Short answer: no.
We're in free-fall around the sun -- we're "weightless" as an
astronaut is in orbit around the Earth. In fact, the only reason we
have weight is because the Earth is pushing against our feet with
electromagnetic forces, to counteract the gravitational forces pulling
down (Newtonian picture). The gravitational force the Sun exerts on us
is almost exactly what's required to keep us in an almost circular
orbit around the sun. Double the mass of the sun and you change our
orbit around the sun, but not the interaction between yourself and the
Earth.
But -- something does change a bit! The tides which are due partly
by the sun and partly by the moon would change in strength -- the sun's
component would double. This effect has a tiny tiny effect on your
weight. If the sun's mass were to double without pushing or pulling on
the Earth, then the Earth's orbit will change to an ellipse which
brings it out to our current radius but spends most of its time closer
to the sun. The tides would probably get even stronger then,
particularly when our orbit takes us closer to the sun.
Tom
(published on 10/22/2007)
