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Suppose there were no Earth to pull us back and we're hanging in the solar system. Assuming no other force of gravity from other bodies, what would be the $g$ from the Sun?

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up vote 8 down vote accepted

You can get this from Newton's law of gravitation: the acceleration due to gravity is then $$ g=\frac Fm =G\frac{mM_\odot }{mr^2}=\frac{GM_\odot}{r^2}, $$ which comes out to about 5 mm/s$^2$. This is of course the orbital acceleration of Earth.

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Would that orbital acceleration be the speed that one object travels along the orbital? How fast an object( typical human) travels along that orbital if $ g= 5 mm/s^2$? – alvoutila Jan 27 '13 at 11:59
You're confusing speed and acceleration. (!). The orbital speed of Earth is about 30 km/s. Anything at Earth's position with an orbital speed smaller than that would go much closer to the Sun; below 3 km/s you're likely to crash into it. – Emilio Pisanty Jan 29 '13 at 12:44

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