How far am I from directly opposite the Ranch?

[David O'Meara]

Following on from the thread here, assuming the Ranch's physical location is Denver, and I'm in Perth, West Oz, what is the approximate distance (as the crow flies) from my location to the point directly opposite the Ranch?
There should be enough research and maths to keep someone out of trouble for a while

[David O'Meara]

and make your answer quotable, I feel a sig coming on.

[HS Thomas]

You should relocate to a location with a latitude 8 degrees North and
be in a timezone GMT + 0200. ( using cac Windows times ).
Denver is 40 degrees North
Perth is 32 degrees South
An GMT hour west of Nairobi ( GMT + 0300) and 8 degrees North of the Equator.
It's 70 miles per degree, I believe.
I am sure if we try hard enough we'll find a town for you, Dave.
Eldoret?
Eldoret is bang on the Equator .
Longitude: 035� 17' E
Latitude: 00� 32' N
A village 560 miles north of Eldoret and a GMT hour west of Nairobi.
Sorry no major cities.
If you like it by the sea, try working the other way.

regards
[ August 27, 2003: Message edited by: HS Thomas ]

[HS Thomas]

Which doesn't answer your question at all does it !
But if you want to be closest to your two fav places , Denver,CO and Perth,Aus now you know.
To be perfectly upside-down from Javaranch I am sure someone will come up with a solution!
regards
[ August 27, 2003: Message edited by: HS Thomas ]

[HS Thomas]

If south is always opposite of north and east is right of west, you will be completely upside down at
40 degrees S and 105 degrees E.
Denver , Colarado is at 40 degrees N and 105 degrees W.
That should take you 70� to the left of Wellngton,NZ 40�S 175�E
40�S 105�E
This confluence has not been visited, or indexed.
Type: Water: 1095 km (680 mi.) from land
regards

[Carl Trusiak]

Hum, I got a little closer on the lat long's
Denver 39.75, 104.91
Perth 31.95, 115.87

public class Klicks{
   static final double EARTH_RADIUS = 6371.0;
    public static void main(String args[]) {
        System.out.println(distance(39.75, 104.91, 31.95, 115.87));
    }
    public static double distance(double lat, double lon, double lat2, double lon2) {
        lat = Math.toRadians(lat);
        lon = Math.toRadians(lon);
        lat2 = Math.toRadians(lat2);
        lon2 = Math.toRadians(lon2);
        double p1 = Math.cos(lat) * Math.cos(lon) * Math.cos(lat2) * Math.cos(lon2);
        double p2 = Math.cos(lat) * Math.sin(lon) * Math.cos(lat2) * Math.sin(lon2);
        double p3 = Math.sin(lat) * Math.sin(lat2);
        return (Math.acos(p1 + p2 + p3) * EARTH_RADIUS);
    }
}

1312.68 Kilometers

[HS Thomas]

I feel a diagram coming up.

            o            o     o
          11 E  Perth  32 S 116 E
          _______x
          |     /
     o    |    /
    8  N  |   /
          |  /
          | /
          |/
          x      o     o
          DOM  40 S 105 E

I have been unreliably informed that :
1 deg lattitude = 111 km
1 deg longitude = 65 km
So the sides of the |_ angled triangle are 888 km (a) and 715 km (b)
The distance between the two points as the crow flies ,c is

       _________
 c = \/ a2 + b2     (Pythogarus)
       _______________
 c = \/ 888^2 + 715^2

= 1140 km approx. for a tunelling crow!
===============
I prefer Carl's way,though (Genius at work)
Pure Math over geography. I can't believe the earth's radius would add approx 200 km to the journey over a few degrees.I must have got it wrong. But then again the earth is huge.
Since DOM point is Type: Water: 1095 km (680 mi.) from land I'd dumb down
Carl's figure to be closer to mine. Crows have small eyes so keep close to the surface(not much higher than a Crow's nest) , unlike eagles who may keep to a higher flight path. :roll:
The poor things have been programmed to think the earth is a perfect sphere.
regards
[ August 27, 2003: Message edited by: HS Thomas ]

[David O'Meara]

From my own research:
Denver is: 39:46:05N 104:52:22W
Perth is: 31:50:00S 116:10:00E
The opposite side from Denver gives you:
39:46:05S 75:07:38E
Distance from 39:46:05S 75:07:38E to 31:50:00S 116:10:00E for cheats is 3778 km.
Apparently this is only 220km from land. How far to crows fly?

[HS Thomas]

The opposite side from Denver gives you:
39:46:05S 75:07:38E

New Delhi has a longitude of 77 degrees E.
By Dave's calculations (presume it is 180 - 105 = 75 ) the opposite of Denver is on the same longitude as New Delhi but 40 degrees S) and not - east is directly right of west - as I had asssumed .
Can anyone explain why the opposite longitude to Denver is 75 degrees E?
regards
[ August 28, 2003: Message edited by: HS Thomas ]

[Jim Yingst]

Can anyone explain why the opposite longitude to Denver is 75 degrees E?
If Denver is at 75 W (75 degrees west of you Greenwichites) then the opposite longitude is 180 degrees away. We could call it 255 W I suppose, but we prefer to measure in the opposite direction (subtract 360 and change sign) to get 75 E.
As for the original question, here's how to calculate the distance along the earth's surface. This assumes the Earth is a perfect sphere, using Carl's numbers. We use the property that the dot product of two vectors is equal to the product of their magnitudes times the cosine of the angle between them - which allows us to solve for that angle if everything else is known.

public class EarthDistances {
    private static double R = 6371.0; // Earth radius in km
    public static void main(String[] args) {
        showDistances("AntiRanch", -39.75, 104.91,
                      "Perth", -31.95, 115.87);
        showDistances("JavaRanch", 39.75, -75.09,
                      "Perth", -31.95, 115.87);
    }
    /** Show distances between two points on Earth given latitudes and longitudes */
    public static void showDistances(String label1, double lat1, double long1, String label2, double lat2, double long2) {
        System.out.println("From: " + lat1 + "\t" + long1 + "\t(" + label1 + ")");
        System.out.println("To:   " + lat2 + "\t" + long2 + "\t(" + label2 + ")");
        double x1 = cosD(lat1) * cosD(long1);
        double y1 = cosD(lat1) * sinD(long1);
        double z1 = sinD(lat1);
        double x2 = cosD(lat2) * cosD(long2);
        double y2 = cosD(lat2) * sinD(long2);
        double z2 = sinD(lat2);
        System.out.println("Straight-line distance:\t" + R*length(x1-x2,y1-y2,z1-z2) + " km.");
        double cosTheta = x1*x2 + y1*y2 + z1*z2;
        double theta = Math.acos(cosTheta); // in radians
        double curveDistance = R * theta;
        System.out.println("Curvilinear distance:\t" + curveDistance + " km.\n");
    }
    /** Get cosine using degrees */
    private static double cosD(double x) {
        return Math.cos(Math.toRadians(x));
    }
    /** Get sine using degrees */
    private static double sinD(double x) {
        return Math.sin(Math.toRadians(x));
    }
    /** Get magnitude of vector, given 3 components */
    private static double length(double x, double y, double z) {
        return Math.sqrt(x*x + y*y + z*z);
    }
}

Since it turns out that the curvature of the Earth makes remarkably little difference in this case, I also calculated how far Dave is from Denver itself, in addition to the distance from the point furthest from Denver:

From: -39.75104.91(AntiRanch)
To:   -31.95115.87(Perth)
Straight-line distance:1310.3612403024747 km.
Curvilinear distance:1312.6819543373913 km.
From: 39.75-75.09(JavaRanch)
To:   -31.95115.87(Perth)
Straight-line distance:12674.443475747288 km.
Curvilinear distance:18702.404841683183 km.

Obviously, I didn't bother to round to significant figures here.

[Michael Matola]

Charts, figures, maps!
It takes a liberal arts major to point out that opposite points on a sphere are "antipodes."

[HS Thomas]

posted by Jim Yingst:
We use the property that the dot product of two vectors is equal to the product of their magnitudes times the cosine of the angle between them - which allows us to solve for that angle if everything else is known.

Tell me that has a Pythagorean ring to it and this luddite Greenwichite (me) hasn't given him (Pythagorus) cause to say "So this is how it feels to play for the Bengals?" or "Maybe I should've inhaled!".
Well, that's two people that go it wrong unless DOM knows something he is not telling us.
regards
[ August 28, 2003: Message edited by: HS Thomas ]