Angular diameter Puns

I have been working on a paraxial optics problem and feel stuck on two of the questions. It is an optical system with two lenses (a positive and a negative) and an aperture stop between two. Their focal lengths, diameters and the spacing between each other is given. I did the YNU raytrace and was able to get the all the quantities that are asked except, diameter of field of view and angular field of view in the image space. They also provided the object distance from the front lens, however no object height is given. I referred Smith's book on optical design as well as Mourolis book on geometrical optics and neither provided any clue to approach this. I'd really appreciate it if anyone could nudge me in the right direction.

Here is the drawing. https://imgur.com/a/i0jIViP Object distance of 400 from left of the lens. Using paraxial ray tracing method find Aperture Stop, field stop, Entrance pupil location and diameter, exit window location..etc. I found all that. But don't know how to proceed with the diameter of field of view and the angular field of view in the image space.

More specifically Nolan Matthews and I measured the angular size of Alnilam and Mirzam using the VERITAS telescope array located at the Whipple Observatory in Arizona on December 15, 2019. The experiment results presented in the paper were over 10+ years in the making.

The reason why these results are important, is that we used Stellar Intensity Interferometry (SII) to make the measurements presented, a technique that was mostly abandoned by the 1970's. Our results show that with modern technology and massive telescopes, SII is much more useful than it used to be and that it can contribute to astronomy in unique and powerful ways. We hope the results will help re-invigorate the field of SII.

One of the most exciting prospects (at least to me) is that we could use SII with the Cherenkov Telescope Array and could possibly make images of stars which are much akin to the famous black hole image, possibly even resolving stellar features like star spots.

I personally created the software ASIIP (pronounced 'a sip' like you are taking a sip of water) which lists which stars are best to measure using SII for any given observatory. I was also helping make additional SII stellar diameter measurements until COVID-19 came around and ruined all the fun we were having.

Fun fact, these measurements take hours to make and it can get pretty boring, so while taking some these measurements, I was browsing memes on Reddit to help keep myself alert while not being too distracted. Lots of things can go wrong when operating the observatory so it is imperative to be alert enough to notice any alarms going off, which means you must stay awake even though you experience some pretty intense 'jet lag' the first few nights. Staying up all night for weeks on end, taking measurements of stars was awesome, but it is also exhausting and not quite as romantic as it may sound.

I will also be entering the Cornell Astronomy and Space Science PhD program this Fall.

Ask me Anything!

Here is a link to the Nature Astronomy paper.

Here is a link to an overview of Stellar Intensity Interferometry written by me if you are curious about a little bit about the science and history of SII.

Here is my [About Me](https://www.astronomaestro.com

One of the way to estimate distances by standard ruler, which basically estimate the angular diameter distance (ADD hereafter). ADD is defined as d_A=d_p/(Angular size); where d_P: physical distance.

As we can think all kind of distance increases w.r.t. redshift (z). But ADD behave in a slightly different way i.e. if first increase upto a particular redshift (~1.6; depending upon cosmological model) and after that it decreases with z. I'm happy with its backgrund calculations, but couldn't understand the concept. I mean I read somewhare that after a particular redshift size of object started to increase (don't know why or/and how?) then ADD decrease...so on.

Could anyone please share your comments on this thread?

To make this measurement, Albert Michelson and Francis Pease built an interferometer and attached it to the 100 in Hooker telescope at Mt. Wilson. This was the first time the angular diameter of a star other than the Sun was measured. Today optical interferometry is continuing to make groundbreaking discoveries about the nature of stars, including the CHARA Array, which is located on Mt. Wilson. By combining the light from separated telescopes, optical interferometry arrays are able to achieve angular resolutions far exceeding any single aperture telescope: CHARA can achieve angular resolutions equivalent to a 330 m telescope! Here's a brief article from a few years ago highlighting some of the work being done in stellar astronomy with CHARA: https://www.discovermagazine.com/the-sciences/seeing-stars

I've always wondered this, but I'm not sure I know how to effectively phrase the question.

Imagine you're looking up at a star - it's basically a point source but it must have SOME area in your visual field. How much of that area is actually the star (as we currently imagine surface of a star), as opposed to the additional surrounding gases, atmospheric distortion here on Earth, etc.

Are we really even seeing the real volume and surface of the star with the naked eye?

To better explain, please see this recent highly upvoted image from the front page:

https://www.reddit.com/r/space/comments/hcwp7l/thats_not_camera_noise_its_tens_of_thousands_of/

Examine the big blue star. The centered, clearly circular "dot" part - is that the surface of the star? It seems like it might be, but the highest resolution image I could find of another star is incredibly poor, even taken from the Very Large Telescope, which makes it seem unlikely that an amateur could directly image the surface as several pixels across. Would the actual volume of the star even encompass a single pixel?

After all, if there were an infinitely dense point with no diameter at the center of a black hole, wouldn't the black hole have to spin infinitely fast?

We know that the sun and moon appear roughly the same size from Earth's surface. Hence Eclipses.

Is there any point or maybe multiple points in outer space, where the sun, earth, and moon all appear the same size?

And would such points exist for any 3 spheres of arbitrary size and position? Or are there limitations?

Help! this is due tonight! I got 137.3 rad/s and thats wrong. Can someone solve for me?

Calculating from the coordinates of the Apollo 17 lunar landing site (20.16° North and 30.77° East),[428] the Earth should be at constant 53.4° above the lunar horizon.[429]

I have this spreadsheet I'm using to help me understand the stats of different eyepieces / barlow setups.

https://docs.google.com/spreadsheets/d/1RxGdp7-KXAebjk2nKTMpNvoLQ-Yi41H2dPiVabIRP2I/edit#gid=0

The APM/Lunt XWA eyepiece I'm getting tomorrow, with no barlow, has a TFOV of 35 arcminutes. When I look in the Night Sky app on my phone, Jupiter is listed with an angular diameter of of 29.8" to 50.1" (arcminutes, right?).

So, does that mean that at any given time, Jupiter would occupy most, all, or more than the telescope image, when using that eyepiece?

Am I right? Am I missing something? Is my spreadsheet wrong?

I wonder if it's possible to get better image of the black hole with newly discovered supermassive Holm 15A*.

Can anyone walk me through? I did 2pi times to get it into radians and then just divided 20pi by 60 to get into hours, and apparently thats wrong. How do I do this? Isn't the formula for angular speed just O/T?

JWST is cited as having a resolution of 100 milli-arcseconds. But the stars with the largest apparent sizes such as Betelgeuse or R Dorado have angular diameters of only half that; and other stars, of course, less.

So my question is: how can JWST "see" something that is too small to be seen?

Moreover, doesn't the question of resolution relate more to the size of the field of view that can be imaged, rather than to the 'size' of individual objects?

In this context, the journalistic trope that JWST's resolution is equal to that of a penny at a distance of 40 km seems misleading or over-simplified at best.

I've created a 2D cross section of the Flat Earth-Sun-Dome system to scale to show in an easy to grasp way how the sun's position and size in the sky changes as observed on the ground. The box on the right visualizes the changing angular diameter

Click Here

Two things to note:

1. The angular diameter changes between 0.09° and 0.61°, depending on location, time of day, and time of year.

2. The sun never sets.

Edit: Updated panel on the right to include the sun's angle over the horizon.

Hey everyone.

I am having a hard time understanding the angular diameter formula and putting it to use.

"Phobos, one of the moons of Mars, is 25 km in diameter, and orbits Mars at 6000 km above its surface. What is the angular diameter of Phobos as seen from Mars?"

Above is the exact question I am working on and this is the formula i am working with however i am finding it more confusing than it likely is so am hoping someone can simplify the process.

Angular diameter linear diameter(km) ------------------------- = ---------------------------- 2.06 x 105 distance(km)

Angular diameter 25km ------------------------- = ---------------------------- 2.06 x 105 6000km

So I get 0.004166. What i am having a hard time understanding is how to apply that to get the angular diameter and my text doesn't clearly outline what that number actually is?

So thankful in advance for any help, guidance. S

Working on my astronomy homework and I can't seem to figure out how to find distance using angular size and diameter. I tried searching for the formula, but each one I find is either too complicated or just a calculator that does it for you. Anyone care to help me out?

Trying to get a quiz done for my astronomy course in collage and I can't seem to figure out how to do it properly. I tried using trigonometry but that didn't work so I tried using "the small angle equation" and I'm still stuck. Here's a picture of the equation. http://m.imgur.com/von9uPm I've tried plugging in a bunch of different numbers in the equation numerous times but I can't seem to get the correct answer. The correct answer is 1 meter. I think I'm getting confused when it comes to the "2 seconds of arc". Can someone point me in the right direction?

Vultures circle their meals before they eat them. If the vulture circles at 3 m/s and each circle has a diameter of 6 m, what is the period, k, of the vulture’s circling.

I know that the vulture makes 1 full rotation every 2 seconds. Can I then deduct that the period would be 2pi?

Jupiter's current angular diameter reaches 49" in its closest approximation from Earth. The Moon reaches 34'6". For it to be as big as the Moon in the sky, its distance would neet to be decreased approximately tg (34'6")/tg (49"), that is, about 41.66 times. Jupiter currently is 588 gigameters from Earth at its closest approximation. This would put it at 14.11 gigameters instead, putting it closer to Earth than Mars or Venus are. What effects could this possibly have? Would Earth orbit Jupiter?

First - Previous

Jennifer arrived ten light hours from the sun.

She didn't want to spook anybody. She needed to do a bit of reconnaissance before deciding how to approach the situation. First impressions were important.

Her eye tentacles spread into the familiar telescopic pattern, providing a clear view of the solar system's features even at this distance.

Uranus was closest. It looked much as she remembered from school, though now she could see it across the full electromagnetic spectrum. So many colors humans had no names for swam in the mix with the familiar steel blue. It was the infrared that was the most telling. There were hotspots in orbit. Little stations with umbilicals dangling down into the planet's cloudy depths. Mining platforms?

One of the stations was considerably larger than the others, and had what looked for all intents and purposes like a massive gun mounted to it, pointing sunward. A delivery system for the mined materials, perhaps? As she watched her suspicions were confirmed. A hot little craft moved from one of the smaller stations to the large one, then departed again. Shortly after, the station's heat signature brightened considerably, then a speck rocketed sunward.

The moons were dotted with hotspots too. By far the most activity seemed to be on the second largest, which had not just isolated spots but a seeming network of structures across its surface. Jennifer tried to remember the name. It was something from Shakespeare, wasn't it? Something with an O. Ophelia? Orlando? Olivia? Oberon! That was it. Her eleventh grade teacher, Mrs. Baker, would be proud. If she wasn't long dead.

Neptune and Saturn seemed to be on the opposite side of the sun at the moment, so the next closest object was Jupiter.

There was a lot of activity around Jupiter. Hundreds of the little orbital platforms, two of the space guns in sight from this angle, and hotspots all over most of the larger moons. All enclosed structures though, it seems no terraforming had been done. Jennifer thought she could see why. Even from this distance the intensity of the radiation around Jupiter was visible to her. An unprotected human likely couldn't survive on any of its moons, even if it had a breathable atmosphere. She idly speculated that they might try to colonize below the moon's surfaces,

Most stars are photographed as point lights, and I've only seen a small handful of pre-New Horizons Pluto style resolved photographs of stars.

The Horsehead Nebula is 1400 light years away, while Proxima Centauri is only 4.

Is it that difficult to get a good exposure, or is it about the size of the stars relative to a nebula?

I've put together a simple and intuitive 2D cross section of the Flat Earth-Sun-Dome system to show the sun's position and size in the sky from the perspective of an observer on the ground as predicted by the flat earth model. The box on the right visualizes the changing angular diameter and height above the horizon.

Click Here

Two things to note:

1. The sun's angular diameter changes between 0.09° and 0.61°, depending on location, time of day, and time of year. Real world observation shows the sun's angular diameter only varies between 0.52° and 0.54° from aphelion to perihelion.

2. The sun never sets. Real world observation shows the sun does set.