N.B. Developed in MSIE 4/6; now maintained in Firefox 3.0; occasionally checked in some other browsers.
Most values entered can now have spaces, e.g. as thousands separators; eval() is used in userIn(). Inputs can be expressions such as 29028*0.3048. Comment is allowed.
Some of these assume a spherical body. For Earth, use a circumference of 40,000 km or better (that matches the originally-intended size of the metre).
Note the scroll bar.
On Earth, the depression in degrees is close to the square root of the height in kilometres.
Use consistent length units; approximate Earth size in kilometres is preloaded.
The initial value of Altitude is roughly correct for ISS; the Viewing Distance for the Glasgow-London latitude difference.
Drawing a matching diagram is left as an exercise for the reader.
The Viewing Distance calculation is iterative.
A distant Orb is viewed, from directly above Longitude 0 on its Equator; its North is at the top. Its surface is seen as a circle, in which one can use centred Cartesian (X, Y) or Polar (r, θ) co-ordinates.
Gregorian. Press any button to calculate its line from the other two entries. Not d/m/y; year>99.
Use Days ± = 0 to check.
Leap Seconds Caveat.
Magnitude is logarithmic; the brightest stars are about Mag 0 and the dimmest visible are about Mag 6. A difference of 5 magnitudes represents a factor of 100 in brightness, so +1 Mag is a factor of about 0.398. Avoid negative brightness. Doubling the distance reduces the magnitude by close to 1.5.
At 1 g in a Newtonian universe it takes a year or so to reach the speed of light. The Solar System is only about a light-day across; the nearest stars are several light-years away. Therefore, at 1 g the Newtonian approximation is good for local and interplanetary travel; but for interstellar travel the journey is substantially relativistic.
For Newtonian travel, mid-point turn-over in order to stop halves the distance and speed.
For telescope resolution, use Baseline for Wavelength and Distance for Aperture; watch the units. Visible light is about 600 nm wavelength; enter about 6E-7 m. Accepts expressions :-