Signpost

Huh?
We have all seen those signposts  the ones stuck in the middle of nowhere with a multitude of signs pointing to famous places (London, New York, Tokyo, Rowville, etc).
 http://images.google.com/images?q=signpost
 http://en.wikipedia.org/wiki/File:Los_Angeles_City_Hall_with_sister_cities_2006.jpg
They all point across the surface of the earth  presumably to follow a great circle to the desired locale.
I want one which points in a true straight line. As the laser shoots. THROUGH THE EARTH! (or is that "as the mole people dig!"?)
“  Make a hole with the gun perpendicular / To the name of this town in a desktop globe
Exit wounds in a foreign nation / Showing the home of the one this was written for 
” 
—They Might Be Giants (Ana NG)

Especially from Australia, this would be pretty neat I think, with North America and Europe being the most 'down' you can get from an Australian perspective. More interesting stuff would be in the directions of Africa, Asia, south America, Antarctica, NZ...
Tell me more, tell me more
For bonus points, instead of a signpost, make it out of actual lasers! (and sealed in a cage with appropriate gas so the line of the laser is visible. Say, ALL lasers always visible in red, then you select a city and it goes GREEN!).
Another method for a permanent exhibit might be to start with a point central to the room, (normal signpost), but then ALSO place markers on the walls and floor of the room to indicate the marker  so as to make clearer the path and descent taken.
Some math
Bearing and Arc Distance
The forumulas to calculate from raw data are given in links below, but for example, this site (http://gc.kls2.com/) will calculate the bearing and great circle distance. The required final data then requires a conversion: the great circle distance into both a straight line (distance), and angle down (0 being tangent to here, 90degrees being straight down). The degrees should remain the same.
Declination and Direct distance
So knowing the arc distance, we can calculate the declination (angle down from tangent to source location), and direct distance via the following:
Declination
 We assume the earth is a sphere, with radius 6371km (the avg radius of the earth, whcih varies in fact between 6356.8 and 6378.1km)
 The declination (angle down) is calculatable from knowing the center angle and distances of the isosceles trangle with points of the two locations, and the center of the earth. In this instance, we know the arc length between two locations, so the center angle can be found with: θ = s/r, where θ is the subtended angle in radians, s is arc length, and r is radius
 From the internal angle, the outer angles are discoverable (π radians in a triangle, thus (πθ)/2 is the internal angle "up" from dropdown angle. We take that from the tangent angle and we get:
 π/2((πθ)/2)
 In degrees: One radian is 180/π, so the inner angle θ=s/r becomes a=180s/πr
 Because we know r=6371km, we can solve to: a=s*0.00899321606...
 The other inner angle is then b=(180a)/2, so our final formula becomes: 90b
 With everything plugged in: 90((180(s*0.00899321606))/2)
In shell script:
echo "scale=2;90((180($arckm*0.00899321606))/2)"  bc
Direct Distance
 Not dissimilarly, knowing two sides (r) and all three angles (a,b,b), we can calculate the third edge length (d) (using the rule of sine)
Results
Data table
The raw data from Canberra (CBR) is:
Location  Code (airport or Lat/Lon) 
Bearing  Arc length  Declination  Direct distance 

North Pole  0E,90N  0° (N)  13911km  62.56°  
Brisbane  BNE  24° (NE)  954km  4.29°  
Anchorage  ANC  26° (NE)  12019km  54.05°  
Seattle  SEA  48° (NE)  12691km  57.07°  
Sydney  SYD  50° (NE)  236km  1.07°  
Honolulu  HNL  50° (NE)  8390km  37.73°  
Los Angeles  LAX  62° (NE)  12282km  55.23°  
New York City  JFK  67° (E)  16239km  73.03°  
Mexico City  MEX  85° (E)  13178km  59.26°  
Miami  MIA  88° (E)  15213 km  68.41°  
Aukland  AKL  102° (E)  2304km  10.37°  
Galapagos Islands  GPS  109° (E)  12710km  57.16°  
Easter Island  IPC  118° (SE)  9255km  41.62°  
Dunedin  DUD  130° (SE)  2123km  9.55°  
Santiago  SCL  146° (SE)  11339km  50.99°  
São Paulo  SBGR  163° (S)  13298km  59.8°  
South Pole  NZSP  180° (S)  6093km  27.4°  
Hobart  HBA  189° (S)  848km  3.82°  
Melbourne  MEL  234° (SW)  470km  2.12°  
Cape Town  CPT  219° (SW)  10780km  48.48°  
Las Palmas Canary Islands 
LPA [Furthest land from CBR?] 
244° (SW)  18349km  82.51°  
Perth  PER  267° (W)  3091km  13.9°  
Adelaide  ADL  269° (W)  972km  4.38°  
Casablanca  CMN  270° (W)  17884km  80.42°  
Cairo  CAI  282° (W)  14259km  64.12°  
Rome  FCO  294° (NW)  16242km  73.04°  
New Delhi  DEL  302° (NW)  10350km  46.54°  
Moscow  SVO  316° (NW)  14490km  65.16°  
London  LHR  316° (NW)  17005km  76.47°  
Darwin  DRW  319° (NW)  3136km  14.11°  
Beijing  PEK  335° (NW)  8992km  40.44°  
Tokyo  NRT  352° (N)  7921km  35.62° 
TODO
 Make a script which can calculate this between any two points, given their long and lat.
 Make a physical sign for same
 Make a smartphone app for the same too (assuming it has a GPS, a compass, and a 3axis accelerometer. eg, iPhone 3GS)