Cape Canaveral in Florida is the sight for NASA's launch center. This
site was chosen because it is one of the most southern points on the
U.S. mainland and closest to the euqator. There is an advantage to
being close to the equator when your goal is to get into orbit.

The European Space Agency also launches from a site close to the equator.

China's launch center is in Gansu province. Why did they choose this
site when they have territory much further south closer to the
equator? The Russian lauch center is in Kazakhstan, not a very
southerly location.

I am interested in this question form a physics perspective. Why do
the Chinese and Russians think that it is not so important to be near
the equator for their launches when the Americans and Europeans have
gone through extra trouble to ensure it?

The reasons are no doubt of a political nature or economic nature.  If
the engineers had their way then it might be very well closer to the
equator.  But just think how much the representatives from a certain
region would want a large research and launch facility in their
region.  It brings economic growth to the region.  You might ask the
additional question - why is Cape C. not even MORE south in Florida,
eg why was the facility built at that location and not say at the
southern tip of florida?  This might bring insight to your question
regarding the Chinese.

NASA isn't more south than where it is because of weather, along with
any particular political and social reasons. Definitely there could be
a reasonable advantage to be closer to the equator, but I think Key
West would be untennable, especially in light of the hurricanes. I
don't really fully go along with the money following the technology,
at least if you look at the demographic map of the residents near Cape
Canaveral. It's easy to see that the growth is in Miami, and Orlando,
and maybe Jacksonville, and much of the growth around the space ports
is directly attributable to the presence of the spaceport, but it's
not exactly a place for inbound economy.

My guess is, however, tied to the previous comment in this: because
China and Russia's spaceports aren't that far out of the way for
government to be in control.

A factor to consider in this is that launching from west to east is
the best way to get into orbit. The earth's spin gives an added boost
to the rocket.

Israel cannot launch in an eastward direction because of hostile
neighbours to their east. So they have to reduce payload and launch
westward over the Mediterranean.

Perhaps similar non-engineering factors have led China and Russia to
choose sites that are not as far south as they can put them.

This is just a speculation - CONSIDERING - similarity of Soviet and Chinese sites:

"..The launch sites are oriented towards the west and the down-range
instrumentation is also in that direction. The desert terrain to the
west allows the firing of surface-to-surface missiles to ranges of up
to 1,100nm within Chinese territory. The pads, associated revetments,
and supportareas in launch complex "A" closely resemble Soviet
facilities at Kapustin Yar used for 700, and probably for 1.,000 n.m.
ballistic missiles. launch complex "C" bears resemblance to other
Soviet cruise missile launching facilities at Kapustin Yar. The two
surface-to-air missile launch sites also resemble SA-2 launch
facilities at Kapustin-Yar. The support facilities are also built on
the Soviet model..."

http://www.fas.org/spp/guide/china/facility/jiuquan.htm

The sites were built during the cold war when the basic scenario for
real war was to launch missiles in direction of the US over the North
Pole.

It is just a guess of course, however now, when we are restarting the cold war 
and embracing pre-emption for all, in may be an interesting mind exercise to
try to recapture the mind set of the fifties ..

Since asking my question I have come to a better understanding. 

Lauching closer to the equator is an advantage but it is not crucial.
So it is a factor to be weighed among many others when choosing a
launch site.

I may be missing something but I don't see any significant advantage
in being right at the equator.  Assuming an approximate earth
circumferance of 24,000 miles, and the fact that the earth performs a
revolution every 24 hours, the boost in speed to a launch vehicle is
about 1000 mph at the equator.

At a different lattitude, the boost in launch speed is given by
multiplying by the cosine of the lattitude.  Hence at a lattitude of
40 degrees, the boost in launch speed is 766 mph.

The difference in boost to launch speed between the equator and a
lattitude of 40 degrees is only 244 mph.  Hardly worth bothering
about!

Here is some good elucidation that I found at:
http://www-istp.gsfc.nasa.gov/stargaze/StarFAQ3.htm

(a)     Why are Satellites Launched Eastward?

1. I believe earth-orbit satellites are launched in either polar or
basically west-to-east orbits. Why do we not launch in a westerly
direction?

Reply
    Concerning your first question, the velocity needed for a stable
orbit around the center of the Earth above the atmosphere is about
8000 meter/second. An object on the surface of the Earth already has
an eastward velocity, because of the Earth's rotation, but it is much
too small: 409 meter/sec on the equator, and 409 times cosL at
latitude L. That is much too small to fling you or me into orbit (for
which we ought to be grateful), but it's still something, and
satellite launchers, eager to make use of the smallest advantage, fire
their rockets eastward. At Cape Canaveral you get a bonus of about 360
m/s.

    Israel has launched two satellites so far (maybe more). Lacking
the choice, it must launch westward over the Mediterranean, and those
360 (or so) meters/sec hinder rather than help its rockets, reducing
the available payload. Yes, it can be done, but when a choice exists,
eastward is preferable.

(b)     Why are satellites launched from near the equator?

    When you calculate the centripetal force at the equator it is
0.033 m/s2 (m v2/R) This means that there is approximately 0.3 %
variation in the force that attracts a body towards the center of the
earth between the equator and the north pole (where without precession
no rotation would be felt). This would mean that it would be
attractive to send rockets from the equator because it would save 0.3%
in fuel. Is this true?

Reply

    Your argument is well known, but it is usually phrased
differently. The centrifugal force acts only in a rotating system.
Once an object is detached from that system, putting the centrifugal
force into a calculation may lead to incorrect result. Example: your
bicycle wheel picks up a piece of mud from the road. As long as the
mud is attached, it feels an outward force, a centrifugal force (in
the frame of reference of the rotating wheel). Once it works loose,
however, it does not fly in the direction of that force, but
tangentially to the wheel!

    However... launching from the equator is still advantageous. A
spacecraft located on the equator is carried by the Earth at about 400
meters/second, or about 5% of the orbital velocity. Even at Cape
Canaveral, one still has a large fraction of that velocity, about 4/5.
That is a significant advantage, and the reason all rocket launches
from Florida are eastward. Polar satellites are usually launched from
Vandenberg in California, and obviously cannot use that advantage.

    Launch sites, of course, are subject to political limitations.
Cape Canaveral is as close as one can get to the equator from the
continental US. The European Space Agency has its launch base at
Kourou in French Guiana, about 5 degrees north of the equator. Israel,
on the other hand, had to launch its satellites westwards, over the
Mediterranean, requiring extra velocity to overcome the rotation.

    The only launch I am aware of that was conducted on the equator
itself was of an Italian "San Marco" satellite, launched from an
off-shore platform near Somalia. Today, with the "Sea-Launch" ship
available for launches (a commercial partnership of Boeing and
Russia), such launches are again practical.

Augusta,

If you are currently in China, you should be aware that you may be
putting yourself in legal jeopardy by pursuing these lines of inquiry.
Matters such as these are considered hihgly sensitive state secrets.
There have been numerous cases of people getting in trouble withthe
authorites for collecting publically available sensitive information
and redistributing it. So be careful!