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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 34 "Mercury 1 - Mercury's day
and year" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 337 "This worksh
eet animates the orbit of Mercury around the sun and indicates its rot
ation. This worksheet shows the motion from the heliocentric (sun-cent
ered) point of view. To begin, we specify the positions of the sun (s
tationary at the origin) and Mercury, and of an object on the surface \+
of Mercury that rotates along with the planet:" }}}{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 "oposx := mposx + 0.5 * cos
(2*t);\noposy := mposy + 0.5 * sin(2*t);\n" }}}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 205 "Now we make circles (large for the sun and smaller for M
ercury) and a line (from the center of Mercury through the position of
the object) so that we can track the positions of things during our a
nimation:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 183 "sun := [sposx+cos(s), sposy+sin(s), s=0..2*Pi];\n\nmercury := [
mposx + 0.5*cos(s), mposy +0.5*sin(s), s=0..2*Pi];\n\nobjectline := [(
1-s)*mposx + s*oposx, (1-s)*mposy + s*oposy, s=0..2];\n" }}}{EXCHG
{PARA 0 "" 0 "" {TEXT -1 24 "Now we do the animation:" }{MPLTEXT 1 0
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "with(plots, animate)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "animate(\{sun, mercury
, objectline\},t=0..2*Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 183 "Th
at one didn't work, because we didn't specify the parameters a and b i
n Mercury's orbit (so Maple had no way of knowing where to draw the pl
anet). We specify them now and try again:" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "b:=15; a:=3;" }}}{EXCHG
{PARA 0 "" 0 "" {TEXT -1 171 "This animation statement has lots of opt
ions specified so that things are drawn to scale and lots of frames be
cause we want to observe a complete revolution of the planet." }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "animate
(\{sun, mercury, objectline\},t=0..2*Pi,color=blue,axes=none, scaling=
constrained,frames=32);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}}{MARK "1 0 0" 12 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }