The Oort Cloud

What's the Oort Cloud?

The Oort Cloud is a spherical halo of comet nuclei gravitationally bound and surrounding the Sun to a distance of 2.000 / 5.000 up to 100.000 / 200.000 AU  (a third of the way to the next closest star), proposed by the Dutch astronomer Jan Oort in 1950.

While direct evidence for the existence of the Oort cloud is currently impossible to obtain, the idea is widely accepted as an explanation for the observed frequency and orbital characteristics of new long-period comets.

The Oort Cloud is believed to contain a population of up to 1012 comet nuclei!

Gravitational perturbations  by passing stars may dislodge Oort Cloud nuclei, causing them to fall sunwards and perhaps to pass through the inner Solar System.

A comet of this nature may return to the far depths of space on a long-period orbit, for example C/1996 B2 HYAKUTAKE, which is not expected to return for 17.000 years !!!

http://www.hvezdarnacb.cz/de/2/79/wallpapers

Refinements of the model from the 1950s onwards led to the suggestion that the Oort Cloud may become more concentrated towards the ecliptic plane at distances of 10.000 to 20.000 AU from the Sun, extending inwards to join the edgeworth-Kuiper Belt.

Interesting sites:
http://abyss.uoregon.edu/~js/ast121/lectures/lec24.html

Reference:
PHILIP’S ASTRONOMY ENCYCLOPEDIA
First published in Great Britain in 1987 by Mitchell Beazley
under the title The Astronomy Encyclopedia (General Editor
Patrick Moore)

Kepler's laws

Enunciate the Kepler's Laws.

Kepler's first law: the orbit of every planet is an ellipse wth the Sun at one of the two foci.

Kepler's second law: a line joining a planet and the Sun sweeps out equal areas during equal intervals of time.

Kepler's third law: the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

\(P^{2} \propto a^{3}\)

\(P = orbital \, period \, of \, a \, planet \)
\(a = semi-major \, axis \, of \, the \, orbit \)

In the case of a circular orbit:

\(4 \pi^{2} / P^{2} = G \cdot M / R^{3} \)

\(M \, is \, the \, mass \, of \, the \, larger \, body \)
\(R \, is \, the \, distance \, between \, the \, centres \, of \, the \, two \, masses\)

Reference:
http://en.wikipedia.org/wiki/User:Gonfer

Let's talk about the Albedo

Give the definition of albedo.

The albedo is the measure of the reflecting power of the surface of a non-luminous body.
It's defined as the ratio of the amount of light reflected by a body to the total amount falling on it.
Albedo values range from 0 for a perfectly absorbing black surface, to 1 for a perfect reflector or white surface.
Albedo is commonly used in astronomy to describe the fraction of sunlight reflected by planets, satellites and asteroids.
Rocky bodies have low values whereas those covered with clouds or ice have high values.
The average albedo of the Moon is just 0.07 whereas Venus, which is covered in dense clouds has a value of 0.76, which is the highest in the solar system!
Earth's albedo is 0.3!

Why is it important to know the albedo of a celestial object?

The albedo of an object provide valuable information about the composition and structure of its surface, while the combination of an object's albedo, size and distance determines its overall brightness.

Reference:
PHILIP’S ASTRONOMY ENCYCLOPEDIA
First published in Great Britain in 1987 by Mitchell Beazley
under the title The Astronomy Encyclopedia (General Editor
Patrick Moore) 
&
http://www.esr.org/outreach/glossary/albedo.html

Lense-Thirring Effect

Explain the Lense-Thirring Effect.

 

look at: http://homepage.univie.ac.at/Franz.Embacher/Rel/

 

 

In general relativity the Lense-Thirring effect is a relativistic correction to the precession of a gyroscope near a large rotating mass such as the earth.

A rotating mass slightly drags the metric of space-time along with it, twisting it  a little or in the extreme case, creating a vortex like structure in space-time.

A free-falling object from the 'OFF' no longer moves in a straight line toward the center of a spherical central mass if it is rotating.

Reference:
Epstein Explains Einstein
An Introduction to both the Special and the General Theory of Relativity
“As simple as possible - but not simpler !”
by David Eckstein

Light Aberration

Explain the Light Aberration phenomenon.

 

Consider a telescope, pointing in a direction perpendicular to the momentary direction of the earth's movement in its orbit: in the time the light of a star needs to arrive from the objective to the eyepiece, the earth has already advanced on its course. I must therefore tip the telescope through an angle \( \alpha\), in order for the star to be presented in the center of the visual field.

This angle defines the light deviation due to the movement of the earth.

The formula to apply in the case of this aberration is:

\( \tan \alpha = v/c \)  where \( v \) is the velocity of the earth in its orbit, \( v \simeq 30 Km/s \).

The angle has a size of approximately 20 arcsecond.

Reference:
Epstein Explains Einstein
An Introduction to both the Special and the General Theory of Relativity
“As simple as possible - but not simpler !”
by David Eckstein

The Twin Paradox

In what consists the Twin Paradox?

I consider twins A and B. 

At the age of 25 B sets off on a  prolonged space journey with \(v=12/13 \cdot c\), while A stays on earth.

After 26 years, earth time, A is precisely 51 years old, as his brother B returns to earth from his journey.

HOW OLD IS B?

I want ignore the short acceleration phases when starting, reversing flight direction and landing and I assume that B flew away for 13 years with velocity \(v\) and afterwards flew back 13 years with velocity \( -v\).

The term \( cos \theta = 5/13\). 

Therefore, for each of the out-bound flight and the return flight B aged only 5 years.

On his return to earth he is therefore only 35 years old, while his twin brother is celebrating his fifty-first.

From the point of view of the space traveller is everything reversed, and thus A must be younger than B!

Actually, however, the whole arrangement is asymmetrical: only A is the whole time at rest in an inertial frame, while B is exposed in different phases of his journey to accelerations. 

During the non-accelerated flight phases B actually has the impression that his brother A works somewhat slowly.

Anyway, the reasoning from A's frame is correct: twin B s younger.

Twin B, in order to leave the earth and travel to a distant galaxy, must accelerate to speed \(v\).

Then when B reaches the galaxy must slow down and eventually turn around and accelerate in the other direction.

Finally when B reaches the earth again he must decelerate from \(v\) to land once more on earth.
Since B's route involves acceleration, his frame cannot be considered an inertial reference frame and thus none of the reasoning like time dilation or length contraction can be applied.

To deal with this situation in B's frame I need a much more complicated analysis involving accelerating frames of reference and General Relativity.

It turns out that while B is moving with speed \(v\) A's clock does run comparatively slow, but when B is accelerating the A's clock run faster to such an extent that the overall elapsed time is measured as being shorter in B's frame.

Thus the reasoning in A's frame is correct and B is younger.

Reference:
Epstein Explains Einstein
An Introduction to both the Special and the General Theory of Relativity
“As simple as possible - but not simpler !”
by David Eckstein
&
http://www.sparknotes.com/physics/specialrelativity/applications/section2.rhtml
Image: http://www.sparknotes.com/physics/specialrelativity/applications/section2.rhtml

The Equivalence Principle

Enunciate the Equivalence Principle in various ways.

1. It is not possible, in a LOCAL experiment, to determine whether a laboratory is suspended in the gravitational field of a large body causing a gravitational acceleration \(g\) or whether it is gravitationally free and being subjected to a constant acceleration \(g\).

2. There are no LOCAL experiments that can distinguish whether a laboratory is free falling in a gravitational field or whether it is resisting UNaccelerated in gravity-free space.

3. In a homogeneous gravitational field all operations run exactly the same way as in a uniformly accelerated, but GRAVITY-FREE reference frame.

4. A laboratory in a gravitational field, falling freely and NOT rotating, is an INERTIAL FRAME in the sense of the Special Theory of Relativity.

5. The effect of gravity can be locally produced or reversed by a suitable acceleration.

Reference:
Epstein Explains Einstein
An Introduction to both the Special and the General Theory of Relativity
“As simple as possible - but not simpler !”
by David Eckstein
Image: http://www.descsite.nl/Gravity_us.htm

Today Let's Talk about Photometric Systems

Give the definition of photometric system.

A standard photometric system is defined by a list of standard magnitudes and colors measured at specific bandpasses for a set of stars that are well distributed around the sky. 

Observed magnitudes are corrected for the attenuation of the Earth’s atmosphere away from the zenith, and the data is then normally extrapolated to zero airmass (outside of the atmosphere).

However, most of the infrared (IR) broad bands are difficult to extrapolate to zero airmass because of the nonlinear behavior with airmass of the \(H_2O\) absorption (Manduca & Bell 1979) compared to the linear behavior of dust, aerosols and Rayleigh scattering, the major components of optical extinction.

Many astronomical photometric systems have been established over the years by different observers with a variety of detectors and passbands. 

Different standard photometric systems usually measure different wavelength bands.

All photometric systems enable the measurement of absolute fluxes, from which can be inferred particular properties (such as temperature, gravity, and metallicity) of the emitting object, but different systems claim to do it more precisely or more efficiently than other systems and some are better suited for hot stars and others for cool stars.

Photometric systems are usually divided into broad band ( λ < 1000 \(\overset{\circ}{A})\), intermediate band (70  \(\overset{\circ}{A}\) < λ < 400  \(\overset{\circ}{A})\), and  narrow band ( λ < 70 \(\overset{\circ}{A})\).
Another category, the ultra–broad band, has been recently proposed to encompass those survey systems, such as Sloan and Hipparcos, whose bandwidths are wider than the well-known BVRI broad-band system. 

Another important difference between systems relates to whether they are closed or open. 

An open system is one whose originators encourage others to duplicate the passbands and detector system and to use the originator’s standard stars and reduction system for their photometric programs.

A closed system is one where a small group of people control the instrumentation and data reduction and only encourage others to use the results but not to attempt to duplicate the system and observe stars for themselves. 

For obvious reasons, systematic errors and the quality of the data are better controlled in a closed system than an open system. In the past, the main disadvantage of a closed system was that your particular star of interest was often not in the catalog. 

However, with the advent of large-scale sky surveys to faint magnitudes, it is likely that, in the future, photometry for most objects of nterest will be provided by closed photometric systems.

Reference:

STANDARD PHOTOMETRIC SYSTEMS

Michael S. Bessell

Annual Review of Astronomy and Astrophysics, Vol. 43: 293 -336 (Volume publication date September 2005)

Interesting links:
http://spiff.rit.edu/classes/phys445/lectures/colors/colors.html
http://www.starlink.rl.ac.uk/docs/sc6.htx/node10.html

Today Let's Talk about Surface Brightness

Give the definition of surface brightness.

The surface brightness of an extended object, for example a galaxy, is the radiative flux per square arcseconds on the sky.


                                            ------- 
---------------------------- |   D   |
             d                            --------

D= area on the sky in [square arcseconds]
d= distance of the galaxy we're considering [parsecs]

This galaxy subtends an angle alpha on the sky:

\[\alpha =\frac {D}{d}\]

If I measure the luminosity L of all the stars into the area D I've the TOTAL flux:

\[F =\frac {L}{ 4 \cdot \pi \cdot (d)^2}\]

So I can define the surface brightness with this formula ( very important):

\[I = \frac{F}{(\alpha)^2} = \frac{F}{ \big(\frac{D}{d}\big) ^2}=\frac {L}{ (4 \pi \cdot (d)^{2}) \cdot \big(\frac{D}{d}\big)^{2}}=\frac {L}{ 4 \cdot \pi \cdot (D)^2}\]

\[I \bigg[\frac{mag} {arcseconds^2}\bigg]\]

References:
 1)http://asd.gsfc.nasa.gov/David.Davis//courses/phys315/week6/week6.pdf
 2)http://www.astro.spbu.ru/staff/resh/Lectures/lec1.pdf 

Today let's talk about Magnitudes

What's the definition of magnitude?

In astronomy the magnitude is the measure of the brightness of an object in logarithmic scale, measured in a certain band, for example the near IR (Infra-Red) or V (violet).

Define the apparent and absolute magnitude and explain how to link the two.

The apparent magnitude m of a celestial object is the brightness of an object as seen from earth, without the influence of the atmosphere.

The formula to remember is:

\[m_{2} -m_{1} = -\log\bigg(\frac{F_{2}}{F_{1}}\bigg)\]

where F2 is the observed flux in a certain band, for example the V one and F1 and m1 are respectively the reference flux and magnitude calibrated for example with the star Vega.

The absolute magnitude M of a star is the apparent magnitude it would have if it were at 10 parsecs.

I can derive the absolute magnitude from the apparent one if I know the distance, so I use the distance modulus relation:

\[m - M = 5\cdot \log(D) - 5\]

D is measured in parsecs.

Reference: http://en.wikipedia.org/wiki/Magnitude_%28astronomy%29