The time period of earth is taken as T and its distance from sun as R. What will be the distance
of a certain planet from sun whose time period is 64 times that of earth?
Hint: By Kepler's third law.
Answers
Answer:
According to the Kepler's third law:
begin mathsize 14px style straight T squared space straight alpha space straight R cubed For space the space Earth colon straight T subscript straight E superscript 2 space space straight alpha space straight R subscript straight E superscript 2 Given space that space for space the space planet colon straight T subscript straight P space equals space 64 space straight T subscript straight E So comma space open parentheses straight T subscript straight E over straight T subscript straight P close parentheses squared equals open parentheses straight R subscript straight E over straight R subscript straight P close parentheses cubed open parentheses fraction numerator straight T subscript straight E over denominator 64 straight T subscript straight E end fraction close parentheses squared equals open parentheses straight R subscript straight E over straight R subscript straight P close parentheses cubed fraction numerator 1 over denominator left parenthesis 4 squared right parenthesis cubed end fraction equals open parentheses straight R subscript straight E over straight R subscript straight P close parentheses cubed straight R subscript straight P equals 16 straight R subscript straight E end style
Explanation:
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