Question

#Moderatorschallenge

pls tell me that why they have taken theta arc/radius. Is this formula of theta or not??


and pls also explain me that by they have taken radius S. As S is not radius it is distance.

pls clear my doubt.I am very confused. i want verified answer ☑️✅



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Answer 1

Measurement of Large Distance :

▪ It is not possible to measure distance between two astronomical objects with the help of meter scale.

▪ We can calculate such a large distance with the help of parallax method.

▪ This method is also called as Triangular method.

⏭ Please see the attachment for better understanding.

• AP = BP = S = radius
• Φ = Parallactic angle
• AB = b = basis

✒ We know that,

• Angle = arc ÷ radius

[Note : unit of angle → Radian]

✴ Therefore, S = Basis ÷ Parallactic angle

๏ Putting the values, we get

• Φ = b / S

• S = b / Φ

⏭ S >> b Therefore you can consider S as the distance b/w two astronomical objects.

✴ Additional information :

• 360° = 2π rad
• 1° = (π/180) rad
• 1° = 60'
• 1' = 60"

Answer 2

Answer:

We know about a formula for plane angle.

➸ Plane angle = Length of arc/radius.

The SI unit of plane angle is radian (rad).

The diagram is in the attachment 1.

➸ Fact : There are to dimensionless units (Plane angle and Solid angle).

DISTANCE OF ANY PLANET FROM EARTH —

The method used to measure large distances is called Parallax method.

For measuring a large distance, two points of observation are taken.

The difference between these two points is called the basis or b.

The distance we want to find is represented by D.

And we let the two points of observation as A and B.

Now, we let the angle between two directions from which the planet is viewed as theta.

This angle is said to be parallax angle or parallactic angle.

We can also say that, the angle theta will be << 1. (Reason : An angle formed from a very large distance is very small)

Now using the formula for solid angle, We. an find the angle :

➸ Plane angle = Length of arc/radius.

➸ Theta = basis/Distance

➸ ∅ = b/D.

Refer the attachment 2 for better understanding.

We can also observe in this situation that the distances of OA and OB is going to be equal. That is OA=OB=D.

Now, We can also conclude by :

➸ Distance * Theta = basis

➸ D * ∅ = b

➸ Distance = basis/Theta

➸ D = b/∅