Near-Side Tidal Weight

MediumPhysElo Quiz #9

52.Near-Side Tidal Weight

+10

A small moon of mass

m

and radius

r

is tidally locked (the same face always points toward the planet) in a circular orbit of radius

d

around a planet of mass

M

, where

M \gg m

and

d \gg r

. An astronaut of mass

m_a

stands on a scale at the sub-planetary point — the point on the moon's surface closest to the planet. What does the scale read?

\dfrac{Gm\,m_a}{r^2}

\dfrac{Gm\,m_a}{r^2} - \dfrac{GM\,m_a}{d^2}

\dfrac{Gm\,m_a}{r^2} - \dfrac{2GM\,m_a\,r}{d^3}

\dfrac{Gm\,m_a}{r^2} - \dfrac{3GM\,m_a\,r}{d^3}

\dfrac{Gm\,m_a}{r^2} + \dfrac{3GM\,m_a\,r}{d^3}

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