highschoolmom2010
The Polish astronomer Nicolaus Copernicus devised a method for determining the sizes of the orbits of planets farther from the sun than Earth. His method involved noting the number
of days between the times that a planet was in the positions labeled A and B in the diagram. Using this time and the number of days in
each planet’s year, he calculated c and d.
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highschoolmom2010
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@ganeshie8
highschoolmom2010
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@thomaster
ganeshie8
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do u see a right triangle in that cosmic jungle ?
ganeshie8
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|dw:1376506909669:dw|
ganeshie8
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lets solve question A first :-
say, x is the distance between Sun and Mars
ganeshie8
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|dw:1376507051350:dw|
ganeshie8
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|dw:1376507103333:dw|
ganeshie8
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can u find that angle ? (look at the cosmic jungle pic again)
ganeshie8
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that angle equals d-c
= 103.8-55.2
= ?
ganeshie8
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once u have that angle, u can find the x easily using an appropriate trig ratio
ganeshie8
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103.8 - 55.2
48.6
ganeshie8
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its just 48.6
ganeshie8
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how did u get 48.68 ?
highschoolmom2010
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103.88accidentally pushed the |dw:1376507391898:dw|
ganeshie8
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lol okie :)
highschoolmom2010
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so now we know that <d =48.6 what do we do
ganeshie8
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|dw:1376507462089:dw|
ganeshie8
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u tell me, which ratio we can use here to find distance between Suna and Mars(x)
highschoolmom2010
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|dw:1376507504635:dw|
ganeshie8
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forget about million years.
lets do the calculations in AUs which are simple
highschoolmom2010
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we know hyp and adj
SOH CAH TOA
we use cos
highschoolmom2010
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how do i do that
ganeshie8
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yes cos !
and pls use AUs...
highschoolmom2010
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how do i do that
ganeshie8
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and the question is also asking u for AUs oly
ganeshie8
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|dw:1376507639742:dw|
ganeshie8
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hyp = x
adj = 1 AU
highschoolmom2010
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oh ok so i just put 1 AU not 93 million okie :D
ganeshie8
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AU is just an unit, like meter or second. so dont bother about it much :)
ganeshie8
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yes :)
ganeshie8
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cos 48.6 = 1/x
solve x
ganeshie8
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do this, and do the Jupiter problem also same way. i need to go have dinner. brb.
highschoolmom2010
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\[\cos 48.6=\frac{ 1 }{ x }\]
\[x *\cos 48.6=\frac{ 1 }{ ?x }*x\]
\[x \cos 48.6=1\]
highschoolmom2010
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\[\frac{x \cos 46.8 }{ \cos 46.8 }=\frac{ 1 }{ \cos 46.8 }\]
\[x=\frac{ 1 }{ \cos 46.8 }\]
highschoolmom2010
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do i do the inverse now
ganeshie8
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just plugin that
\(\large x = \frac{1}{\cos 48.6}\)
ganeshie8
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you should get x = 1.5 AU approx..
try the Jupiter problem...
highschoolmom2010
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|dw:1376587258601:dw|
highschoolmom2010
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|dw:1376587399528:dw|
highschoolmom2010
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\[\cos 100.8=\frac{ 1 }{ x }\]
\[(x)* \cos 100.8=\frac{ 1 }{ x }*x\]
\[ X \cos 100.8=1\]
\[\frac{ x \cos 100.8 }{ \cos 100.8 }=\frac{ 1 }{ \cos 100.8 }\]
ganeshie8
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angle is not 100.8
ganeshie8
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|dw:1376587971593:dw|
ganeshie8
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for jupitor c = 21.9, d = 100.8
angle = d-c
= ?
highschoolmom2010
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oh...
78.9
ganeshie8
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yes do it again :)
highschoolmom2010
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\[\cos 78.9=\frac{ 1 }{ x }\]
\[(x)* \cos 78.9=\frac{ 1 }{ x }*(x)\]
\[x \cos 78.9=1\]
\[\frac{ x \cos 78.9 }{\cos 78.9 }=\frac{ 1 }{ \cos 78.9 }\]
\[x \approx 5.19\]
highschoolmom2010
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@ganeshie8
ganeshie8
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perfect !
ganeshie8
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now tell me this, did u get why we have been doing d-c for angle ?
highschoolmom2010
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no not really
ganeshie8
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look at the origianal cosmic pic, you wil understand
ganeshie8
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observe that, \(d\) is the angle moved by earth
ganeshie8
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and \(c\) is the anle movied by the other planet in same time
highschoolmom2010
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i see that
ganeshie8
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\(d-c\) gives u the angle in that right triangle (visually u need to **see** it)
ganeshie8
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|dw:1376589514631:dw|
ganeshie8
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|dw:1376589569683:dw|
ganeshie8
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that entire angle is \(d\)
highschoolmom2010
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|dw:1376589610421:dw| right ?
ganeshie8
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that part is \(c\)
ganeshie8
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yes, right !
ganeshie8
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So, whats the angle in that triangle ?
ganeshie8
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|dw:1376589698138:dw|
ganeshie8
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uhh i mean in terms of \(d\) and \(c\)
highschoolmom2010
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im not sure what u mean
ganeshie8
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|dw:1376589806634:dw|
ganeshie8
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angle in the triangle equals \(d - c\)
you worked the problem correctly ! just wanted u to see why we did \(100.8-21.9 \)
ganeshie8
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hope it makes sense, the problem is easy actually - except for the fancy copernicus and planets words..
highschoolmom2010
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yea the AU threw me off
ganeshie8
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haha i thought so :)
highschoolmom2010
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i think that was just uncalled for work
ganeshie8
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hmm -_-
highschoolmom2010
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ty @ganeshie8
ganeshie8
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np :)