two satellites of a planet have period 32 day and 256 days if the radius of orbit of former is R, find the orbital radius of the letter

Asked by rk7213908 | 31st Mar, 2022, 12:28: PM

Expert Answer:

T1 = 32 days 
T2 = 256 days
R1 = R 
R2 = ?
fraction numerator T subscript 2 superscript 2 over denominator T subscript 1 superscript 2 end fraction space equals space fraction numerator R subscript 2 superscript 3 over denominator R subscript 1 superscript 3 end fraction space
R subscript 2 superscript 3 space equals space open parentheses 256 over 32 close parentheses squared R cubed subscript 1
space equals space 8 R cubed
R subscript 2 superscript 3 space equals open parentheses space 2 R close parentheses cubed space
R subscript 2 space equals space 2 R 
 Orbital radius of later is 2R 

Answered by Shiwani Sawant | 31st Mar, 2022, 09:41: PM