The short answer is NO! In order for a star to
ignite its fuel of H to make He , its temperature
must reach about 15 million degrees Kelvin, and it
is at very high pressure, due to the effects of
its huge mass. Now, that mass limit (since mass is
what controls the core temperature and pressure
due to compression) is about 7% the mass of the
Sun. In other words, the smallest star is of mass
equal to about 7% of that of the Sun. Jupiter’s
mass, BY FAR, the most massive planet is less than
0.1 % of the Sun's mass , nowhere near the limit
of 7 per cent!
Then you can see that Jupiter is just too wimpy
of a place to ever become a star and ignite the
proton -proton chain, and form Helium by nuclear
Unfortunately Jupiter is too small to ignite.
Even the smallest stars that we know about 15
times heavier than Jupiter
and these are brown dwarf stars which are
different from and dimmer than our own sun.
A huge temperature and pressure is required to
start a fusion reaction, and this must be
maintained to keep the reaction going. If we
could "ignite" a fusion reaction in Jupiter
somehow it would just go out because there isn't
enough gravity to maintain enough temperature and
pressure for fusion.
The planets orbit around the center of mass of
the solar system which happens to be the sun
because it's so heavy, about 1000 times heavier
than the rest of the planets combined. Even if
the sun goes out the material is still there and
its mass will still be in the center of the solar
system so we'll continue to orbit it.
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