What would be the Roche limit (in units of Earth radii) if the Earth had the same mass, but its radius was increased to 1.5 Earth radii?

Question

What would be the Roche limit (in units of Earth radii) if the Earth had the same mass, but its radius was increased to 1.5 Earth radii?
First calculate the density of this new, larger, Earth. Now use this new density and the new radius in the calculator above to determine the Roche limit for this new larger ‘Earth.

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Thiên Di 5 years 2021-08-15T21:30:02+00:00 1 Answers 81 views 0

Answers ( )

  1. Gerda
    0
    2021-08-15T21:31:20+00:00
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    Answer:

    Roche limit = 1.89 of earth radius

    Explanation:

    We know that,

    Mass of earth = 5.972 × 10²⁷ g

    New radius = 1.5(old radius) = 1.5(6.371 × 10⁸) = 9.5565 × 10⁸

    Density of earth = 5.5132 g/cm³

    New density of earth = Mass of earth / (4/3)πr³

    New density of earth = 5.972 × 10²⁷ kg / (4/3)(22/7)( 9.5565 × 10⁸)³

    New density of earth = 1.634 g/cm³

    Roche limit = [2(Density of earth)/(New density of earth)]¹/³r

    Roche limit = 1.89 of earth radius

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