Please read the description in the Help and Infos panels to find out how this App works. Note: if Ground on the Options panel is selected, the ground is drawn in green if the points are viewed from above the surface, and brown if viewed from below the surface.
GNSS Data File: Rainy_Lake_Radius_of_Earth
Click the button Get App Parameters and copy the parameters at the begin of your data file (see Upload Geo Data) so this App starts with the current setting when called with your data.
Red, Blue and Green Info Boxes
Hell: Height of point above Reference Ellipsoid
Hgeo: Geoid height wrt. Reference Ellipsoid
Leng: Distance of data point to the center of the earth
Dref: line of sight distance to Reference Point
Hlvl: distance of the point width the same color as the info box to the eye level plane of the other point
Rell: Geocentric Radius of Ellipsoid = distance of ellipsoid at point location from the center of the earth
ECEF: data source for this value is Earth Centered Earth Fixed coordinates
EGM96: data source for this value is Earth Gravitaional Model 1996 (Geoid)
Elev: Elevation = Height above Geoid EGM96
Hsrf: Height above Surface, depending on SurfaceElevation (Camera panel)
Zang: Zenith angle at the location of the point with the same color as the info box to the other point
Angl: Angle between perpendiculars of point with the same color as the info box and the red reference point
Rmer: Meridial Ellipsoid Radius = radius of ellipsoid at point location in north–south meridian direction
Rver: Prime Vertical Ellipsoid Radius = radius of ellipsoid at point location in east-west direction
Note: if no elevation data is specified for the data points, a mean Geoid height may be entered in the field GeoidHeight on the Camera panel. In this case Elev and Hsrf are only estimations and indicated by a ~ before the value and user is indicated as the data source behind the value.
Magenta Info Box (displayed if blue and green Points are selected)
Leng: distance of line of sight between blue and green point
Angl: angle between the vectors perpendicular to the reference ellspsoid at the blue and green points. R = Leng / Angl gives an approximation of the radius of the earth (Angl in radian, see Options panel).
R3pt: Measured radius of the earth from 3 selected data points, see Method to calculate the Radius of the Earth from 3 Points. The line below indicates the maximal deviation of the calculated radius from the ellipsoid radii Rmer or Rver in km and %. If the sign is +/- then the calculated radius lies between the two ellipsoid radii. The correct radius is dependent on the direction of the data points and lies between the two ellipsoid radii. So a +/- sign indicated a minimal error in the measurement (max ~0.5%).
For the calculations the red point is projected onto the plane defined by the blue and green point and the perpendiculars of the blue and green points. The calculated center of the arc is drawn as a big blue cross (zoom out to see it). To get correct results, use only points with the same elevation (minimal value dHel) and the greatest distance between the points.
Dref: shortest distance of red Reference Point from line of sight between blue and green point (magenta line)
Hlvl: vertical distance of line of sight between blue and green points to the eye level plane of the Reference Point.
Sref: horizontal distance of line of sight between blue and green points along the eye level plane to the red Reference Point.
Re12: Radius of ellipsoid calculated from length of line of sight between projection of blue and green point onto ellipsoid and angle Angl between the verticals of this points. This value sould lie between Rmer and Rver in the red info box. It is approximately equal to Re12 ≈ Leng / Angl.
Rerr gives the maximal error margin in the calculated earth radius R3pt per cm uncertainty in the elevation of the selected points. It is calculated by varying the elevations of the 3 point +/- 1 cm and taking the biggest differences in R2pt.
dHel: maximal difference in ellipsoid height of the selected points. Chose points where this difference is minimal for most accurate calculation of radius R3pt.
The measured radius of the earth from 3 points R2pt differs from the Geocentric Radius of the Ellipsoid Rell, the Meridial Ellipsoid Radius Rmer and the Prime Vertical Ellipsoid Radius Rver due to Geoid variations and uncertainties in the measured elevations. The calculated radius is very sensitive to elevation uncertainties ΔH: typically ΔR/ΔH ≈ 300 m/mm and more for a distance between the outer 2 points of about 30 km. The longer the distances between the measured points is, the more accurate the calculated radius. Distances of less than 10 km may result in errors in the measured radius of hundreds of km or 5 to 10%.
The radius Re12 is the best approximation of the actual radius of the ellipsoid at the location of the red reference point.
Mouse Controls: Use the following controls while the mouse pointer is in the window above:
Zoom using the mouse wheel. Press the Ctrl key to increas or the Alt key to decrease the increment.
Rotate around the viewing center by click and move. Press the Ctrl key to increas or the Alt key to decrease the increment.
Note the camera position changes. Click the display button 3 to reset the camera position to the last stored position, if button 3 is selected (green triangle). Click the display button 1 to reset the view to the initial setting.
Pan by Shift click and move. The camera position will not change. Panning sets the View Center Mode to fixed, indicated by the green triangle above the display button 3. Click the display button 2 to center the view on the selected red Reference Point without changing the camera position.
Set Camera to any Point location by Shift+Ctrl click a point. The camera will be aimed to the red Reference Point. The View Center mode changes to fixed to prevent camera movement by panning around or selecting other points. The camera position will be stored and can be recalled by clicking the display button 3.
Note: the camera data point is not visible. You have to increase the Camera Distance as described below to get this point into view.
Change the Camera Distance along the line of sight using the mouse wheel while pressing the shift key. Note that changing the camera distance looks almost the same like changing the Zoom value, but if you are near the data points moving the camera changes the perspective drastically and may distort the image unnaturally in extrem cases, while zooming does not.
Select the red Reference Point by clicking it without any keyboard keys pressed or by clicking the corresponding line in the table below. If the View Center mode is Ref Point (indicated by the green triange above display button 2), the camera moves to the new point without changing Azimuth, Elevation and Distance, so that the new Reference Point is centered and viewed from the same perspective. If the View Center mode is fixed (green triangle is above button 3) the viewing angle and camera position stay fixed.
Note: Azimuth and Elevation to the camera are calculated with respect to the local North/East/Up coordinate system of the red Reference Point.
The data of the Reference Point is displayed in the red info box if Visuals = Infos is selected in the Info panel.
Select the blue Point to get measurements with respect to the red Reference Point by clicking it while pressing the shift key on the keyboard. To deselect the point, shift click anywhere on the display.
You can also select/deselect the blue point by shift click any point in the table below.
Select the green Point to get measurements with respect to the red Reference Point by clicking it while pressing the ctrl key on the keyboard. To deselect the point, ctrl click anywhere on the display.
You can also select/deselect the blue point by ctrl click any point in the table below.
If both the blue and the green point are selected, a magenta line between this two points is drawn and additional data between all selected points is calculated and displayed in the magenta info box.
To read a description of the values in the info boxes select the Infos panel above.