I feel like this is more of a Deck Navigation thing but we are covering this in our course now as a minor subject.

Hello,

Would this be the place to ask for help concerning spherical trigonometry (related to astronomy)?

Here's a draw to better picture the situation -> https://i.imgur.com/Qiok1kA.png

And now the explanation:

Let's say I am standing at a point in the earth surface (at sea level elevation). I know exactly the latitude and longitude of where I am at. (34° 36´ S and 58° 22´ W).

Now I want to know the latitude of a point located at exactly 50 km far from me, to the East, also at sea level elevation.

How can I calculate it?

Hope you can explain me that one. Thanks for reading.-

TL; DR: Just read the below first paragraph in bold and tell me if my assumption is correct or not (and why not, if that's the case, please)

.

My assumption is that any two great circles in a sphere intersect one to the other always at two unique points . Those two points are antipodal and divide each great circle in two equal halves.

Visual example:

https://imgur.com/1mNvgQ5

Starting from that assumption, If I can trace the perpendicular distance from the "Midpoint" between the antipodals of one great circle (one of the two arcpoints at 90° of the antipodals) to the plane of the other great circle, and I also know the radius of the sphere, using arcsin [perpendicular distance from midpoint great circle one to plane of great circle two/ radius sphere] I can obtain the angle of relative inclination (obliquity) of the two great circles about the pivotal line that connect the two antipodals.

Knowing the obliquity then It's quite straight-forward to express points of one great circle in terms of coordinates of the other great circle.

All of that I wrote just above are assumptions that I've made and, since I am far away from being knowledged in maths, I really don't know if they are correct. So I'd be very thankful if you could review this and tell me if what I've said it's correct or not, and in case it's not explain me why.

Take in consideration that I don't know how to operate with vectors in 3D and only know to add and substract vectors and to work with right angle main trigonometric functions (sin, cos, tg, arcsin, arccos, arctg), so if you had to give me some advice it would be easier for me if you could do it with tools that don't need to imply knowledge in the above things I stated I don't know at the moment -hope I'll learn them soon though.

Thanks for reading.-

So this is it:

ArcSin(3.3433822*Sin(57.653pi/180-(x)))=x

That's the formula, which in the origin is something like this

Sin(x)=3.3433822*Sin(57.653pi/180-(x))

If you want a bit more of context, it's actually something from spherical trigonometry. See this picture to better grasp it:

https://imgur.com/f3oW3bq

You have two geodesic arcs. Don't pay much attention the concentric circles. The point is that this is a two dimensional view of the "celestial sphere". The center of the concentric circles is the where the earth axis pass ideally intersecting ninety degrees the plane. The greatest of the circles in that plane would be the equator. And then you see those two geodesic arcs (poorly drawn ngl) that intersect at one point and I want to know the angle value of that point of intersection. The zero point is the point of intersection between one the geodesic arcs (which is half of the ecliptic great circle) with the equator. The other geodesic arc is one half of an astronomical geocentric horizon. Both geodesic arcs cross the center of the sphere since they are part of great circles as you can see.

What I'm trying to calculate is angle, in equatorial degrees, of the point of intersection between the astronomic geocentric horizon with the ecliptic (which is called the "right ascension of the ascendant").

I know NOTHING about spherical triangles (or almost nothing) and NOTHING about logarithms (if that has any relationship with this). I've been able to design different formulas to obtain this value but I always no matter what end in numerical approximation tedious way of calculation -even if an app can make the calculation in a matter of seconds and give me the output correct value, I would like to have a way to obtain the value by other means.

Is there something that I can do with the formula Radius of Sphere= √(x^2+y^2+z^2)?

The only things that I know are the obliquity of both geodesics and the right ascension angular values of the points of intersection of the geodesics with the equator.

Any valuable input you could provide me about how should I proceed, what should I learn in order to be able to solve this would be greatly appreciated.

Thanks in advance.-

Hello,

I'm a geology student and currently working on an independent research project wherein I need to use some trig and spherical geometry; maybe a tad bit of calculus too.

To try and better understand what Im trying to do I'll need to explain a tad bit of geology background:

The question I'm trying to ultimately work out is this: How much has a tectonic plate subducted at a specific location (a point) in the past 130 million years?

Subduction is where one tectonic plate collides with another and results in one of the plates being pushed down underneath the overlying colliding plate. I'll try to hopefully make this more relatable/understandable with an analogy: this process would be like being in a pool with your friend and you and he push two boogie boards (the tectonic plates) together. One of these boogie boards will end up dipping below the other and going underwater, aka being subducted. If you pushed your Boogie board at a constant velocity while your friend held his still, you could predict how much of your boogie board is underwater at a given time (relative to the position of his fixed board) with some basic math.

The math can be spiced up a bit by changing the angle you are pushing against your friend's boogie board. Instead of pushing directly against your friend's board, you push at an angle to his fixed board. Your board is still being pushed underwater, but now with a decreased velocity as you now have to resolve the magnitude of the velocity into separate components. Still not too bad.

Now, here's where I get confused. In my analogy above, this could be calculated using cartesian coordinates, however, the Earth is a Sphere and I dont believe the math I'd use to model "how much my boogie board has subducted in the past 130 million years" would be quite the same. Could someone help me out with the trig (& possibly multi-variable calculus) needed to calculate this?

I have this data to work with:

Velocity Magnitude (y-axis) vs Time (x-axis) (All these are relative to referenced point (lat, long) on the boundary of the subducting Plate)

Velocity Azimuth vs Time

Angular Velocity vs Time

Lattitude vs Time

Longitude vs Time

Velocity Colattitude vs Time

Velocity Longitude vs Time

Thank you very very much for your time and help!

Hello guys,

i'm going to have a course in college called Higher Geodesy

and this is the contact of the course:

Spherical Trigonometry: Elements of spherical trigonometry: sphere, small circles, great circle, spherical twoangle, spherical triangle, fundamental rules in the spherical triangle, equations of Delambre and Napier, Napier’s rule, differential formulas, applications. Forward and reverse computations for orthodromic and loxodromic curves on the sphere. Mathematical Geodesy: Reference ellipsoid: ellipsoid parameters, latitudes, curvature radii. Three-dimensional geodesy: 3D ellipsoidal and Cartesian coordinates, coordinates in local geodetic and astronomical frame, coordinate conversion, observation equations in three-dimensional geodesy. Differences between natural end ellipsoidal coordinates. The geodesic curve on the rotational ellipsoid: normal section curve and geodesic, mathematical description of the geodesic. Angle and distance corrections from observed to ellipsoidal values: azimuth and angle corrections, distance corrections. Direct and reverse problems of geodesy: computation of distance and azimuths of a geodesic, coordinate transfer to a new point. Geodetic mapping of the ellipsoid surface onto a mapping plane: general relationships, important mappings (Mercator, Gaussian, UTM. Lambert, polar stereographic). Mapping equations, magnification (point scale factor), meridian convergence, (T-t) correction, distance correction. Overview of other mappings. Geodetic datums: comparison of different geodetic datums, transformation parameters, transformation equations, Molodensky transformation.

So i'm currently studying calculus on Khanacdemy.. Would any one tell me where can i find this kind of Math "Spherical Trigonometry" And where I can find materials for the rest content?

I have been doing Kerbin re-entries from a 0 inclination orbit in all of my KSP playing, and have established a procedure that can consistently land my capsule within a few km of KSC: start with a 0 inclination 100km circular orbit, and burn until Pe = 0km when I reach 174.5 E longitude (KSC is at 74.5W)

However I don't know how to calculate at what longitude to start my burn if the orbit is not at a 0 degree inclination. I've never studied spherical trigonometry, although I am comfortable with the sin/cos/tan functions in planar trig. Any help?

Thanks in advance.

Image of the problem

1. I understand how the teacher goes from formula 1 to 2, and from 2 to 3.
2. Problem: Where does formula 1 come from? ACK is a right angle if i'm right so These right angle formulas should be applicable. But the only rule that looks like this one is R10. For some reason there's 90°-AC which i completely do not understand.

Please help me because stuff like this is in my whole course of celestial navigation and nobody seems to get it and just study it by heart without understanding :/

Books, online guides, or whatever are just fine. I'm working on a game, and a big part of it I wanted to model the surface of a planetoid, I found out really quickly that my grounding in plane geometry and linear algebra is not quite up to snuff with spheres and I wanted to learn more. I actually hadn't remembered Spherical Trig was its own thing until I started digging around. So how about it, anyone care to get me going on the right path?

Hi. I need 47% to pass the year on this exam and everyone is pretty sure they're gonna fail. I got two questions that I think if I can get answered properly, I might be able to pass...

NOTE: I LITERALLY KNOW NOTHING ABOUT THIS SUBJECT!

1. If I have a sphere and I draw a triangle on it, how do I know the area of the triangle and how do I calculate the size of the angles?

2. Suppose a sphere with radius R > 0 is tiled with 6 spherical squares. What is the spherical angle at each of the vertices?

If anyone could do anything to explain these problems, I'd be forever in your debt.

In my math history class we studied this topic on a day I was absent, so my professor's notes (which he posted online) make no sense. Give me a simple way of understanding this? Please, Reddit, I need you!

TL;DR - I put the lat-lon of all 30 NFL venues into an Excel spreadsheet that computes the great-circle distances between them, and found that the Seahawks in 2025 will travel enough to circumnavigate the Earth.

Recently, in light of thinking about the NFL's looming logistical issues, I was wondering just how far our teams have to travel to meet all their road dates in a season. To me, it's rather impressive that 32 teams from all across the mass that is the continental US can just meet up for 18 Sundays out of the year and play, and in largely alternating home/away fashion.

To find the distances involved, what I did was go to Wikipedia, copy down the latitude and longitude (to 6 decimal places) from each stadium's page, and put it all in an Excel spreadsheet. Then, by using simple^relativelyspeakinghehe spherical trigonometry, Excel can give me the great circle distance across the surface of the Earth from any venue to any other.

The formula is as follows:

2*6371.009*arccos(sin(lat1)*sin(lat2) + cos(lat1)*cos(lat2)*cos(|lon1-lon2|))

The x2 at the start makes this a round trip, 6371.009 is the radius of the Earth in kilometers, and the arc cosine and everything in its brackets is to compute the central angle between the described points, given their lat/lon in radians. The || that encapsulates lon1-lon2 means I want the absolute difference.

Possible errors in my calculation include the fact that I carried each degree lat-lon to 6 decimal places, and THEN convert it to radians in the middle of the formula; that my great circle math assumes the Earth is a perfect sphere (fun fact: it isn't! It's slightly fatter at the equator, forming an "oblate spheroid" or a "geoid", but it's within +/- .05%); and, since feeding the same location as both is SUPPOSED to give you zero distance, but for some coordinates it doesn't, I fear I may have run into the limits of Excel's floating-point precision.

NOTE: From this point on, all distances will be in kilometers and will describe a round trip between the points described.

Finding this answer in a round-robin league, such as that of the English Premier League, is simple. Just calculate all round-trip distances between every venue and every other, and add up. Everyone has one road game against every other competitor after all. However, thanks to the limited and rotating schedules of the NFL, I also have to figure out the rotations of matchups, home/away designations, and take into account the

How can I calculate the area of certain parts of my conworld or the distances between them provided that I have a predetermined area in my mind for the world as a whole?

https://preview.redd.it/m1tjq1t2xga81.jpg?width=1080&format=pjpg&auto=webp&s=43bebe223dd9b399418ad3deb4236cbf7d29c306

Jai Singh II was more than just a shrewd statesman and soldier, who could “run with the hares and hunt with the hounds” when necessary. He was also a scholar par excellence, a scientist and planner, and a patron of art, architecture, literature, with the traditionally admired penchant for acts of charity and public welfare. Well acquainted with Indian and Creek mathematics, Jai Singh was aware of contemporary developments in Europe in the field of mathematics. He had various Greek and Arabic works, as well as other European texts dealing with plane and spherical trigonometry, and the use of logarithms etc., translated into Sanskrit. His library included translations and commentaries of the works of astronomers like Aryabhatt, Brahmagupta, Bhaskaracharya, Ptolemy, Mirza Ulugh Beg, Nasir-ul-Din al Tusi, and many others.

Having heard through Portuguese missionaries about the progress in the field of astronomy in Portugal, Jai Singh sent his own men, accompanied by one of the missionaries, to the court of the Portuguese king Emmanuel in 1727-30. Emmanuel, in turn, sent his envoy, Xavier de Silva, with De la Hire’s tables to Jai Singh. When he compared the tables with his own, Jai Singh was able to point out that the Portuguese tables were less exact and had certain errors, which he attributed to the inferior diameters of the instruments used. Jai Singh’s own almanack compilation is known as the Jiz-e-Muhammad-Shahi, taking its name from the Mughal emperor Muhammad Shah.

No navy, air force or commercial shipping company - in fact, no one whose life, mission or cargo depends on knowing where you are and where you are going - navigate by flat-Earth concepts.

Sure, if you're not going far, you can use dead-reckoning, but even the charts that you plot course and position on are projections of a curved surface on to a flat one. You can literally see it.

And celestial navigation? Based on spherical trigonometry.

No navigation textbook anywhere starts with a flat Earth. Why is this? Wouldn't the company, nation or empire who navigates by this much simpler concept hold an invaluable tactical advantage?

I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.

Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.

This review consists of two parts: an overview with marked spoilers and unmarked mild thematic spoilers to help potential readers decide if this work is right for them, and a more in-depth analysis, which contains unmarked moderate spoilers for Orthogonal.

#Overview

Tenet: Don't try to understand it, feel it.

Me: Oh come on, Nolan. That's just lazy, now. You call this sci-fi? You know you can't just slap some vague technobabble on it and call it a day, right? I hate how so much science fiction feels the need to dumb it down for the masses. What's the point of hiring renowned physicists to consult on your movies if you end up with scenes where your pilot has to have wormholes explained to him when he's literally in sight of the one he's about to fly through? I wish there was something out there that puts in some actual effort in the worldbuilding, something smart. Something that doesn't treat its audience like idiots. Such a shame, too. Inverted matter looks really cool.

Monkey's paw: *curls*

...

Well, the good news is, I found a story like that. The bad news is, having read it, I now feel like an idiot.

Welcome to the world(s) of Greg Egan, who puts the 'hard' in 'hard science fiction' in more ways than one.^1 He's the author of works such as Permutation City and Sqchild's Ladder, which are considered some of the hardest science fiction novels ever. But while those are set in more-or-less our world, Egan's most valuable contribution to the genre (at least, in my opinion), is his alternate universes, which run on different laws of physics from ours.

Orthogonal is a trilogy of novels (The Clockwork Rocket, The Eternal Flame, & The Arrows of Time; roughly 1100 pages total) set in one such universe. I chose it as my first Egan work to read largely because of its concept, which was just too intriguing for me to resist. From the blurb on the website:^2

>In Yalda’s universe, light has no universal speed and its creation generates energy.

>On Yalda’s world, plants make food by emitting their own light into the dark night sky.

>As a child Yalda witnesses one of a series of strange meteors, the Hurtlers, that are entering the planetary sys

Alot of great jokes get posted here! However just because you have a joke, doesn't mean it's a dad joke.

THIS IS NOT ABOUT NSFW, THIS IS ABOUT LONG JOKES, BLONDE JOKES, SEXUAL JOKES, KNOCK KNOCK JOKES, POLITICAL JOKES, ETC BEING POSTED IN A DAD JOKE SUB

Try telling these sexual jokes that get posted here, to your kid and see how your spouse likes it.. if that goes well, Try telling one of your friends kid about your sex life being like Coca cola, first it was normal, than light and now zero , and see if the parents are OK with you telling their kid the "dad joke"

I'm not even referencing the NSFW, I'm saying Dad jokes are corny, and sometimes painful, not sexual

So check out r/jokes for all types of jokes

r/unclejokes for dirty jokes

r/3amjokes for real weird and alot of OC

r/cleandadjokes If your really sick of seeing not dad jokes in r/dadjokes

Punchline !

Edit: this is not a post about NSFW , This is about jokes, knock knock jokes, blonde jokes, political jokes etc being posted in a dad joke sub

Edit 2: don't touch the thermostat

Do your worst!

Ants don’t even have the concept fathers, let alone a good dad joke. Keep r/ants out of my r/dadjokes.

But no, seriously. I understand rule 7 is great to have intelligent discussion, but sometimes it feels like 1 in 10 posts here is someone getting upset about the jokes on this sub. Let the mods deal with it, they regulate the sub.

They were cooked in Greece.

I'm surprised it hasn't decade.

Don't you know a good pun is its own reword?

Two muffins are in an oven, one muffin looks at the other and says "is it just me, or is it hot in here?"

Then the other muffin says "AHH, TALKING MUFFIN!!!"

For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.

I said "hey look, an escaPEA"

No one near me but it didn't half make me laugh for a good hour or so!

Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂

It really does, I swear!

How the hell am I suppose to know when it’s raining in Sweden?

And now I’m cannelloni

Because she wanted to see the task manager.

But that’s comparing apples to oranges

And boy are my arms legs.