What Is This, Amateur Hour? by Roger Pink

Thanks Jorrie, that's pretty cool! I didn't know the Jovian moons had similar spacings.

Thanks for your really cool hard work Roger. Lots of cool information.

Jupiter is indeed a great object and easy to find. Just find the ecliptic and look for the brightest jewel.

Neat things I would like to learn more about; especially the math, is Kepler's Laws. Bode's Law is indeed interesting but Kepler's Laws are what I believe to be fundamental principles in Astronomy.

It would be neat if I could calculate the Orbital Speed of an object in elliptical orbit as a function of semi-major axis and distance from primary focus.

I thought it was really neat when I put Newton's Law of Gravity on one side of an equation and centrepital force on the other side, then solving for Velocity it happens to be the Orbital Speed for a Circular Orbit.

Also I would like to have a better understanding of the Orbital Elements. Especially "Vernal Equinox" as it relates to the others. I struggle with that.

I have come to the conclusion that our solar system, like the Earth - Moon system is bary-centric. Is that right? If so what could that mean in terms of orbital perturbation of the planets over a time scale of millions of years? Could there be such a thing as "orbital resonance?"

I have also come to the conclusion that Specific Orbital Energy defines both orbital period and therefore semi-major axis and is independent of eccentricity.

Astronomy is given as the 7th Liberal Art for a reason.

Is C = Ceres in the Bode's Law Diagrams?

Gavilan wrote: "I have also come to the conclusion that Specific Orbital Energy defines both orbital period and therefore semi-major axis and is independent of eccentricity."

No, you also need specific angular momentum (L/m) of the orbit. The two parameters (L and E) are constants and hence define the eccentricity and the semi-major axis of the orbit.*

Yes, the "C" in the log-linear plot is the dwarf-planet Ceres.

-J

* For Newtonian orbits:

where the tilde means specific energy or momentum and the subscript N means "Newtonian", because relativistic values differ from these.

Jorrie;

You are awesome and never fail to put my nose back into a book.

Does a highly elliptical orbit and a circular orbit with the same semi-major axis have the same specific orbital energy?

I don't suppose I could get you to help me calculate instantaneous orbital speed of an elliptical orbit?

Thanks !!

G'day folks,

Since we're talking about Jupiter and how at the moment after the Moon and Venus it's the brightest star in the night sky I thought you might like to have a look at the image below.

It's about a quarter of a much larger patch of sky that I imaged on the 21^st February with Jupiter as the primary target. It was taken using a Nikon D5100 camera which has a 16 Mpix CMOS sensor. I used a 300 mm f:5.4 lens and a 15 second exposure which was too long for Jupiter but you can clearly see the 4 inner moons and possibly some of the outer ones as well, although I haven't been able to confirm that there are other moons of Jupiter present in the image yet.The CR4 image compression also wipes out several hundred background stars in the segment of the image alone.

The camera was piggybacked on my 125 mm diameter 1,900 mm telescope which was set to track Jupiter hence there is no blurring of the image due to the Earth's rotation that you would normally get with a 15 second exposure. It's actually part of a sequence of 100 15 second images taken that night which I will ultimately stack to form a final much clearer image that has more detail, but unfortunately I was plagued with intermittent cloud cover so I have to sort through the 100 images and figure out which ones are suitable to stack.

Also the nights observing session revealed a problem with free play in the altitude drive system that I am currently in the process of fixing. It wasn't a problem in these images as Jupiter was rising in the sky the whole time, but if it reach its highest point and the mechanism had to change direction there would have been about 5 times the diameter of Jupiter variation in the position of everything. The stacking software would have taken care of that, but if I were using the telescopes optics with its 1,900 mm focal length compared to the 300 mm lens I used it would have meant that Jupiter would probably have come close to disappearing from the field of view.

Hopefully I will have the problem remedied in the next couple of days. I'm also waiting on an adaptor that will allow me to use the telescopes optics and its 1,900 mm focal length with the Nikon D5100 rather than a 300 mm telephoto lens that's piggybacked on the telescope. Time is of the essence at the moment as we are rapidly moving away from Jupiter and it will become more difficult to image even with a 1,900 mm telescope.

March is also a good month for meteor showers originating in the constellation Virgo. There should be peaks on 6^th, 17^th, 18^th and 20^th of March. The Virginid meteor showers aren't known for their concentration of meteors but an hours' worth of observing should net you up to 10 meteors. If you have a wide angle lens and camera that can take sequences of say 30 second exposures it might be worth attaching it to a tripod, pointing it in the direction of Virgo and letting it take a couple of hundred images. You will almost certainly throw out at least 90% of the images but with a bit of luck you should have some meteor streaks in at least a few of the images and since images now just cost battery power a couple of hundred images to get 10 good ones is a bargain.

That's awesome! Thanks for responding. I would love to see that image at a higher resolution. Any chance you could post it somewhere (like flickr) and post the link to it here?

"Any chance you could post it somewhere (like flickr) and post the link to it here?"

G'day Roger,

I certainly can and when I have stacked it I will publish the final image on my public Google Drive. Unfortunately I haven't been able to figure out how to publish images on Flickr using raw image formats like TIFF or FITS which for a 16 Mpix image come to about 90 MB per image and you lose a lot if you compress it into a JPEG image. For example in the image above I just did a count of the background stars in strip across the top and down the side and then use it to estimate how many background stars there were. In the compressed image you can probably see about 100 background stars while in the raw uncompressed image there are somewhere between 1,000 and 2,000 background stars and possibly even more will emerge when it's stacked. So it's critical to use a camera that can take images and store them in some sort of raw format that doesn't compress the image. This pretty much means using a DSLR camera and as expected each camera manufacturer has their own way of storing raw format images. Fortunately a really nice guy who's name is Dave Coffin has written a great bit of code called DCRAW that can read the raw images from just about every camera there is on the market and if there is one he has missed he will gladly add that to DCRAW if you send him the information needed.

What's stacking I hear you ask?

Well back in the dark ages (about 10 years back at most) astronomers used to use film to take images of the night sky (yes I know it sounds unbelievable but it's true) and they would take exposures that were hours or even days long. However, even with a specially constructed extremely low noise CCD or CMOS sensor that is chilled to -70°C or less about the maximum exposure time you can get is about 30 minutes, and that's using a sensor that will set you back about US$14,000.⁰⁰ which is out of the reach of most amateur astronomers and still nothing like as good as film.

Now the people at NASA had the same problem when they built the Hubble Space Telescope because they couldn't keep sending space shuttles up with new roll of film every month so they had no option but to use electronic imaging systems, but this limited the exposure time even though if the camera was as low noise as was possible and if kept away from sunlight could be cooled to about -120°C.

So instead of taking 1 very long exposure they took lots of shorter exposures an then stacked them on top of each other or rather added the pixel values of each image together to get a final image that would have picked up even the faintest star that maybe only an handful of photons arrived from in some frames.

But you can't just add all the raw images together because all you would end up with is a white frame due to things like background noise from the electronics, stray infrared light sneaking in from all angles et cetera so you need to find some way of counteracting this which is where the following comes in.

• Dark Frames: These are 15 to 20 frames taken immediately after the sequence of 100 or more images that you intend to stack. The only difference is that they are taken with the lens cap on using the same exposure setting and they should be completely dark hence the name. These are used to get rid of the noise that the sensor will pick up due to stray infrared light seeping into the sensor and background noise. After the 20 frames are averaged the result is subtracted from the final image and hopefully counteracts the natural noise. But it's important that dark frames be taken immediately after the sequence of real images because the background noise is very much dependant on the temperature of the sensor so the easiest way to do this is simply put the lens cap on and take another 20 images.
• Offset or Bias Frames: These are another 15 to 20 frames taken at the end of a an imaging session. Again these are taken with the lens cap on but this time with the exposure time cranked down to the shortest possible time the camera will take. These are again averaged and used to calculate the noise created by the electronics reading the value of each of the pixels. Again at the end of the stacking process these are subtracted from the final stacked image.
• Flat Frames: Yet another 15 to 20 frames taken using the cameras auto exposure system so that you get a neutral exposure of a flat white object that has even illumination. They have to be taken at the end of your session before you touch or alter any of the optical settings of the lens and are used to correct for things like vignetting, flaws in the optics, dust that often shows up as orbs and people are prone to calling UFS et cetera. These are somewhat more difficult to take as you can't touch any of the optical settings and you need a flat white surface that is perfectly and evenly illuminated. A lot of people create special light boxes that they can fit over the end of their telescope, but the easiest and probably most effective way of getting an evenly illuminate white surface is to use the screen of a laptop or similar flat liquid crustal computer display. All you need to do is to open up a word processing document and then enlarge the size of it so that there is a large enough area of the screen that is white which you can use to get your flat frames. Once you have your white screen you just hold the lens right up against the screen so it's completely out of focus and let it click away taking the 15 or 20 images needed.

Now you have your images you need to stack or combine them and this is done using some very sophisticated software called DRIZZLE that the kind people at NASA have made available to the public free of charge. It's called drizzle as it goes along pixel by pixel colour by colour adding the values of each sub-pixel sort of like drizzling water into the cubes on an ice tray section by section. It also corrects for any movement of the image and de-rotates the images by matching up the bright spots that appear in every image. This is really helpful as it means that unlike with film where you must keep the telescope pointed at exactly the correct spot in the sky you can get away with some movement. In fact you can use it to expand the field of view provided about 25% of the image is common to every frame.

There are numerous free software packages that can be downloaded from the net that combine DCRAW and DRIZZLE that you can use to stack you raw images taken directly from your camera regardless of the brand and stack them together to reveal details that would otherwise be invisible.

On a completely different topic but still talking about astronomical objects, I was experimenting with my new Nikon D5100 back on 18^th of December 2013 using a fixed tripod and 2 second exposures with the sensitivity cranked up to almost the maximum. Now while the stars do move from image to image the short 2 second exposure time isn't long enough for the stars to move far enough to cause any major distortion and I got a set of surprisingly clear images.

Now when I downloaded the images from my camera and scanned through them it quick succession out of the corner of my eye I noticed something that was moving the same way the stars were. Just to make it more intriguing the object was moving in the opposite direction to the stars and varying in intensity from being as bright as some of the stars to not there at all. Now if it were an object in orbit I calculated that it would be at an altitude of approximately 15,500 km but in a retrograde orbit or orbit where the satellite travels from east to west rather than the norm which is west to east. The reason for the west to east orbit or prograde orbit being the norm is that you are already travelling at about 1,500 km/h from west to east due to the Earth's rotation so that's 1,500 km/h less you need to add to your final speed and that means less fuel and a smaller rocket. On the other hand for a retrograde orbit you have to get up to about 1,500 km/h just to get you orbital speed to zero then you have to start from scratch. Now having to add another 3,000 km/h too you orbital speed means a much bigger rocket as you not only have to accelerate the payload but all the rocket's upper stages with their fuel to 3,000 km/h just to get to where you started on the launch pad with a prograde orbit. Roger may be able to give you more accurate figures but if memory serves correctly to put a satellite into a retrograde orbit requires a rocket that's somewhere between 30 and 50% larger than a prograde orbit.

Anyway, you can see the series of 95 images in JPEG format on my Flickr page set entitled Mystery Object or see the originals in Nikons raw NEF format on my google drive. You can view them directly from the drive but they are compressed to minimise the data traffic so to view the ones on google drive with full raw definition you will need to download them to your computer and use Nikons ViewNX 2 software to view them. However, be warned the 95 NEF images and software total about 1.2 GB worth of data so if you are on package that limits the amount of data you can download it's probably not worth downloading.

Also in the images on Flickr I have marked the position of the mystery object in the first 6 frames so you will know what I'm talking about. Once you know where to look in the start it's pretty easy to follow.

If you really want to get into trying to identify the mystery object which is obviously tumbling hence the dramatic variation in brightness then you will need the following details.

• Date of Images: 18^th December 2013
• Time of First Exposure: 10:18:17.8 UTC
• Exposure Duration: 2 seconds
• Exposure Period: 4 seconds
• Location: Sydney Australia 33° 54' 34" South 151° 15' 27" East
• Reference Star: Canopus_{(Brightest star)}
  
• Right Assentation: 06_h 33_m 57.1_s
• Declination: -52° 41' 42"

Have fun, I've been trying to figure out what it is for some time now and while it's almost certainly a piece of space junk that's out of control and tumbling there's always the chance it's an asteroid that happened to wander past just as I had the camera pointed at that patch of sky. By the way if you think the asteroid is totally improbable bear in mind that only 13 days later an asteroid crashed into the mid-Atlantic ocean and that wasn't discovered until a mere 18 hours before it impact.

My apologies for the long winded answer, but you know how carried away I get when I'm talking about something that I find fascinating and astronomy is certainly that, even if there has been one half descent night for astronomy in Sydney Australia so far this year.

That is a lot of awesome information. Thank you for sharing it. I looked at the flicker images and definitely see what you're talking about. It does appear to be tumbling, as you said, based on the dramatic variations in brightness. How did you even spot that at first? It's so dim when you first point it out.

I don't have time to look into it now, but maybe I'll do a blog about near Earth objects (satellites, asteroids, space junk) and revisit the question then.

In the meanwhile, bravo on your amateur Astronomy.

PS. In college I learned a tiny bit (not much) about a technique called Bayesian Image Analysis. I'm not sure if drizzle uses that or not. I'm curious if it would be of any use to you to further improve your images. Take a look into the subject if you have the time, and if you have any questions, let me know here and I'll see if I can help.

Either way, thank you for your posts, they have been very informative!

"How did you even spot that at first?"

When you enlarge the images so they fill the screen and you are looking at the centre of the screen it just happens that the initial position falls onto your peripheral vision which is much more sensitive to light and changes in intensity, hence when flicking through the images in quick succession it was easy to spot the change between one frame and the next.

Mind you, when you get to the last half dozen images when it really brightens up and then almost disappears only the brighten even more it's hard not to see that something strange is going on and from there it's just a matter of backtracking to find its original position.

Looking at dim objects out of the corner of your eye is a very old astronomer's trick as you don't have any colour sensing cells in your peripheral vision and that makes you peripheral vision much more sensitive to light than your central vision which detects colour as well as intensity. Unfortunately the colour receptors require much more light to work and as a result dim objects will disappear when you look directly at them.

Most people will have experienced this phenomenon when they think they have seen something out of the corner of their eye but when they look for it there's nothing there.

Hi Masu,

I took your TIFF and cropped it to just Jupiter and its Galilian moons. As you note you lose a bit of the resolution and I recommend others view the original TIFF file you mentioned in your last comment.

Pretty cool! You can easily see the Galilean moons. I tried to figure out which moon was which using a labelled image taken about a month earlier (found in google image) and extrapolating based on the orbital periods of the moons but I failed miserably and gave up. Awesome image though.

"I tried to figure out which moon was which using a labelled image taken about a month earlier (found in google image) and extrapolating based on the orbital periods of the moons but I failed miserably"

Unless you have a series of images taken over a period of several days it's very difficult. However we may be able to identify at least one of the moons. If you look one appears to be slightly higher than the other three which appear to be in a straight line. Now the moons don't orbit in exactly the same plane but are inclined relative to Jupiter's equator as follows:

• Io 0.050°
• Europa 0.471°
• Ganymede 0.204°
• Callisto 0.205°

Now Jupiter's orbit itself is inclined to the ecliptic (the plane the Earth orbits in) by 1.305° and its axis is tilted by 3.13° so we could be looking at the plane of Jupiter's equator from slightly above or below it but even so considering Europa's orbit is inclined by over twice that of the others and the second moon out on the right is higher than the rest by just a smidgeon then there's a chance that it's Europa.

But it's only a possibility because the inclination of Jupiter's orbital plane and axis could cause a similar effect if we were viewing the equatorial plane from below and the second moon on the right were closer to us it would appear higher. But the other moons appear to be in almost a straight line which would suggest we are viewing the orbital planes from pretty much side on.

What do you think?

PS: I just wish I had the adapter that would have allowed me to use the telescopes 1,900 mm focal length instead of the 300 I was limited to with the camera's lens. Just viewing it through a 25 mm eyepiece which is the smallest magnification eyepiece I have you could clearly see the bands of storms around Jupiter. The weather forecast here for the next week is crap and even if I do manage to get the adapter I doubt I will have the opportunity to use it for at least a weak. On the good side I've been able to isolate and rectify the cause of the 7 to 10 minutes of arc deadband in the Altitude drive train so that next time I have the scope out the tracking will be even better.

Your theory regarding Europa sounds reasonable. I agree that "series of pictures over several days" would probably work best. That would do the trick since then you could see how quickly everything is moving and have a pretty good idea which moon is which.

The images looked great though, though so big! That TIFF was 92 MB!

"though so big! That TIFF was 92 MB!"

That's the problem with hi resolution TIFF files they are enormous and when you take a series that consists of hundreds of images you quickly start eating disk space. Just as well my new laptop has two 750 GB hard drives one of which I have dedicated to astrophotography.

Fortunately the raw Nikon NEF files only take up 12 MB per images with no data loss because they only use 12 bits per colour which is all that the sensor is capable of differentiating, still it's a much higher definition than a bitmap file which only uses 8 bits per colour per pixel.

When I uploaded the 90 plus 12 MB per image NEF images of the mystery object to my Google Drive it took ages and was a case of going off to do something else and having a look at how it was going every now and then. If memory serves correctly it took a couple of hours and it fell over a couple of times so I had to restart it from where it left off. That was a bit confusing because for some reason it didn't upload them in the order I selected them but rather some order it made up, so every time it fell over it was a matter of finding out which files it hadn't uploaded and just selecting them. Anyway, after four attempts I managed to get all 97 images uploaded.

I saw in in a program appropriately called "Stargazing" that showed how astronomers intend to send a telescope into space with a 1 Giga Pixel sensor that covers an area of about 1 m². The idea is to monitor the position of all the stars in a patch of the Milky Way to an unprecedented level of accuracy so they can determine how fast and in which direction they are moving. I don't know how many bits they are using per pixel but at a bare minimum it wold have to be 1 GB per image and that's if it were just monochromatic. TIFF use 16 bits per colour so that would add up to 12 GB per image, but they may be using even higher intensity resolution so 24 GB an image wouldn't be out of the question. I was still flabbergasted at the 1 Giga Pixel 1 m² sensor to pay attention to the intensity resolution. They plan to take millions of images over a period of a decade to calculate the motion of individual stars to an astonishing level of accuracy.

To think we're worried about a meagre 92 MB per image.