the brightness decreases by a factor of 10*2/5 and since in going from m to n there are exactly n- m steps, the apparent brightness of the nth—magnitude star is smaller than that of the mth star by the factor
(n — m) factors
10*2/5 x 10*2/5 x 10*2/5 x ….10*2/5 x = 10*2/5(n-m)
We thus have
bm/bn = 10*2/5(n-m)
15.15 Relationship between Brightness and Magnitude
Since the power to which 10 must be raised to give any particular number is called the logarithm of that number to the base 10, we have
log10 (bm/bn) = 2/5 (n — m)
if we now consider the star of the nth magnitude as being a kind of standard to which we may refer all other stars, we have
log10 bm = -0.4 m +B
where bm refers to the apparent brightness of any star of apparent magnitude m and B is a constant. This gives the relationship between apparent brightness and the apparent magnitude.
Relation between m and M.
To find the exact relationship between m and M we must know how the apparent brightness of a star changes when the distance changes. The apparent brightness of a celestial body varies inversely as the square of its distance from us, because its light moves uniformly in all directions, spreading out in concentric spheres. Thus, the intensity falls off inversely as the square of the distance from the star because the energy in the light is spread uniformly oven larger and larger spherical surfaces.
If we keep this in mind, it is easy to find M, if m and d are known. Let us consider a star at distance d and suppose that it is brought to a distance of l0 parsecs. If we compare its apparent brightness, bm, at the distance d with its apparent brightness, BM (its abso1ute brightness), at 10 parsecs, we have from the inverse-square law described above
bm/BM = 10*2 / d*2
where d is to be measured in parsecs.
On the other hand, we may look upon the star when it is at a distance d and the same star when it is at 10 parsecs as being two different stars having magnitudes m and M respectively, and we may then as how two such stars compare in apparent brightness. We gave the answer to this question in the previous section [ Equation (15.7)], where we saw that since each magnitude step represents a brightness ratio of 10*2/5, two stars having magnitudes m and M will have a brightness ratio of 10*2/5(M-m), there being just M-m steps in going from m to M. In other words, We must have
bm/BM = 10*2/5(M-m)
It we compare this with our previous equation for bm/BM we see that
10*2/5(M-m) = (10/d)*2
or 10*(M-m)/5 = 10/d
so that d = 10* (5-M+m)/5
From this it follows that
log10 d = (5-M+m)/5
or M = m + 5 -5 log d
Since d = l/p”, (note that - log d = +log p”), we see, finally that
M = m + 5 + 5 log p”
From this equation we can determine the absolute magnitude of any star if its apparent magnitude and parallax are known.
Stellar Luminosities
Since we shall express the luminosities of all stars in terms of the sun’s luminosity, Lo , we must begin by finding the absolute magnitude of the sun, for once we know this, we can find the luminosity of any star from a knowledge of its absolute magnitude by means of the relationship
log (L/Lo) = 0.4(Mo - M),
where L and M represent the luminosity and absolute magnitude of the given star. Since we know that Lo = 3.90 x 10*33 ergs/sec, we can at once find L from this equation if we know Mo
To find the absolute magnitude of the sun, we use the equation M = m + 5 - 5 log d, with m = -26.78 and d = 1/206 265, since this the distance of the sun in parsecs; we thus have
Mo = - 26.78 + 5 + 5 log 206 265,
or Mo = +4.71
Hence if the luminosity L of a star is expressed in solar units we have
log10 L = 0.4M — 1.884.
ejemplo:
Consider α Centauri, which, at a distance of 1.3 parsecs, has an apparent magnitude of 0. At 10 parsecs its distance wou1d be 10/1.3 = 8 times larger and its luminosity would be reduced by a factor of (8)*2, or 64. This corresponds to about 4.5 magnitudes. Thus, the absolute magnitude of α Centauri is approximate 0 + 4.5 = 4.5 magnitudes.
The Sun and α Centauri are closer than 10 parsecs, and their absolute magnitudes are therefore fainter than their apparent magnitudes. Most stars, however are at distances greater than 10 parsecs. For example Spica, or α Virginis, has a parallax of 0”.02 and an apparent visual magnitude of +1.2. The following steps lead to the determination of its absolute magnitude:
1. The distance of Spica is 1/0.02 = 50 parsecs.
2. Spica is, then, 5 times farther away than 10 parsecs.
3. The brightness of Spica at a distance of 10 parsecs would therefore be (5)*2, or 25, times greater than it is at 50 parsecs.
4. The corresponding change in magnitude is about 3.5.
5. Since Spica would be brighter at 10 parsecs than at 50 parsecs, the difference of 3.5 magnitudes must be subtracted from its apparent magnitude:
Mspica = m – Δm = +1.2 - 3.5 = -2.3 mag.
The absolute visual magnitude of Spica is therefore, -2.3.
Since the absolute magnitudes may be derived from either visual, photographic, or bolometric apparent magnitudes, it is necessary to distinguish between visual, photographic, and bolometric absolute magnitudes.
Two observational quantities are necessary for the determination of the absolute magnitude of a star: its parallax and its apparent magnitude. The most luminous stars have absolute bolometric magnitudes of the order of -10 and absolute visual magnitudes of the order of -7. The intrinsically faintest known stars have absolute bolometric magnitudes of the order of +18 and absolute visual magnitudes of the order of +19. The range in bolometric brightness is, then, about 28 magnitudes.
Struve
Stellar Parallaxes.
The determination of the trigonometric parallaxes of stars is of fundamental importance in stellar astronomy, for without knowledge of the stellar distances very little information concerning their brightnesses, sizes and distribution in space could be obtained.
The linear distance (in kilometers) of a star whose parallax is known can easily be found, since the parallax of a star is the angle subtended by the radius of the earth’s orbit as seen from the star.
The parallax of the nearest star, α Centauri, is 0”.751. Since one astronomical unit = 1.5 x 10*8 km, the distance to α Centauri may be found from the ratio
p” α Cen / (360x60’x60”) = 1.5 x 10*8 /(2pi d α cen)
Or, since p” α Cen = 0”.751
d (α Cen) = 4.1 x 10*13 km
Units of Distance.
Since stellar distances are large, to new units of length are used. The parsec is defined as the distance from which the radius of the earth’s orbit subtends an angle of one second of arc:
1 parsec distance of a star whose parallax is one second of arc
in kilometers, this distance is given by the ratio
1/(360x60’x60”) = 1.5 x 10*8 km/ (2 pi dpc)
or 1 parsec = 3.1 x 10*13 kilometers
Thus, the distance to α Centauri is
d(α Centauri) = (4.1 x 10*13)/(3.1 x 10*13) = 1.3 pc
By definition, a star whose parallax is 1 second of arc is at a distance of one parsec. If it has a parallax of ½”, or 0.5”, it is at a distance of two parsecs. In general,
d (in parsecs) = 1/p”
For α Centauri dα Centauri = 1/0”751 = 1.3 parsecs
The other unit of distance is the light year:
1 light year = distance traveled by light in one year.
1 light year = 3 x 10*5 x 3.16 x 10*7 kilometers, 1 ly = 9.5 x 10*12 km.
The distance to Centauri in light years is, then:
d(α Centauri) = 4.1 x 10*13 light years
Extensive programs of parallax rneasurements are being carried out at many observatories. Several thousand stars have been found to have measurable parallaxes, but because of the technical difficulties in measuring very small relative displacements of star images on photographic plates, the lower limit of an observable parallax is about 0”.01; that is, the trigonometric parallax method of determining stellar distances is useful only up to distances of the order of 100 parsecs. Subsequent chapters of this book will describe other methods of estimating stellar distances. All of them, however, are based ultimately upon trigonometric parallax determinations of the nearest stars.
Motz, essentials of astronomy
The brightness ratio for stars of different magnitudes
We shall see how to assign magnitudes to stars that are not exactly 100 times fainter than (that is 1/100 as bright as) the standard first-magnitude star. W can do this by determining how much two stars differ in brightness if they differ by one magnitude. To ascertain this from our scale let b1 be the apparent brightness of a star of the first-magnitude, b2 the apparent brightness of a star of the second magnitude, etc., so that bm is the apparent brightness of a star of the mth magnitude. The factor bm/bm +1 is then the number of times an mth magnitude star is brighter than a star of magnitude m + 1. Let us call this factor, a, so that a star of the first magnitude is a times as bright as one of the second magnitude; a star of the second magnitude is a times as bright as one of the third magnitude, etc. In other words we have
(b1/b2) x( b2/b3)x(b3/b4)x(b4/b5)x(b5/b6)=b1/b6=100
a x a x a x a x a = a*5 = 100.
We see from this that a is equal to the fifth root of 100 or, what is the same thing,
a = 10*2/5 ,
which is very nearly equal to 2.512. Thus a star of any magnitude is somewhat more than 2 1/2 times brighter than the star of the next higher magnitude. Note that the larger magnitudes are associated with the fainter stars.
Let us now consider two stars, one of which is of the mth apparent magnitude, and the other of the nth apparent magnitude, and let bm and bn be their apparent brightnesses respectively. What is the ratio of these brightnesses? We know that for each magnitude step the brightness decreases by a factor of 10*2/5 and since in going from m to n there are exactly n- m steps, the apparent brightness of the nth—magnitude star is smaller than that of the mth star by the factor
(n — m) factors
10*2/5 x 10*2/5 x 10*2/5 x ….10*2/5 x = 10*2/5(n-m)
We thus have
bm/bn = 10*2/5(n-m)
15.15 Relationship between Brightness and Magnitude
Since the power to which 10 must be raised to give any particular number is called the logarithm of that number to the base 10, we have
log10 (bm/bn) = 2/5 (n — m)
if we now consider the star of the nth magnitude as being a kind of standard to which we may refer all other stars, we have
log10 bm = -0.4 m +B
where bm refers to the apparent brightness of any star of apparent magnitude m and B is a constant. This gives the relationship between apparent brightness and the apparent magnitude.
Relation between m and M.
To find the exact relationship between m and M we must know how the apparent brightness of a star changes when the distance changes. The apparent brightness of a celestial body varies inversely as the square of its distance from us, because its light moves uniformly in all directions, spreading out in concentric spheres. Thus, the intensity falls off inversely as the square of the distance from the star because the energy in the light is spread uniformly oven larger and larger spherical surfaces.
If we keep this in mind, it is easy to find M, if m and d are known. Let us consider a star at distance d and suppose that it is brought to a distance of l0 parsecs. If we compare its apparent brightness, bm, at the distance d with its apparent brightness, BM (its abso1ute brightness), at 10 parsecs, we have from the inverse-square law described above
bm/BM = 10*2 / d*2
where d is to be measured in parsecs.
On the other hand, we may look upon the star when it is at a distance d and the same star when it is at 10 parsecs as being two different stars having magnitudes m and M respectively, and we may then as how two such stars compare in apparent brightness. We gave the answer to this question in the previous section [ Equation (15.7)], where we saw that since each magnitude step represents a brightness ratio of 10*2/5, two stars having magnitudes m and M will have a brightness ratio of 10*2/5(M-m), there being just M-m steps in going from m to M. In other words, We must have
bm/BM = 10*2/5(M-m)
It we compare this with our previous equation for bm/BM we see that
10*2/5(M-m) = (10/d)*2
or 10*(M-m)/5 = 10/d
so that d = 10* (5-M+m)/5
From this it follows that
log10 d = (5-M+m)/5
or M = m + 5 -5 log d
Since d = l/p”, (note that - log d = +log p”), we see, finally that
M = m + 5 + 5 log p”
From this equation we can determine the absolute magnitude of any star if its apparent magnitude and parallax are known.
Stellar Luminosities
Since we shall express the luminosities of all stars in terms of the sun’s luminosity, Lo , we must begin by finding the absolute magnitude of the sun, for once we know this, we can find the luminosity of any star from a knowledge of its absolute magnitude by means of the relationship
log (L/Lo) = 0.4(Mo - M),
where L and M represent the luminosity and absolute magnitude of the given star. Since we know that Lo = 3.90 x 10*33 ergs/sec, we can at once find L from this equation if we know Mo
To find the absolute magnitude of the sun, we use the equation M = m + 5 - 5 log d, with m = -26.78 and d = 1/206 265, since this the distance of the sun in parsecs; we thus have
Mo = - 26.78 + 5 + 5 log 206 265,
or Mo = +4.71
Hence if the luminosity L of a star is expressed in solar units we have
log10 L = 0.4M — 1.884.
ejemplo:
Consider α Centauri, which, at a distance of 1.3 parsecs, has an apparent magnitude of 0. At 10 parsecs its distance wou1d be 10/1.3 = 8 times larger and its luminosity would be reduced by a factor of (8)*2, or 64. This corresponds to about 4.5 magnitudes. Thus, the absolute magnitude of α Centauri is approximate 0 + 4.5 = 4.5 magnitudes.
The Sun and α Centauri are closer than 10 parsecs, and their absolute magnitudes are therefore fainter than their apparent magnitudes. Most stars, however are at distances greater than 10 parsecs. For example Spica, or α Virginis, has a parallax of 0”.02 and an apparent visual magnitude of +1.2. The following steps lead to the determination of its absolute magnitude:
1. The distance of Spica is 1/0.02 = 50 parsecs.
2. Spica is, then, 5 times farther away than 10 parsecs.
3. The brightness of Spica at a distance of 10 parsecs would therefore be (5)*2, or 25, times greater than it is at 50 parsecs.
4. The corresponding change in magnitude is about 3.5.
5. Since Spica would be brighter at 10 parsecs than at 50 parsecs, the difference of 3.5 magnitudes must be subtracted from its apparent magnitude:
Mspica = m – Δm = +1.2 - 3.5 = -2.3 mag.
The absolute visual magnitude of Spica is therefore, -2.3.
Since the absolute magnitudes may be derived from either visual, photographic, or bolometric apparent magnitudes, it is necessary to distinguish between visual, photographic, and bolometric absolute magnitudes.
Two observational quantities are necessary for the determination of the absolute magnitude of a star: its parallax and its apparent magnitude. The most luminous stars have absolute bolometric magnitudes of the order of -10 and absolute visual magnitudes of the order of -7. The intrinsically faintest known stars have absolute bolometric magnitudes of the order of +18 and absolute visual magnitudes of the order of +19. The range in bolometric brightness is, then, about 28 magnitudes.
viernes, 4 de septiembre de 2009
1) porque mercurio no tiene una atmosfera apreciable?
2) cuanto tendra que esperar un astronomo para que regrese un pulso que hizo rebotar en mercurio?
3) cuanto mas flujo (energia/m2) del sol recibe Venus cada segundo comparado con el de la tierra? Esta diferencia es significativa?
4) cual es el diametro angular de Venus cuando se encuentra mas proximo a la tierra? Se podria ver a Venus en este punto de su orbita?
5) cual es la velocidad de escape de mercurio?
6) el semi eje mayor de Venus es de 0.72 UA. Utilice la tercera ley de Kepler para calcular su periodo
7) suponga que se establece una colonia en marte. Cuanto le llevara a un doctor en marte enviar y recibir una respuesta de una consulta a un colega en la tierra?
2) cuanto tendra que esperar un astronomo para que regrese un pulso que hizo rebotar en mercurio?
3) cuanto mas flujo (energia/m2) del sol recibe Venus cada segundo comparado con el de la tierra? Esta diferencia es significativa?
4) cual es el diametro angular de Venus cuando se encuentra mas proximo a la tierra? Se podria ver a Venus en este punto de su orbita?
5) cual es la velocidad de escape de mercurio?
6) el semi eje mayor de Venus es de 0.72 UA. Utilice la tercera ley de Kepler para calcular su periodo
7) suponga que se establece una colonia en marte. Cuanto le llevara a un doctor en marte enviar y recibir una respuesta de una consulta a un colega en la tierra?
devoir_01
Devoir 01
Para entregar el 2 de septiembre
1) Cual es el cociente de la fuerza gravitacional del sol sobre la tierra al de la fuerza graviatacional de la luna sobre la tierra?
2) si miras exactamente sobre la cabeza y encuentras que la luna se encuentra ahí, en que fase lunar se encuentra?
3) (a) cuanto varia la declinación del sol a lo largo del año? (b) su ascencion recta, aumenta o disminuye de dia en dia?
4) cuantos grados, minutos de arco y segundos de arco se mueve la luna a traves del cielo en 1 hora? Cuanto le llevara a la luna moverse en el cielo una distancia igual a su propio diametro?
5) partiendo del hecho que a la luna le toma 29.5 dias completar un cliclo completo de fases muestre que la luna sale en promedio 48 minutos mas tarde cada noche
6) cual es la altitud de Polaris vista desde latitudes de 90, 60, 30 y 0 grados
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