Calculate Photons/Angstrom at Cassegrain Telescope - V=9, zenith=60°

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In summary, to calculate the photons expected at the focus of a 30cm Cassegrain telescope for a star of V magnitude 9.0 observed at a zenith distance of 60 degrees, first calculate the total extinction of the star by multiplying the extinction coefficient and airmass. Then, convert the V magnitude to a flux density and calculate the telescope's collecting area. Finally, use the formula to calculate the number of photons expected per Angstrom, resulting in a total of 321 photons.
  • #1
goleafsgo113
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ok the question is,
Calculate the photons you expect to receive per Angstrom at the focus of a Cassegrain telescope of aperture 30cm for a star of V magnitude 9.0, observed at a zenith distance of 60 degrees. Assume extinction coefficient of 0.15 magnitudes per airmass, reflectivity at each surface = 90%, wavelength = 5500 Angstrom.

I'm overwhelmed with all the numbers given and cannot find any equations that are useful to this question. If anyone has an idea please give me a hint on where to start or how to approach this question. Thanks in advance.
 
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The first step is to calculate the total extinction of the star. To do this, calculate the airmass, which is equal to the secant of the zenith distance (60 degrees). This will give you an airmass of 2.00. Then, multiply the extinction coefficient (0.15) by the airmass (2.00) to get the total extinction of 0.30 magnitudes. Next, convert the V magnitude of the star (9.0) to a flux density in Janskys (Jy). To do this, use the formula: Flux Density (Jy) = 10^(-(V Magnitude - 0.03)/2.5) This gives you a flux density of 0.001 Jy. Now, calculate the telescope's collecting area. To do this, use the formula: Collecting Area (cm^2) = 3.14 * Aperture Diameter (cm)^2 This gives you a collecting area of 706.5 cm^2. Finally, calculate the number of photons you expect to receive per Angstrom at the focus of the telescope. To do this, use the formula: Number of Photons (per Angstrom) = Flux Density (Jy) * Collecting Area (cm^2) * Reflectivity (0.90) * Wavelength (5500 Angstroms) This gives you a total of 321 photons per Angstrom.
 
  • #3


I can provide some guidance on how to approach this question. First, we need to understand some key concepts and equations related to the telescope and the observation.

1. Aperture: The aperture of a telescope is the diameter of its primary lens or mirror. In this case, the aperture is given as 30cm.

2. Extinction coefficient: This is a measure of how much light is absorbed or scattered by the Earth's atmosphere. It is given as 0.15 magnitudes per airmass. Airmass is a measure of the thickness of the atmosphere that the light has to pass through to reach the telescope.

3. Reflectivity: This is the measure of how much light is reflected by the telescope's surfaces. In this case, it is given as 90%.

4. Magnitude: Magnitude is a measure of the brightness of a star. A lower magnitude number indicates a brighter star. In this case, the star has a magnitude of 9.0.

5. Wavelength: This is the specific color or frequency of light that we are observing. In this case, it is given as 5500 Angstroms.

Now, we can use the following equation to calculate the number of photons per Angstrom at the focus of the telescope:

N = (F * T * R * T * 10^(-0.4m)) / (A * d^2)

Where,
N = number of photons per Angstrom
F = aperture of the telescope
T = transmission of the telescope (1-R)
R = reflectivity of the telescope
m = magnitude of the star
A = area of the telescope's primary mirror
d = airmass (calculated using the zenith distance)

Using the given values, we can plug them into the equation and solve for N.

N = (0.3m * 0.1 * 0.9 * 0.1 * 10^(-0.4*9.0)) / (pi * (0.15/0.15)^2) = 7.27 x 10^7 photons/Angstrom

Therefore, we can expect to receive approximately 7.27 x 10^7 photons per Angstrom at the focus of the Cassegrain telescope under these conditions. Keep in mind that this is just an estimate and the actual number may vary due to factors such as atmospheric conditions and telescope performance.
 

1. How do you calculate the number of photons per Angstrom at a Cassegrain telescope with a visual magnitude of 9 and a zenith angle of 60 degrees?

To calculate the number of photons per Angstrom at a Cassegrain telescope, you will need to use the formula: Number of photons per Angstrom = Flux (in photons/cm^2/s/A) x Telescope area (in cm^2) x Exposure time (in seconds) x Transmission efficiency. The visual magnitude of 9 and zenith angle of 60 degrees will be used to determine the Flux value.

2. What is the significance of the zenith angle in calculating photons per Angstrom at a Cassegrain telescope?

The zenith angle is important because it represents the angle at which the telescope is pointed towards the sky. This angle affects the amount of light that the telescope can gather and therefore, impacts the number of photons per Angstrom that can be detected. A higher zenith angle means that the telescope is pointed closer to the horizon and will receive less light compared to a lower zenith angle.

3. How does the visual magnitude of a star affect the calculation of photons per Angstrom at a Cassegrain telescope?

The visual magnitude of a star is used to determine the Flux value in the formula for calculating photons per Angstrom. The lower the visual magnitude, the brighter the star and the higher the Flux value will be. This means that a star with a visual magnitude of 9 will have a higher Flux value compared to a star with a visual magnitude of 10, resulting in a higher number of photons per Angstrom at the telescope.

4. What is the role of exposure time in the calculation of photons per Angstrom at a Cassegrain telescope?

Exposure time is a crucial factor in calculating photons per Angstrom at a Cassegrain telescope. It determines how long the telescope will be exposed to light from the star. A longer exposure time means that more photons will be collected, resulting in a higher number of photons per Angstrom. However, a longer exposure time may also increase the amount of noise in the data, so it is essential to find a balance between exposure time and the desired signal-to-noise ratio.

5. How does the transmission efficiency of the telescope impact the calculation of photons per Angstrom?

The transmission efficiency of a telescope refers to how much light is passing through the telescope's optics without being absorbed or scattered. This efficiency can vary depending on the type and quality of the telescope's optics. A higher transmission efficiency means that more light will reach the detector, resulting in a higher number of photons per Angstrom. Therefore, it is essential to consider the transmission efficiency of the telescope when calculating photons per Angstrom.

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