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Astronomy Calculations


My Excel sheet collection.

This is a new page and I will add more information later how to use it.

I don't take any responsible for this, they can have errors in it! Use them at your own risk!

Astronomical Calculations

Contents

  • Introduction
  • Data bases
  • FOV Calculations
  • Simulation of Vignetting
  • Free Opening inside tube
  • Magnitude
  • Temperature coefficients focus
  • Angle Conversations
  • Back ground magnitude
  • Orbit Calculator NEW
  • Download Excel sheet

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    Introduction:

    Over the years I have done a lot of calculations when investigating how to construct different things. Normally you find at internet what you looking information for, but sometimes it could be comfortable to have your own calculations that you can adapt for your own purpose. Here are my collection of Excel files, maybe parts of it can be interested for you too? It's my personal and could be difficult for others to use. But I have clean them up, translated them to English and given a short tutorial to each of them down here. I'm not sure if this is useful for others, but if you find it interesting, take a look.

    At bottom you can download the file which have all this equations under different maps at bottom of the Excel sheet.

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    Telescope data base:

    After over and over again writing all data I needed for the calculations I got tired on it. I added three pages with data bases over my equipment and other items that I wanted to investigate.

    There are three of them, Camera, Telescope and lens, and a Coma and Flat field corrector data base.

    Telescope data base:

    Telescope data base

    Here are the telescopes and lenses I have done calculation on. You find this page at bottom of the Excel sheet. It's very easy to expand to more telescopes if you want, but let the first and last row always be untouched. The blue fields has equations, don't erase them. Lot of this data are calculated and not real but will not be far from correct and you can always overwrite it with your own data.

    Camera data base:

    Camera data base

    Here is the camera data base. In all data bases, mark with one X in the first column which item you want to include in your calculations. Just one row with a X, erase earlier X! The x at the bottom row shall always be there!

    Most of the data that I couldn't find at manufactures page are estimated or calculated. If you have better data you can overwrite it in the fields.

    Field flattener and Coma corrector data base

    Flat field and Coma corrector data base

    Similar to the other data bases, but if you don't have any corrector, chose the first alternative with no corrector. What I miss here are the inlet and outlet lens diameters and distances of different correctors. The Riccardi 2.5" and the TS coma corrector I have it to.

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    FOV Calculations:

    FOV analyze

    This is the most important calculations. It gives the telescope / camera systems FOV and pixel scale, both  x and y axis and the diagonal pixel scale. It get the most of its data from the data bases.

    The theoretical resolution are calculated at different wavelengths. At the end you get a hint if the pixel scale is correct based at the 2x Nyqvist sampling theorem. You can set the tolerance of it.

    Only change values in the red fields, the green ones comes from the data bases and the blue ones are the result from the calculations done.

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    Simulation of Vignetting:

    Similation of Vignetting

    With this it's possible to see how big opening is needed of the focuser's inlet and outlet holes and other items that could block the light ray and give vignetting, it depends partly on the FOV calculations. If possible, try to hold the signal over 70% at the edges, more vignetting than that is not good.

    With a reducer it can miss calculate a bit, but still give ideas how to design the different parts. Do you need a 2" or 3" focuser?

    You shall always compare with others calculations, this is not a high precision calculation, the coma and field flattener optical layout are not known in detail.

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    Free Opening inside tube:

    Calculation of clearenace inside tube

    This one calculates how big the openings inside the tube has to be at different distances from sensor. Here you see that the focuser must have a bigger hole than a 2" focuser can give on the incoming side. A Canon DSLR camera house has a back focus of 44 mm, according to this calculation of my telescope the opening have to be 49 mm or more in the entrance of bayonet. You can also get the optical axis distance to the pickup prism of the off-axis adapter. Don't change the green fields, it takes data from the X market row you have set in the data bases.

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    Magnitude relations:

    Magnitude relations

    Calculate magnitudes to linear relations and distance from apparent magnitude and absolute Magnitude.

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    Temperature coefficients focus:

    Temperature compensation coefficents

    This calculate the needed coefficient to your focuser if you have a temperature compensation function. Here I can see that 169 my / Celsius or 97 step / Celsius is the most accurate calibration (linear regression). I always reset the digital scale to zero at bottom (full in) of focuser. That's normally the values you set up your motor focus controller with.

    See the focus diff column. Very strange behavior, it compensate ten times more and with wrong sign compare to the behavior of aluminium at changed temperature. I have got the explanation that this come from the temperature compensated triple lens cell and glas behavior. It compensates for the color correction, not the focal change.

    You can read more here:
    ../projects/project-motor-focus/project-motor-focus.html

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    Angle Conversations:

    Degree Radians transformation

    This transform between degrees, minutes, seconds to degree decimals or radians. You can also go from radians to degrees. Write in your angle in the red fields that you want to transform.

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    Background magnitude:

    Background Light Pollution calculation

    This is the latest calculations. With that you can calculate your background magnitude from a reference star and background signal. The background comes mostly from light pollution, normal places about 19.5 mag / arcsec^2 and perfect places over 21 mag / arcsec^2. It depends also very much if you measure the whole visual band or a filtered narrow band, the red part of the spectrum are normally more influenced by light pollution then shorter wavelenghts.

    You can take the signal from rgb filtered or narrow band filtered images like H-Alpha. Narrow band images will have very low background signal.

    It's not fully tested yet.

  • Here is a map over our problems:

    Light Pollution map
    (https://www.lightpollutionmap.info/)
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    Orbit Calculator:

    Gravity, Kepler and Newton are exiting physics. Here I have made an orbit calculator. Simplified to only circular orbits.

    There are two forces that push and pull radially on a planet in an orbit around the Sun. To get them in equilibrium the forces have to be equal strong. We don't want the planet crash into the Sun or escape and fly away.

    Force Equations
    In this case Solar system, simple case when Suns mass is much bigger then any planet mass:

    Gravity force between two masses Inward force +   Comments
    F1 = G*M1*m2/r2 G=gravity constant M1=mass (Sun) m2=mass (planet)
     
    Centripetal force from rotation Outward force -    
    F2=-m2*omega2*r omega=rad/sec omega=v/r v=orbital speed
     
    Set F1+F2 = 0 and solve for v      
    v = square rot (G*M1/r) v=orbital speed r=distance between objects

    In binary star systems it's common that the masses of the stars are note very different. We can't simplified the equations as much as we did above. The center of mass is somewhere between the stars. Both stars orbit around this point.

    Orbital period, tangential speed and common mass center (barycenter)
    We need more precise equations:

    Orbital period Comments
    T = square rot (4*pi*a3/G(m1+m2) ) T=orbital period m1, m2 mass of the stars a=semi major axis
     
    Tangential speed    
    V1 = 2*pi*a1
    V2 = 2*pi*a2
    Vx=tangential speed of star x ax=semi major axis star x
     
    Center of mass      
    a1 = m1*a / (m1 + m2)
    a2 = m2*a / (m1 + m2)
    ax=distance mass center star x

    Put the equations in an Excel sheet like the one below:

    Orbit Calculator

    Play around with the figures and help Newton. You only need the distance between the object to the Sun or the Earth, write it in the red fields.

    The escape velocity from Earth is 11.2 km/sec, compare that with ISS station orbital speed above.

    Both objects rotate around a common gravity center, but if one of the objects has much more mass it's like that one is still and the other rotate around the heavy one.

    More about gravity and forces:

  • Gravity force
    (Gravity, Wiki)
  • Centripetal force
    (Centripetal force, Wiki)
  • Escape velocity
    (Escape velocity, Wiki)
  • Kepler's Laws
    (Kepler's Laws, Caltech)
  • Barycenter
    (Barycenter, Wiki)
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    Download of Excel sheet

    Here you can download my Excel sheet. But remember this is very simple made, don't trust it and use it alone for decision to which camera or telescope to buy.

    You download this and use it on your own risk! I don't take any responsible for it:

  • Excel sheet: Astronomy Calculations
  • History:

    version 20171119 (latest)
    Orbital Calculator
    Added binary star system

    version 20171118
    Added Orbital Calculator

    version 20171027
    Rewrote the temperature coefficient of focus to be more general
    Cosmetic corrections of others

    version 20171025
    Cleaned up and translated to English

    Note:
    It could of course be some mistake in my calculation, I correct it when I found something.

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