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Out in Space

A space craft is ten thousand kilometres from the centre of the Earth moving away at 10 km per second. At what distance will it have half that speed?

Planetary Motion

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The Setting: A distant planetary system consists only of two planets, Iapetus and Atlas orbiting about the star GXZ-216. At one particular night, the two planets are observed to be aligned with the star in such a way, that Atlas is causing a stellar eclipse on the surface of Iapetus.

 

The Data: It is estimated that the two planets are a distance of 90 million kilometers apart, and observations have shown that both are at the perihelion of their orbits (i.e. their distance from the star is minimal). Atlas' distance from GXZ-216 is estimated to be 30 million kilometers. A full year of Atlas is recorded to take 200 Earthly days.

 

The Question: At a later time, Atlas was observed in the aphelion of its orbit, i.e. the point of maximal distance from the star. Can you calculate the location of Iapetus from GXZ-216 at that particular time?