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Suppose There Existed a Planet that Went Around the Sun Twice as Fast as the Earth.What Would Be Its Orbital Size as Compared to that of the Earth? - Physics

Suppose there existed a planet that went around the sun twice as fast as the earth.What would be its orbital size as compared to that of the earth?

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Solution 1

Lesser by a factor of 0.63

Time taken by the Earth to complete one revolution around the Sun,

Te = 1 year

Orbital radius of the Earth in its orbit, R= 1 AU

Time taken by the planet to complete one revolution around the Sun, `T_P = 1/2T_e = 1/2` year

Orbital radius of the planet = Rp

From Kepler’s third law of planetary motion, we can write:

`(R_p/R_e)^3 = (T_p/T_e)^2`

`(R_p/R_e) = (T_p/T_e)^(2/3)`

`=((1/2)/1)^(2/3) = (0.5)^(2/3) = 0.63`

Hence, the orbital radius of the planet will be 0.63 times smaller than that of the Earth.

Solution 2

Here, `T_e = 1 "year"`, `T_p = T_e/2 = 1/2` year

`r_c = 1 A.U.`

Using Kepler's third law,we have `r_p = r_c (T_p/T_e)^(2/3)`

`=>r_p = 1("1/2"/1)^(2/3)` = 0.63 AU

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NCERT Class 11 Physics Textbook
Chapter 8 Gravitation
Q 3 | Page 201
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