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# Luminosity

Luminosity is the measurement of brightness. Depending on the field of study, luminosity is defined differently depending on what is being measured. In astronomy, luminosity measures the total amount of energy emitted by a star or other astronomical object per unit time.  Luminosity is an intrinsic measurable property of a star independent of distance. The concept of magnitude however incorporates distance.

The Stefan-Boltzmann equation applied to a black body gives the value for luminosity for a black body. The equation for this is

L = σAT4

Where

A is the area

σ is the Stefan-Boltzmann constant of 5.67 x 108 W m-2K-4

For a point source of light of luminosity L that radiated equally in all directions the equation is as follows:

F = L/A

Where

A is the area of the illuminated surface

F is the flux density of the illuminated surface

In scattering theory and acceleratory physics, luminosity is the number of particles per unit area per unit time multiplied by the opacity of the target. It is important to characterize the performance of an accelerator.

### Luminosity Magnetar Burst

The total luminosity at all wavelengths of the magnetar burst observed on December 27, 2006, was approximately 10^14 L. At what distance from the magnetar would the brightness of the burst have been equal to the brightness of the Sun as seen on Earth? Can you give the answer in AU and in parsecs.

At one stage during its birth, the protosun had a luminosity of 1000L and a surface temperature of about 1000K. What was its radius at this time? Please give the answer in three different ways: As a multiple of the sun's present day radius, In kilometers, and In astronomical units.

### Hertzsprung-Russell diagram

In order to make a HR diagram of a globular cluster, which properties do you have to measure for each star of the cluster? The graph (see attached file problem 5) show the HR diagram of three real star clusters. Which cluster is the youngest?

### Calculate the distance of this star.

8) Sirius is one of our nearest and brightest neighbors at a distance of 2065 pc. By a careful comparison of the spectral lines, a second star is known to have an intrinsic brightness, or luminosity, very similar to that of Sirius, even though it appears one hundred times fainter from earth. Calculate the distance of this star.

### Different Types of Astronomical Measurements

After many differnt typs of astronomical measurements, it is now that believed that X-1 is a black hole a. Find the location of this black hole relative to earth b. Caculate Schwarzchild radius of the Cygnus X-1 black hole Help I haven't been able to find the mass of Cygnus X-1. I cannot caculate the schwarzchild rad

### Calculating the Radius for Pluto

Spectroscopic observations suggest that Pluto is covered with icy frost and thus has a high albedo (0.5). The brightness of Pluto at opposition (38 AU from the Earth) is 2 x 10^-17 as bright as the Sun (1 AU from the Earth). From these two observations, calculate a radius of Pluto.