Question

If angular diameter of earth is radian observed from a far planet. If distance between two extreme points on earth is D then distance of planet from earth is

Answer 1

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Answer 2

Answer:

Concept :

The distances between planets will differ depending on where they are in their orbit around the Sun. At times, the distances will be shorter, but at other times, they will be longer. Because the planets have eccentric orbits, none of them are perfect circles, this is the case. Mercury's distance from Earth, for example, can fluctuate from 77 million kilometres at its closest point to 222 million kilometres at its furthest point. The distances between planets vary greatly based on their position in their orbit path.

Given :

If the earth's angular diameter is measured in radians from a distant planet. If the distance between two earth's most extreme points is D, then distance of planet from earth is

Find :

To find the distance of planet from earth

Answer :

the distance of planet from earth is

$d=\frac{D cosec .\pi }{2}$

The Earth orbits the Sun at a distance of 149 million kilometres (93 million miles). Venus orbits the Sun at a distance of around 108 million kilometres (67 million miles).

Steps :

$\frac{sin.\pi }{2} =\frac{D}{d}$

$d=\frac{D}{sin\frac{\pi }{2} }$

$d=\frac{D cosec \pi }{2}$

With Venus at its farthest from the Sun and Earth at its closest, the closest approach would be 39.5 million kilometres (23.6 million miles). This is a once-in-a-lifetime incident. When Venus would be between the Sun and earth, a position called as "inferior conjunction," it comes the closest to Earth of any planet. It is located in an inferior conjunction at a distance of 41 million kilometres. Venus is around 264 million kilometres from the Earth at'superior conjunction,' when she is on the opposite side of the Sun and not visible to us.

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