Question

S. 0.10701
When the planet Jupiter is at a distance of
824.7 million kilometers from the Earth,
its angular diameter is measured to be
35.72" of arc. Calculate the diameter of
the Jupiter.​

Answer 1

Answer:

vnmurty

Angular diameter is the angle subtended by the diameter of the planet at the eye..

let the angular diameter be Ф.

Let the eye be at A,  the center of the planet be O, and the diameter of the planet perpendicular to the line AO be BOC.

   Ф = angular diameter = angle CAB = 2 * angle OAC

     OB = OC = radius of the planet.

       AO = 824.7 million km

   tan (Ф/2) =   OB / OA

  Diameter of Jupiter = 2 * OB = 2 * 824.7 * 10⁶ * tan [ 35.72 / (2 * 60 *  60) ]⁰

                     =   142, 817.8 km

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Answer 2

Given information:-

r = 824.7*10^6 km , Θ = 35.72" arc

To find

l = ?

Solution

First convert Θ value in kilometres.

$\frac{35.72}{3600} \times \frac{22}{ 7 \times 180} rad \\ \\ 824.7 \times 10 ^{6} km$

Note:- here, we divided by 3600 that is to convert in kilometres and then π\180 to convert in radian.

Now, Θ = l / r , r*Θ = l

$324.7 \times 10 ^{6} \times \frac{35.72}{3600} \times \frac{22}{7 \times 180} = l$

$= \frac{142.87 \times 10 ^{6} }{10 ^{3} }$

$= 142.87 \times 10 ^{3}$

So, when we convert in scientific notation then,

$= 1.42 \times 10 ^{5} km$

Therefore , Diameter of Jupiter = 1.42*10^5km