Flat discs have been fixed to the Earth’ s surface at the observe’ s locations representing their horizon. These are marked with compass points NESW. The blue dot on the animation represents the line between the target and the centre of the Earth. This is the distance we need to calculate. The green line is the base distance between observers. This can be calculated from their Lat. and Long. coordinates. The pink and red lines represent the lines of sight between the observers and the target. The true angle between these lines is the ? parallax? angle. Each observer will see the object in a slightly different position against the same background of distant stars. The shift between the apparant target positions can be calculated as an angle by measuring the target? s celestial coordinates against known star positions. The resulting angle is the measured parallax angle and this can be used to calculate the distance of the object from Earth.
If the target was above the base line (the green line passed through the blue dot) and the simultaneous parallax observation was made when the target was equidistant from both observers (the blue dot was on the centre of the green line), the maths would be relatively easy. Unfortunately this is rarely the case!
Notice how the apparent length of the green base line changes as the earth revolves. Notice also how the lengths of the pink and red lines change. The complicated relationship between these lines needs to be represented mathematically in order to make the calculations accurate. It looks likely that the observers will need to make an accurate measurement of the direction and altitude of the target at the time of observation in order for these factors to be included in the calculations.
It is interesting to see how the angles of the pink and red lines change relative to the discs on each position (proving I suppose that the Sun really does rise in the east and set in the West!) It may be enough to note the compass bearing of the target. I am hoping to work out how these problems can be solved and welcome any suggestions or solutions.
This model has been created to demonstrate the relationship between two observers, a stationary target object in space and the Earth as it rotates. The animation begins as the target rises above the horizon in the East for the LA observer. It ends as the object sets in the West for the London observer. Although this represents a period of over 4 hours the optimum window for simultaneous observation would probably be reduced by local geography.
