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Please tell me how did the distance varies with time as the planets orbits are constantly progressed at different speeds in the question i asked early.
  Planets are very faint compared to the stars they orbit. Moreover, they are very close
to their parent star compared to the distance between stars. On the 1-to-10 billion
scale, where the Sun is the size of a grapefruit and Earth is a pinhead about 15 meters
way, the nearest star is several thousand kilometers away. Together, this makes it
extremely difficult to distinguish the faint light of a planet from the star it orbits.
(Nevertheless, massive Jupiter-like planets have been indirectly detected orbiting
around nearby stars.


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