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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.
 8 months ago
 8 months ago
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.
 8 months ago
 8 months ago

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ganeshie8Best ResponseYou've already chosen the best response.1
do u see a right triangle in that cosmic jungle ?
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
dw:1376506909669:dw
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
lets solve question A first : say, x is the distance between Sun and Mars
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
dw:1376507051350:dw
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
dw:1376507103333:dw
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
can u find that angle ? (look at the cosmic jungle pic again)
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
that angle equals dc = 103.855.2 = ?
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
once u have that angle, u can find the x easily using an appropriate trig ratio
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
how did u get 48.68 ?
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
103.88accidentally pushed the dw:1376507391898:dw
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
so now we know that <d =48.6 what do we do
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
dw:1376507462089:dw
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
u tell me, which ratio we can use here to find distance between Suna and Mars(x)
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
dw:1376507504635:dw
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
forget about million years. lets do the calculations in AUs which are simple
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
we know hyp and adj SOH CAH TOA we use cos
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
how do i do that
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
yes cos ! and pls use AUs...
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
how do i do that
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
and the question is also asking u for AUs oly
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
dw:1376507639742:dw
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
oh ok so i just put 1 AU not 93 million okie :D
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
AU is just an unit, like meter or second. so dont bother about it much :)
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
cos 48.6 = 1/x solve x
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
do this, and do the Jupiter problem also same way. i need to go have dinner. brb.
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
\[\cos 48.6=\frac{ 1 }{ x }\] \[x *\cos 48.6=\frac{ 1 }{ ?x }*x\] \[x \cos 48.6=1\]
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
\[\frac{x \cos 46.8 }{ \cos 46.8 }=\frac{ 1 }{ \cos 46.8 }\] \[x=\frac{ 1 }{ \cos 46.8 }\]
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
do i do the inverse now
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
just plugin that \(\large x = \frac{1}{\cos 48.6}\)
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
you should get x = 1.5 AU approx.. try the Jupiter problem...
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
dw:1376587258601:dw
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
dw:1376587399528:dw
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
\[\cos 100.8=\frac{ 1 }{ x }\] \[(x)* \cos 100.8=\frac{ 1 }{ x }*x\] \[ X \cos 100.8=1\] \[\frac{ x \cos 100.8 }{ \cos 100.8 }=\frac{ 1 }{ \cos 100.8 }\]
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
dw:1376587971593:dw
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
for jupitor c = 21.9, d = 100.8 angle = dc = ?
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
\[\cos 78.9=\frac{ 1 }{ x }\] \[(x)* \cos 78.9=\frac{ 1 }{ x }*(x)\] \[x \cos 78.9=1\] \[\frac{ x \cos 78.9 }{\cos 78.9 }=\frac{ 1 }{ \cos 78.9 }\] \[x \approx 5.19\]
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
now tell me this, did u get why we have been doing dc for angle ?
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
no not really
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
look at the origianal cosmic pic, you wil understand
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
observe that, \(d\) is the angle moved by earth
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
and \(c\) is the anle movied by the other planet in same time
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
\(dc\) gives u the angle in that right triangle (visually u need to **see** it)
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
dw:1376589514631:dw
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
dw:1376589569683:dw
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
that entire angle is \(d\)
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
dw:1376589610421:dw right ?
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
So, whats the angle in that triangle ?
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
dw:1376589698138:dw
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
uhh i mean in terms of \(d\) and \(c\)
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
im not sure what u mean
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
dw:1376589806634:dw
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
angle in the triangle equals \(d  c\) you worked the problem correctly ! just wanted u to see why we did \(100.821.9 \)
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
hope it makes sense, the problem is easy actually  except for the fancy copernicus and planets words..
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
yea the AU threw me off
 8 months ago

ganeshie8Best ResponseYou've already chosen the best response.1
haha i thought so :)
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
i think that was just uncalled for work
 8 months ago

highschoolmom2010Best ResponseYou've already chosen the best response.1
ty @ganeshie8
 8 months ago
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