Wednesday 17 June 2009

gravity - What is the gravitational force felt on Earth from the other planets in our solar system?

Because of the inverse square law for Newtonian gravity we have the acceleration due the gravity $g_b$ at the surface of the Earth due to a body of mass $m_b$ at a distance $d_b gg r_e$ (where $r_eapprox 6371 mbox{km}$ denotes the radius of the Earth, note all distances will need be in $mbox{km}$ in what follows) is:
$$
g_b=gtimes frac{m_b}{m_e}times left(frac{r_e}{d_b}right)^2
$$
where $g$ is the usual accelleration due to gravity (from the Earth at the Earth's surface $approx 10 mbox{m/s}^2$, and $m_eapprox 6.0 times 10^{24} mbox{kg}$. We get the maximum acceleration due to a body when that body is at its closest to the Earth, which is what we do from now on (except for the Sun and Moon where the mean distance is used).



Now for the Moon $r_bapprox 0.384 times 10^6 mbox{km}$, and $m_bapprox 7.3 times 10^{22} mbox{kg}$, so the accelleration at the Earth's surface due to the Moon $g_bapprox 3.3 times 10^{-5} mbox{m/s}^2$



Then putting this relation and Solar-System data into a spread sheet we get:
enter image description here

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