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Recently I bought a telescope after a very good conversation with an astronomer friend of mine. The main goal is to see planets.

However, Mars is so difficult and is far to find it in opposition. I really like the views of the Moon and there is where I spend most of my time observing. But I really want to go view the planets, but I seem a bit without an objective. I don't want only to see them at random; I want to do some kind of study using my observations. So, can you suggest something to do with my telescope to start some serious study?

I have a good base of Physics (I'm a computer engineer) and I really like Math, but I'm a complete amateur in astronomy.

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    $\begingroup$ astronomy.stackexchange.com/questions/23676/… $\endgroup$
    – Florin Andrei
    Commented Feb 19, 2019 at 18:40
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    $\begingroup$ astronomy.stackexchange.com/questions/24287/… $\endgroup$
    – Florin Andrei
    Commented Feb 19, 2019 at 18:40
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    $\begingroup$ You can put a Raspberry Pi camera at the focal plane of your telescope and capture images, play with image stacking and lucky imaging. See also Cepheid Variable Stars, Supernovae and Distance Measurement and also en.wikipedia.org/wiki/Cepheid_variable You can visually estimate or use your Raspberry Pi camera (or a real camera) and measure the brightness digitally too. $\endgroup$
    – uhoh
    Commented Feb 21, 2019 at 17:16
  • $\begingroup$ @uhoh I'm obviously interested in taking pictures of the space, but I have a bad experience with my smartphone (sometimes I take some amazing pictures, like this, but is an exception) and I'm worried about to take pictures with a digital device. Is the quality of the Raspberry PI camera good enough to invest in? Ah, and thank you for your previous answer, is exactly what I was expecting. $\endgroup$
    – Linnc
    Commented Feb 23, 2019 at 19:58
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    $\begingroup$ @Linnc The hard part about using a fixed lens camera is lining it up correctly to the eyepiece, getting the eyepiece's exit pupil coincident w/ the pupil of the camera's lens and the axes coincident. It's a 5 degree of freedom problem. When we look through an eyepiece we learn to do it automatically and subconsciously. Just a few millimeters makes the difference between a beautiful image and total frustration. What makes everything easier is to get rid of all the lenses at that end of the telescope; the eyepiece and the camera lens, and just put a bare CCD sensor at the telescope's focus. $\endgroup$
    – uhoh
    Commented Feb 23, 2019 at 23:13

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There is a wonderful intersection of Physics, Mathematics, Applied Math (numerical analysis) and Observational Astronomy in a systematic analysis of the movement of four bright Galilean moons of Jupiter!

They are easy to see in a small telescope, they have well defined orbits around Jupiter, and they have some trick up their sleeves that you can analyze.

Here's an exercise you can do right now. When Jupiter is anywhere near quadrature, it's shadow extends behind it by an angle of almost 11 degrees, so the moons will often be eclipsed. That means instead of appearing or disappearing into Jupiter's overwhelming brightness, they can "pop" in or out of visibility as they pass out of or into Jupiter's shadow.

                a (km)
Io             421,800
Europa         671,100
Ganymede     1,070,400
Castillo     1,882,700

Jupiter radius  71,492

You can predict when these happen, and then watch to see them and confirm your calculations. You can start timing them to get more accurate information.

From a mathematical perspective you can check the periods of their orbits (from your measurements, or from a table) to see if there are any surprising numerical relationships!

You can check the inclination of their orbital plane to see if the eclipses always happen or sometimes don't.

You can read the answers to When will the next series of mutual eclipses of Jupiter's moons begin? and start planning for 2021 when these begin again!

You can learn to do numerical integration of solar system bodies to simulate their orbits, or use the Python package Skyfield or the JPL Horizons website for high accuracy positional information.

These can also help you calculate the eclipse times by Jupiter, and the mutual eclipses of Jupiter's moons.

Finally, you can try to measure the speed of light by seeing that the eclipses come sooner or later than average when Jupiter is closer or farther than average from the Earth. This is one of the early ways that the finite speed of light was verified.

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