Question

let the period of revolution of a Planet at the distance R from a Star be T .prove that if it was at distance of 2R from the star, its period of revolution will be √8 T.

Answer 1

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һєяє' ʏȏȗя ѧṅśwєя ʟȏȏҡıṅɢ ғȏя________
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✯According to Kepler's law ,
T^2a^3
Here T denotes the time period and a denotes the distance between two objects

♦ distance between planet and star is R then time period is T
means T^2 = kR^3[ here k is proportionality constant ]----(1)

♦ Let the time period is T' when distance between planet and star is 2R
T'² = k(2R)^3 = k.8R^3-----(2)

Dividing equation (1) by (2)
T^²/T'^2 = kR^3/k8R^3 = 1/8
T'^2 = 8T^2
square root both sides,
$t = \sqrt{8} t$
T
Hence, time period will be
$\sqrt{8t}$
, when distance between planet and star will be 2R.
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HOPE IT HELPS!!✌✌✔✔✔

Answer 2

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✯According to Kepler's law ,

T^2a^3

Here T denotes the time period and a denotes the distance between two objects

♦ distance between planet and star is R then time period is T

means T^2 = kR^3[ here k is proportionality constant ]----(1)

♦ Let the time period is T' when distance between planet and star is 2R

T'² = k(2R)^3 = k.8R^3-----(2)

Dividing equation (1) by (2)

T^²/T'^2 = kR^3/k8R^3 = 1/8

T'^2 = 8T^2

square root both sides,

t =$\sqrt{8}$tt=

8

t

T

Hence, time period will be

$\sqrt{8t}$

8t

, when distance between planet and star will be 2R.

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HOPE IT HELPS!!✌✌✔✔✔