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'
a star and planetary system governed by newton's laws.
'
when the escape velocity of a planet is exceded, it's trajectory turns red
'
the range of x values on the screen is -130 to +130
'
the range of y values on the screen is -100 to +100
WINDOW
-640
,
-512
,
640
,
512
func
gryb
(
yb
,
yp
,
ys
,
yt
) =
mp
* (
yp
-
yb
) /
rbp
+
ms
* (
ys
-
yb
) /
rbs
+
mt
* (
yt
-
yb
) /
rbt
func
grxb
(
xb
,
xp
,
xs
,
xt
) =
mp
* (
xp
-
xb
) /
rbp
+
ms
* (
xs
-
xb
) /
rbs
+
mt
* (
xt
-
xb
) /
rbt
func
gryp
(
yb
,
yp
,
ys
,
yt
) =
ms
* (
ys
-
yp
) /
rps
+
mb
* (
yb
-
yp
) /
rbp
+
mt
* (
yt
-
yp
) /
rpt
func
grxp
(
xb
,
xp
,
xs
,
xt
) =
ms
* (
xs
-
xp
) /
rps
+
mb
* (
xb
-
xp
) /
rbp
+
mt
* (
xt
-
xp
) /
rpt
func
grxs
(
xb
,
xp
,
xs
,
xt
) =
mp
* (
xp
-
xs
) /
rps
+
mb
* (
xb
-
xs
) /
rbs
+
mt
* (
xt
-
xs
) /
rst
func
grys
(
yb
,
yp
,
ys
,
yt
) =
mp
* (
yp
-
ys
) /
rps
+
mb
* (
yb
-
ys
) /
rbs
+
mt
* (
yt
-
ys
) /
rst
func
grxt
(
xb
,
xp
,
xs
,
xt
) =
mb
* (
xb
-
xt
) /
rbt
+
mp
* (
xp
-
xt
) /
rpt
+
ms
* (
xs
-
xt
) /
rst
func
gryt
(
yb
,
yp
,
ys
,
yt
) =
mb
* (
yb
-
yt
) /
rbt
+
mp
* (
yp
-
yt
) /
rpt
+
ms
* (
ys
-
yt
) /
rst
PRINT
"
automatic momentum zero
"
INPUT
"
central mass (50000)
"
; mb
xb
=
0
:
yb
=
0
INPUT
"
primary mass (2000)
"
; mp
INPUT
"
initial primary x (400)
"
; xp
INPUT
"
initial primary y (0)
"
; yp
zxp
= -
yp
* (
mb
/ (
xp
^
2
+
yp
^
2
) ^
1.5
) ^ .
5
zyp
=
xp
* (
mb
/ (
xp
^
2
+
yp
^
2
) ^
1.5
) ^ .
5
INPUT
"
circular orbit ? y/n
"
; acc$:
IF
acc$ =
"
y
"
THEN
GOTO
10
PRINT
"
primary x-circular velo.=
"
; zxp
INPUT
"
initial dx/dt
"
; zxp
PRINT
"
primary y-circular velo.=
"
; zyp
INPUT
"
initial dy/dt
"
; zyp
10
INPUT
"
secondary mass (1000)
"
; ms
INPUT
"
initial secondary x (0)
"
; xs
INPUT
"
initial secondary y (300)
"
; ys
zxs
= -
ys
* (
mb
/ (
xs
^
2
+
ys
^
2
) ^
1.5
) ^ .
5
zys
=
xs
* (
mb
/ (
xs
^
2
+
ys
^
2
) ^
1.5
) ^ .
5
INPUT
"
circular orbit ? y/n
"
; acc$:
IF
acc$ =
"
y
"
THEN
GOTO
20
PRINT
"
secondary x-circular velo.=
"
; zxs
INPUT
"
initial secondary dx/dt
"
; zxs
PRINT
"
secondary y-circular velo.=
"
; zys
INPUT
"
initial secondary dy/dt
"
; zys
20
INPUT
"
tertiary mass (500)
"
; mt
INPUT
"
initial tertiary x (-300)
"
; xt
INPUT
"
initial tertiary y (-400)
"
; yt
zxt
= -
yt
* (
mb
/ (
xt
^
2
+
yt
^
2
) ^
1.5
) ^ .
5
zyt
=
xt
* (
mb
/ (
xt
^
2
+
yt
^
2
) ^
1.5
) ^ .
5
INPUT
"
circular orbit ? y/n
"
; acc$:
IF
acc$ =
"
y
"
THEN
GOTO
30
PRINT
"
tertiary x-circular velo.=
"
; zxt
INPUT
"
initial tertiary dx/dt
"
; zxt
PRINT
"
tertiary y-circular velo.=
"
; zyt
INPUT
"
initial tertiary dy/dt
"
; zyt
30
INPUT
"
final t (1600)
"
; tf
INPUT
"
number of intervals (800000)
"
; n
zxb
= -(
mp
*
zxp
+
ms
*
zxs
+
mt
*
zxt
) /
mb
zyb
= -(
mp
*
zyp
+
ms
*
zys
+
mt
*
zyt
) /
mb
h
=
tf
/
n
CLS
FOR
q
=
1
TO
n
rbp
= ((
xb
-
xp
) ^
2
+ (
yb
-
yp
) ^
2
) ^
1.5
rbs
= ((
xb
-
xs
) ^
2
+ (
yb
-
ys
) ^
2
) ^
1.5
rps
= ((
xp
-
xs
) ^
2
+ (
yp
-
ys
) ^
2
) ^
1.5
rbt
= ((
xb
-
xt
) ^
2
+ (
yb
-
yt
) ^
2
) ^
1.5
rpt
= ((
xp
-
xt
) ^
2
+ (
yp
-
yt
) ^
2
) ^
1.5
rst
= ((
xs
-
xt
) ^
2
+ (
ys
-
yt
) ^
2
) ^
1.5
kxb1
=
h
* zxb:
lxb
=
h
*
grxb
(
xb
,
xp
,
xs
,
xt
)
kyb1
=
h
* zyb:
lyb
=
h
*
gryb
(
yb
,
yp
,
ys
,
yt
)
kxp1
=
h
* zxp:
lxp
=
h
*
grxp
(
xb
,
xp
,
xs
,
xt
)
kyp1
=
h
* zyp:
lyp
=
h
*
gryp
(
yb
,
yp
,
ys
,
yt
)
kxs1
=
h
* zxs:
lxs
=
h
*
grxs
(
xb
,
xp
,
xs
,
xt
)
kys1
=
h
* zys:
lys
=
h
*
grys
(
yb
,
yp
,
ys
,
yt
)
kxt1
=
h
* zxt:
lxt
=
h
*
grxt
(
xb
,
xp
,
xs
,
xt
)
kyt1
=
h
* zyt:
lyt
=
h
*
gryt
(
yb
,
yp
,
ys
,
yt
)
kxb2
=
h
* (
zxb
+ .
5
*
lxb
)
kyb2
=
h
* (
zyb
+ .
5
*
lyb
)
kxp2
=
h
* (
zxp
+ .
5
*
lxp
)
kyp2
=
h
* (
zyp
+ .
5
*
lyp
)
kxs2
=
h
* (
zxs
+ .
5
*
lxs
)
kys2
=
h
* (
zys
+ .
5
*
lys
)
kxt2
=
h
* (
zxt
+ .
5
*
lxt
)
kyt2
=
h
* (
zyt
+ .
5
*
lyt
)
nxb
=
xb
+ .
5
* kxb1:
nyb
=
yb
+ .
5
* kyb1
nxp
=
xp
+ .
5
* kxp1:
nyp
=
yp
+ .
5
* kyp1
nxs
=
xs
+ .
5
* kxs1:
nys
=
ys
+ .
5
* kys1
nxt
=
xt
+ .
5
* kxt1:
nyt
=
yt
+ .
5
* kyt1
rbp
= ((
nxb
-
nxp
) ^
2
+ (
nyb
-
nyp
) ^
2
) ^
1.5
rbs
= ((
nxb
-
nxs
) ^
2
+ (
nyb
-
nys
) ^
2
) ^
1.5
rps
= ((
nxp
-
nxs
) ^
2
+ (
nyp
-
nys
) ^
2
) ^
1.5
rbt
= ((
nxb
-
nxt
) ^
2
+ (
nyb
-
nyt
) ^
2
) ^
1.5
rpt
= ((
nxp
-
nxt
) ^
2
+ (
nyp
-
nyt
) ^
2
) ^
1.5
rst
= ((
nxs
-
nxt
) ^
2
+ (
nys
-
nyt
) ^
2
) ^
1.5
lxb
=
h
*
grxb
(
nxb
,
nxp
,
nxs
,
nxt
)
lyb
=
h
*
gryb
(
nyb
,
nyp
,
nys
,
nyt
)
lxp
=
h
*
grxp
(
nxb
,
nxp
,
nxs
,
nxt
)
lyp
=
h
*
gryp
(
nyb
,
nyp
,
nys
,
nyt
)
lxs
=
h
*
grxs
(
nxb
,
nxp
,
nxs
,
nxt
)
lys
=
h
*
grys
(
nyb
,
nyp
,
nys
,
nyt
)
lxt
=
h
*
grxt
(
nxb
,
nxp
,
nxs
,
nxt
)
lyt
=
h
*
gryt
(
nyb
,
nyp
,
nys
,
nyt
)
kxb3
=
h
* (
zxb
+ .
5
*
lxb
)
kyb3
=
h
* (
zyb
+ .
5
*
lyb
)
kxp3
=
h
* (
zxp
+ .
5
*
lxp
)
kyp3
=
h
* (
zyp
+ .
5
*
lyp
)
kxs3
=
h
* (
zxs
+ .
5
*
lxs
)
kys3
=
h
* (
zys
+ .
5
*
lys
)
kxt3
=
h
* (
zxt
+ .
5
*
lxt
)
kyt3
=
h
* (
zyt
+ .
5
*
lyt
)
nxb
=
xb
+ .
5
* kxb2:
nyb
=
yb
+ .
5
* kyb2
nxp
=
xp
+ .
5
* kxp2:
nyp
=
yp
+ .
5
* kyp2
nxs
=
xs
+ .
5
* kxs2:
nys
=
ys
+ .
5
* kys2
nxt
=
xt
+ .
5
* kxt2:
nyt
=
yt
+ .
5
* kyt2
rbp
= ((
nxb
-
nxp
) ^
2
+ (
nyb
-
nyp
) ^
2
) ^
1.5
rbs
= ((
nxb
-
nxs
) ^
2
+ (
nyb
-
nys
) ^
2
) ^
1.5
rps
= ((
nxp
-
nxs
) ^
2
+ (
nyp
-
nys
) ^
2
) ^
1.5
rbt
= ((
nxb
-
nxt
) ^
2
+ (
nyb
-
nyt
) ^
2
) ^
1.5
rpt
= ((
nxp
-
nxt
) ^
2
+ (
nyp
-
nyt
) ^
2
) ^
1.5
rst
= ((
nxs
-
nxt
) ^
2
+ (
nys
-
nyt
) ^
2
) ^
1.5
lxb
=
h
*
grxb
(
nxb
,
nxp
,
nxs
,
nxt
)
lyb
=
h
*
gryb
(
nyb
,
nyp
,
nys
,
nyt
)
lxp
=
h
*
grxp
(
nxb
,
nxp
,
nxs
,
nxt
)
lyp
=
h
*
gryp
(
nyb
,
nyp
,
nys
,
nyt
)
lxs
=
h
*
grxs
(
nxb
,
nxp
,
nxs
,
nxt
)
lys
=
h
*
grys
(
nyb
,
nyp
,
nys
,
nyt
)
lxt
=
h
*
grxt
(
nxb
,
nxp
,
nxs
,
nxt
)
lyt
=
h
*
gryt
(
nyb
,
nyp
,
nys
,
nyt
)
kxb4
=
h
* (
zxb
+
lxb
):
kyb4
=
h
* (
zyb
+
lyb
)
kxp4
=
h
* (
zxp
+
lxp
):
kyp4
=
h
* (
zyp
+
lyp
)
kxs4
=
h
* (
zxs
+
lxs
):
kys4
=
h
* (
zys
+
lys
)
kxt4
=
h
* (
zxt
+
lxt
):
kyt4
=
h
* (
zyt
+
lyt
)
xb
=
xb
+ (
kxb1
+
2
*
kxb2
+
2
*
kxb3
+
kxb4
) /
6
yb
=
yb
+ (
kyb1
+
2
*
kyb2
+
2
*
kyb3
+
kyb4
) /
6
xp
=
xp
+ (
kxp1
+
2
*
kxp2
+
2
*
kxp3
+
kxp4
) /
6
yp
=
yp
+ (
kyp1
+
2
*
kyp2
+
2
*
kyp3
+
kyp4
) /
6
xs
=
xs
+ (
kxs1
+
2
*
kxs2
+
2
*
kxs3
+
kxs4
) /
6
ys
=
ys
+ (
kys1
+
2
*
kys2
+
2
*
kys3
+
kys4
) /
6
xt
=
xt
+ (
kxt1
+
2
*
kxt2
+
2
*
kxt3
+
kxt4
) /
6
yt
=
yt
+ (
kyt1
+
2
*
kyt2
+
2
*
kyt3
+
kyt4
) /
6
zxb
=
kxb4
/
h
:
zyb
=
kyb4
/
h
zxp
=
kxp4
/
h
:
zyp
=
kyp4
/
h
zxs
=
kxs4
/
h
:
zys
=
kys4
/
h
zxt
=
kxt4
/
h
:
zyt
=
kyt4
/
h
IF
q
=
n
THEN
GOTO
200
IF
(
INT
(
q
/
400000
) -
q
/
400000
) <>
0
THEN
GOTO
200
CLS
200
IF
zxp *
zxp
+
zyp
*
zyp
>
2
*
mb
/ (
rbp
^ (
1
/
3
))
THEN
cp
=
4
ELSE
cp
=
9
IF
zxs *
zxs
+
zys
*
zys
>
2
*
mb
/ (
rbs
^ (
1
/
3
))
THEN
cs
=
4
ELSE
cs
=
3
IF
zxt *
zxt
+
zyt
*
zyt
>
2
*
mb
/ (
rbt
^ (
1
/
3
))
THEN
ct
=
4
ELSE
ct
=
6
PSET xb,
yb
,
5
: PSET xp,
yp
,
cp
: PSET xs,
ys
,
cs
: PSET xt,
yt
,
ct
NEXT
q
END
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