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contribution.
Before moving on to the higher order calculations, however, it is instructive to see that such a
cancellation really occurs in the field and consequently the equations of motion up to 0.5 PN
order.
First, we show the independence of the body zone radius 
in the 0.5 PN field. Returning back to
the derivation of the 1 PN 
with care for the 
dependence (see Equation (128
)), we get
as 
where 
does not depend on 
while 
does. In order to
evaluate the 
dependent part of 
, 
, we use the fact that the integral of 
over the near
zone does not depend on the size of the body zone. (Notice that 
is defined as the volume integral of
over 
.) In fact, from the relevant expression of the pseudotensor, we obtain at the lowest order
Hence we find 
The above equation shows us that the 0.5 PN field is
independent of 
and fully expressed by the 
independent energy 
, or mass up to 0.5 PN
order.
In the similar manner we split 
as 
and obtain 
from the definition of 
. Thus from the fact that 
, we find
that the 0.5 PN momentum-velocity relation does not depend on 
: 
.
Finally evaluating the surface integrals in the general form of equations of motion using the
“renormalized” (barred) moments, we find that the equations of motion are independent of 
as was
expected.
As remarked in Section 4.5 from now on we use the same symbol for the renormalized moments as for the “bare” moments henceforth as before for notational simplicity.
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