<s>
A	O
numerical	B-Algorithm
model	I-Algorithm
of	I-Algorithm
the	I-Algorithm
Solar	I-Algorithm
System	I-Algorithm
is	O
a	O
set	O
of	O
mathematical	O
equations	O
,	O
which	O
,	O
when	O
solved	O
,	O
give	O
the	O
approximate	O
positions	O
of	O
the	O
planets	O
as	O
a	O
function	O
of	O
time	O
.	O
</s>
<s>
The	O
simplest	O
way	O
to	O
solve	O
these	O
is	O
just	O
the	O
Euler	B-Language
algorithm	O
,	O
which	O
in	O
essence	O
is	O
the	O
linear	O
addition	O
described	O
above	O
.	O
</s>
<s>
This	O
is	O
what	O
happens	O
when	O
using	O
the	B-Algorithm
Runge-Kutta	I-Algorithm
method	I-Algorithm
,	O
especially	O
the	O
one	O
of	O
grade	O
4	O
or	O
5	O
are	O
most	O
useful	O
.	O
</s>
<s>
The	O
most	O
common	O
method	O
used	O
is	O
the	O
leapfrog	B-Algorithm
method	I-Algorithm
due	O
to	O
its	O
good	O
long	O
term	O
energy	O
conservation	O
.	O
</s>
<s>
If	O
this	O
is	O
not	O
done	O
one	O
is	O
almost	O
certain	O
to	O
see	O
a	O
simulation	O
abandoned	O
in	O
the	O
middle	O
of	O
a	O
calculation	O
on	O
a	O
floating	B-Algorithm
point	I-Algorithm
overflow	B-Algorithm
or	O
underflow	B-Algorithm
,	O
and	O
if	O
not	O
that	O
bad	O
,	O
still	O
accuracy	O
is	O
likely	O
to	O
get	O
lost	O
due	O
to	O
truncation	B-Algorithm
errors	O
.	O
</s>
