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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 34 "Mercury 2 - Mercury's day
and year" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 73 "This workshe
et animates the orbit of Mercury around the sun and indicates" }}
{PARA 0 "" 0 "" {TEXT -1 94 "its rotation. This worksheet shows the mo
tion from the point of view of the center of Mercury." }}{PARA 0 "" 0
"" {TEXT -1 76 "To begin, we specify the positions of the sun (station
ary at the origin) and" }}{PARA 0 "" 0 "" {TEXT -1 87 "Mercury, and of
an object on the surface of Mercury that rotates along with the plane
t:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "sposx := 0;\nsposy :=
0;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "mposx := a*cos(t);
\nmposy := b*sin(t);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "o
posx := mposx + 0.5 * cos(2*t);\noposy := mposy + 0.5 * sin(2*t);\n" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Don't forget to define a and b:
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "a:=3; b:=15;" }}}{EXCHG {PARA
0 "" 0 "" {TEXT -1 205 "Now we make circles (large for the sun and sma
ller for Mercury) and a line (from the center of Mercury through the p
osition of the object) so that we can track the positions of things du
ring our animation:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 183 "sun := [sposx+cos(s), sposy+sin(s), s=0..2*Pi];\n\nm
ercury := [mposx + 0.5*cos(s), mposy +0.5*sin(s), s=0..2*Pi];\n\nobjec
tline := [(1-s)*mposx + s*oposx, (1-s)*mposy + s*oposy, s=0..2];\n" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 93 "Now we move Mercury to the center
of the picture by subtracting its position from everything:" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "spos2x
:= sposx - mposx;\nspos2y := sposy - mposy;\n\nmpos2x := mposx - mpos
x; \nmpos2y := mposy - mposy;\n\nopos2x := oposx - mposx;\nopos2y :=
oposy - mposy;\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Now we need \+
the circles and lines for these new positions:" }}{PARA 0 "> " 0 ""
{MPLTEXT 1 0 194 "sun2 := [spos2x+cos(s), spos2y+sin(s), s=0..2*Pi];\n
\nmercury2 := [mpos2x + 0.5*cos(s), mpos2y +0.5*sin(s), s=0..2*Pi];\n
\nobjectline2 := [(1-s)*mpos2x + s*opos2x, (1-s)*mpos2y + s*opos2y, s=
0..2];\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Now we can animate:"
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(plots,animate);" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "animate(\{sun2, mercury2, objectli
ne2\}, t=0..2*Pi,axes=none, color=blue, frames=32, scaling=constrained
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0"
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