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highschoolmom2010

  • 2 years 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.

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  1. highschoolmom2010
    • 2 years ago
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  2. highschoolmom2010
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  3. highschoolmom2010
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    @ganeshie8

  4. highschoolmom2010
    • 2 years ago
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    @thomaster

  5. ganeshie8
    • 2 years ago
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    do u see a right triangle in that cosmic jungle ?

  6. ganeshie8
    • 2 years ago
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    |dw:1376506909669:dw|

  7. highschoolmom2010
    • 2 years ago
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    yes

  8. ganeshie8
    • 2 years ago
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    lets solve question A first :- say, x is the distance between Sun and Mars

  9. ganeshie8
    • 2 years ago
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    |dw:1376507051350:dw|

  10. ganeshie8
    • 2 years ago
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    |dw:1376507103333:dw|

  11. ganeshie8
    • 2 years ago
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    can u find that angle ? (look at the cosmic jungle pic again)

  12. ganeshie8
    • 2 years ago
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    that angle equals d-c = 103.8-55.2 = ?

  13. ganeshie8
    • 2 years ago
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    once u have that angle, u can find the x easily using an appropriate trig ratio

  14. highschoolmom2010
    • 2 years ago
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    48.68

  15. ganeshie8
    • 2 years ago
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    103.8 - 55.2 48.6

  16. ganeshie8
    • 2 years ago
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    its just 48.6

  17. ganeshie8
    • 2 years ago
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    how did u get 48.68 ?

  18. highschoolmom2010
    • 2 years ago
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    103.88accidentally pushed the |dw:1376507391898:dw|

  19. ganeshie8
    • 2 years ago
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    lol okie :)

  20. highschoolmom2010
    • 2 years ago
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    so now we know that <d =48.6 what do we do

  21. ganeshie8
    • 2 years ago
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    |dw:1376507462089:dw|

  22. ganeshie8
    • 2 years ago
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    u tell me, which ratio we can use here to find distance between Suna and Mars(x)

  23. highschoolmom2010
    • 2 years ago
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    |dw:1376507504635:dw|

  24. ganeshie8
    • 2 years ago
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    forget about million years. lets do the calculations in AUs which are simple

  25. highschoolmom2010
    • 2 years ago
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    we know hyp and adj SOH CAH TOA we use cos

  26. highschoolmom2010
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    how do i do that

  27. ganeshie8
    • 2 years ago
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    yes cos ! and pls use AUs...

  28. highschoolmom2010
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    how do i do that

  29. ganeshie8
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    and the question is also asking u for AUs oly

  30. ganeshie8
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    |dw:1376507639742:dw|

  31. ganeshie8
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    hyp = x adj = 1 AU

  32. highschoolmom2010
    • 2 years ago
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    oh ok so i just put 1 AU not 93 million okie :D

  33. ganeshie8
    • 2 years ago
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    AU is just an unit, like meter or second. so dont bother about it much :)

  34. ganeshie8
    • 2 years ago
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    yes :)

  35. ganeshie8
    • 2 years ago
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    cos 48.6 = 1/x solve x

  36. ganeshie8
    • 2 years ago
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    do this, and do the Jupiter problem also same way. i need to go have dinner. brb.

  37. highschoolmom2010
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    \[\cos 48.6=\frac{ 1 }{ x }\] \[x *\cos 48.6=\frac{ 1 }{ ?x }*x\] \[x \cos 48.6=1\]

  38. highschoolmom2010
    • 2 years ago
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    \[\frac{x \cos 46.8 }{ \cos 46.8 }=\frac{ 1 }{ \cos 46.8 }\] \[x=\frac{ 1 }{ \cos 46.8 }\]

  39. highschoolmom2010
    • 2 years ago
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    do i do the inverse now

  40. ganeshie8
    • 2 years ago
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    just plugin that \(\large x = \frac{1}{\cos 48.6}\)

  41. ganeshie8
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    you should get x = 1.5 AU approx.. try the Jupiter problem...

  42. highschoolmom2010
    • 2 years ago
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    |dw:1376587258601:dw|

  43. highschoolmom2010
    • 2 years ago
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    |dw:1376587399528:dw|

  44. highschoolmom2010
    • 2 years ago
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    \[\cos 100.8=\frac{ 1 }{ x }\] \[(x)* \cos 100.8=\frac{ 1 }{ x }*x\] \[ X \cos 100.8=1\] \[\frac{ x \cos 100.8 }{ \cos 100.8 }=\frac{ 1 }{ \cos 100.8 }\]

  45. ganeshie8
    • 2 years ago
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    angle is not 100.8

  46. ganeshie8
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    |dw:1376587971593:dw|

  47. ganeshie8
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    for jupitor c = 21.9, d = 100.8 angle = d-c = ?

  48. highschoolmom2010
    • 2 years ago
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    oh... 78.9

  49. ganeshie8
    • 2 years ago
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    yes do it again :)

  50. highschoolmom2010
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    \[\cos 78.9=\frac{ 1 }{ x }\] \[(x)* \cos 78.9=\frac{ 1 }{ x }*(x)\] \[x \cos 78.9=1\] \[\frac{ x \cos 78.9 }{\cos 78.9 }=\frac{ 1 }{ \cos 78.9 }\] \[x \approx 5.19\]

  51. highschoolmom2010
    • 2 years ago
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    @ganeshie8

  52. ganeshie8
    • 2 years ago
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    perfect !

  53. ganeshie8
    • 2 years ago
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    now tell me this, did u get why we have been doing d-c for angle ?

  54. highschoolmom2010
    • 2 years ago
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    no not really

  55. ganeshie8
    • 2 years ago
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    look at the origianal cosmic pic, you wil understand

  56. ganeshie8
    • 2 years ago
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    observe that, \(d\) is the angle moved by earth

  57. ganeshie8
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    and \(c\) is the anle movied by the other planet in same time

  58. highschoolmom2010
    • 2 years ago
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    i see that

  59. ganeshie8
    • 2 years ago
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    \(d-c\) gives u the angle in that right triangle (visually u need to **see** it)

  60. ganeshie8
    • 2 years ago
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    |dw:1376589514631:dw|

  61. ganeshie8
    • 2 years ago
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    |dw:1376589569683:dw|

  62. ganeshie8
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    that entire angle is \(d\)

  63. highschoolmom2010
    • 2 years ago
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    |dw:1376589610421:dw| right ?

  64. ganeshie8
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    that part is \(c\)

  65. ganeshie8
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    yes, right !

  66. ganeshie8
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    So, whats the angle in that triangle ?

  67. ganeshie8
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    |dw:1376589698138:dw|

  68. highschoolmom2010
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    78.9

  69. ganeshie8
    • 2 years ago
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    uhh i mean in terms of \(d\) and \(c\)

  70. highschoolmom2010
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    im not sure what u mean

  71. ganeshie8
    • 2 years ago
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    |dw:1376589806634:dw|

  72. highschoolmom2010
    • 2 years ago
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    oh ok

  73. ganeshie8
    • 2 years ago
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    angle in the triangle equals \(d - c\) you worked the problem correctly ! just wanted u to see why we did \(100.8-21.9 \)

  74. ganeshie8
    • 2 years ago
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    hope it makes sense, the problem is easy actually - except for the fancy copernicus and planets words..

  75. highschoolmom2010
    • 2 years ago
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    yea the AU threw me off

  76. ganeshie8
    • 2 years ago
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    haha i thought so :)

  77. highschoolmom2010
    • 2 years ago
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    i think that was just uncalled for work

  78. ganeshie8
    • 2 years ago
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    hmm -_-

  79. highschoolmom2010
    • 2 years ago
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    ty @ganeshie8

  80. ganeshie8
    • 2 years ago
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    np :)

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