the longest and shortest distance of eareth from sun are r1 and r2. what is the distance of the earth from the sun when it is perpendicular to it
To find the distance of Earth from the Sun when it is perpendicular to it, we need to understand the concept of Earth's orbital eccentricity.
The Earth's orbit around the Sun is not a perfect circle but rather an ellipse. As a result, the distance between the Earth and the Sun varies throughout its orbit. The point in the orbit where Earth is closest to the Sun is called perihelion, and the point where it is farthest is called aphelion.
Given that the longest and shortest distances of Earth from the Sun are denoted as r1 and r2 respectively, we can infer that r1 represents the distance at perihelion (closest distance), and r2 represents the distance at aphelion (farthest distance).
When Earth is perpendicular to the Sun, it is neither at perihelion nor aphelion. It is at a point in between these two extremes, which is called the semi-major axis. The semi-major axis is equal to the average distance between the Earth and the Sun throughout its elliptical orbit.
To find the distance of the Earth from the Sun when it is perpendicular, we need to calculate the semi-major axis. This can be done by using the formula:
semi-major axis = (r1 + r2) / 2
So, the distance of Earth from the Sun when it is perpendicular is equal to the semi-major axis value obtained from the formula.