Question

planet is observed from two diametrically opposite points A and B on the earth. The
angle subtended at the planet by the two directions of observation is 1012l
. Given the
diameter of the earth to be about 1.276x 107 m, compute the distance of the planet
from the earth.

Answer 1

Explanation:

The moon is observed from two diametrically opposite points A and B on Earth

The moon is observed from two diametrically opposite points A and B on earth. The angle subtended at the moon by two directions of observation is 1∘54′. The diameter of the earth is 1. 276×107m .

Answer 2

Given :-

▪ A planet is observed from two diametrically opposite points A and B on the earth.

▪ The angle subtended at the planet by the two direction of observations is 1°12' .

▪ The diameter of the earth is 1.26 × 10⁷ m

To Find :-

▪ Distance of the planet from the earth.

Solution :-

Imagine the planet as a vertex of a hypothetical Isosceles triangle whose base is the diameter of the earth and the other two sides be the distance of the planet from the earth which are at an angle of 1°12'.

First, we have to convert the angle into radians.

We know,

⇒ 60 minutes = 1°

So, 12 minutes will have

⇒ 1/60 × 12

⇒ 1/5

⇒ 0.2°

Angle between the two direction of measurements in radians

⇒ 1° + 0.2°

⇒ 1.2°

Multiply the given value by π/180

⇒ 1.2 × π/180

⇒ π / 150

⇒ 3.14 / 150 [ take , π = 3.14 ]

⇒ 0.0209 rad

Using the parallax method, we have

⇒ Distance from earth = radius / θ

⇒ d = (6.38 × 10⁶) / 0.0209

⇒ d = 305.26 × 10⁶

⇒ d = 3.05 × 10⁸ m

Hence, The distance of the planet from the earth is 3.05 × 10⁸ m.