In Module 8, Test Question 8, if centripetal force depends on the inverse of r, why is the closer satellite the one that moves faster?

Jan 19, 2022

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You have to set the gravitational force equal to the centripetal force to understand the relationship between the two satellites. After all, the gravitational force IS the centripetal force:

Fc = (m_sat)x(v)^2/r

Fg = Gx(m_earth)x(m_sat)/r²

Gx(m_earth)x(m_sat)/r²= (m_sat)x(v)^2/r

Gx(m_earth)/r = v²

v = square root (Gx(m_earth)/r)

This equation shows you that the smaller the r, the greater the v.