Repped for the longitude rhyme ... now I can finally remember which is which!
How to navigate on a planet with the SRV
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Man, it's a good thing there are no students in my vicinity, I laughed like a braying donkey at that. You guys keep cracking me up . . .
This will not end well
This will not end well
Well, vector sums use trigonometric functions which all begin 0º on the east as the unit circle will tell you
Come on folks, this isn't Floweys fault, it's down to the teacher, curriculum and where Flowey is in it.
Flowey, you're not really not helping yourself either though mate with some of those responses.
Anyway, to explain, coming back to your original point:
0º isn't East in Physics. You can use 0º as East, but you're also free to use 0º as any other direction. There's no inherent 'Eastness' about it. There's also no inherent co-ordinate system. Everything is relative, and you can use any valid co-ordinate system.
So, I would guess that for what you're been doing, you've been using cartesian (x,y) co-ordinates, and following the convention that the positive x axis is 0º, and the positive y-axis is 90º. When you've been looking at your problems, you'll then have metaphorially been overlaying that over a map. What you are essentially doing there is going, 'x-axis is left and right, y-axis is up and down, so I'm going to put that over the map in the way the map has left and right, and up and down' or to put it another way, what you're doing is saying 'for the purpose of this problem, I will define the x-axis being East and the y-axis as being North'. Which is all absolutely fine, but you could also overlay your x-y axis onto the map at any other angle (or even flip it) and everything would still work.
That make sense?
So anyway in a general sense you are wrong, but don't take it to heart - it's fairly standard for things to be taught to students in a way which will make sense to them, and for things not to be fully explained until much later.
Also, if you actually like physics, then there's actually a big bonus to all this for you as we've actually touched on something of quite a lot of significance - the principle that there is no inherent co-ordinate system is actually very important for Physics (and for the universe and life as we know it).
Happy to elaborate a bit more if you want.
Flowey, you're not really not helping yourself either though mate with some of those responses.
Anyway, to explain, coming back to your original point:
0º isn't East in Physics. You can use 0º as East, but you're also free to use 0º as any other direction. There's no inherent 'Eastness' about it. There's also no inherent co-ordinate system. Everything is relative, and you can use any valid co-ordinate system.
So, I would guess that for what you're been doing, you've been using cartesian (x,y) co-ordinates, and following the convention that the positive x axis is 0º, and the positive y-axis is 90º. When you've been looking at your problems, you'll then have metaphorially been overlaying that over a map. What you are essentially doing there is going, 'x-axis is left and right, y-axis is up and down, so I'm going to put that over the map in the way the map has left and right, and up and down' or to put it another way, what you're doing is saying 'for the purpose of this problem, I will define the x-axis being East and the y-axis as being North'. Which is all absolutely fine, but you could also overlay your x-y axis onto the map at any other angle (or even flip it) and everything would still work.
That make sense?
So anyway in a general sense you are wrong, but don't take it to heart - it's fairly standard for things to be taught to students in a way which will make sense to them, and for things not to be fully explained until much later.
Also, if you actually like physics, then there's actually a big bonus to all this for you as we've actually touched on something of quite a lot of significance - the principle that there is no inherent co-ordinate system is actually very important for Physics (and for the universe and life as we know it).
Happy to elaborate a bit more if you want.
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I do understand that strictly speaking there's no preferential frame of reference but then I'd like to know why there's a disparity between 0º in mathematics (between the 1st & 4th cuadrant in the cartesian plane) & 0º in cartography (on the north), the issue I see is that trig functions begin all at 0º on the "East" & I'm sure they are used in navigation.
The distances only hold true for a planet with the diameter of Earth. Smaller planets will have shorter distances to travel for each degree and minute - which, given my level of accuracy at dropping out of Orbital Cruise at the right coordinates, is just as well.
East is also the freezing point of water.
No, the freezing point of water is 32 degrees, which puts it about a little north of north east !
In Cº, not º.
Simply put, one really doesn't have anything directly to do with the other.
Cartography was well advanced before the discovery of trigonometry, but they both kind of developed in parallel, and while trig has absolutes that lend themselves to the standardization we know today, cartography and navigation on the other hand is a bit more relative. Latitude and the equator makes a nice logical baseline because it can be defined as an absolute. Measurement of longitude on the other hand is relative. Hell, we didn't have a standardized Prime Meridian until 134 years ago, this month in fact.
Honestly, that doesn't explain very much as even before the establishment of the Greenwich Meridian 0º was still North. Could you elaborate?
That's actually starboard.
Latitude was well established because it is fixed and easily measurable. The equator was one of the very first defined and established navigational references on early maps across multiple civilizations. The direction we call north was also established and accepted very early on. Since latitude in general, and specifically the equator was a standard, defined, fixed reference, it made sense to label it as 0 latitude, increasing and decreasing incrementally north and south respectively. Since early navigation was based on non-changing points, aside from the equator, the northern direction was the other main standard across most early maps. So now we have two baselines, the equator, and the direction North. This was well established way before Cartesian coordinates were invented.
Since latitude could be measured, and was the same no matter where one was, going up and down in relation to the equator formed a natural axis of measurement. It just made sense to have the axis which had fixed distances regardless of where one was on the axis to be the primary reference axis, hence the up and down axis has zero at the top.
Latitudinal distance is fixed, independent of longitude, where as longitudinal distance is dependant on latitude, making the up and down axis primary.
A simpler explanation is that mathematics, and navigation standards have nothing to do with each other, simply happen to use similar terminology, and when it came to standardization, the mathematicians and cartographers just decided to do things differently from one another, and standardize things differently.
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We could really have some fun by adding in the z and w axis.
To help Flowey in what seems to be an already lost argument I just want to mention that there was a time - though quite long ago - when maps were facing east instead of north.
That's where the word "orientation" came from.
https://en.wikipedia.org/wiki/Map#Orientation_of_maps
Maybe Floweys Physics teacher comes from this time...
That's where the word "orientation" came from.
https://en.wikipedia.org/wiki/Map#Orientation_of_maps
Maybe Floweys Physics teacher comes from this time...
Well, they're conventions, so you'd need to know the history of how those conventions were arrived at, which I don't. But there being a disparity doesn't really matter.
"the issue I see is that trig functions begin all at 0º on the "East" & I'm sure they are used in navigation." Ok, so this is the key bit I think. There's no issue at all. When you're thinking of the trig functions like that, it's just a diagramatic representation. There is no connection whatsoever between the alignment of that diagram and the direction East. It's simply an abstract, and there's no physical direction involved. (Assuming that I'm interpreting what you're saying correctly and you're talking about the kind of thing where which trig functions are positive and negative are shown in quadrants of a circles.)
To illustrate further, let's look at the following diagram (with apologies for the quality - I'm no Jim'll Paint It!):
Then:
Let's use the x-axis as East and the y-axis as North.
Now let's say you're heading on a bearing of 15º - that's 15º clockwise from North. You travel a mile on that bearing and want to convert it to your position in x,y / Compass directions.
So Theta = 15º and Phi = 90º - 15º = 75º
The hypotenuse = h = 1 mile
For Theta, x is the opposite, and y is the adjacent
For Phi, x is the adjacent and y is the opposite
Sin = o/h, Cos = a/h Tan = o/a
So, using the compass bearing, x = h*sin(Theta), y=h*cos(Theta)
And using East is 0º and North = 90º then x = h*cos(Phi), y = h*sin(Phi)
h = 1 so it's just trig functions.
So, compass bearing, x = sin (15) = 0.259, y = cos (15) = 0.966
And using East is 0º and North = 90º then x = cos (75)= 0.259, y = sin (75) = 0.966
Now let's say you're heading on a bearing of 15º - that's 15º clockwise from North. You travel a mile on that bearing and want to convert it to your position in x,y / Compass directions.
So Theta = 15º and Phi = 90º - 15º = 75º
The hypotenuse = h = 1 mile
For Theta, x is the opposite, and y is the adjacent
For Phi, x is the adjacent and y is the opposite
Sin = o/h, Cos = a/h Tan = o/a
So, using the compass bearing, x = h*sin(Theta), y=h*cos(Theta)
And using East is 0º and North = 90º then x = h*cos(Phi), y = h*sin(Phi)
h = 1 so it's just trig functions.
So, compass bearing, x = sin (15) = 0.259, y = cos (15) = 0.966
And using East is 0º and North = 90º then x = cos (75)= 0.259, y = sin (75) = 0.966
And there you go, no difference in the result whichever of the conventions you use.
The other thing to bear in mind is that North, South, East, West are all directions around a sphere and they only correspond to cartesian co-ordinates on a small scale.
For example, if you're on the equator, and define an x = East, y = North cartesian co-ordinate system there, then 1 mile traveled East there corresponds to +1 mile in the x-direction, but 1 mile traveled East at the opposite side of the globe corresponds to -1 mile in the x-direction.
The big problem when it comes to navigation is that in the general case, it's dealing with a spherical surface, and normal trig only works on a flat surface. Consider if you have a cartesian plane, and draw a line straight up from x = 1, that line will always stay a distance of 1 from the y-axis. However, if you start at with two points on the Earth which are 1 unit East/West of each other and draw a line North from each of them, then the two lines will meet.
Anyway, lots of stuff there, but it all boils back to the concept of East most definitely not being something which is in any way intrinsically tied with the Trig functions.
Hope that all makes a bit of sense!
Hopefully Flowy is not a flat earther.
Excellent elaboration Cmdr Thatchinho!
Excellent elaboration Cmdr Thatchinho!
Compasses don't use batteries, and while influenced by magnetic fields they don't require access to satellites.
Sounds like your physics teacher confused - maybe confused you with - Easting (X) and Northing (Y) with geographical coordinates. Easting and Northings are used on planar, projected grids.
S