maximum elongation in the case of a planet is 50 degree find the distance between the planet and sun and the distance between the planet and earth. also find the orbital time period of the planet in years
Answers
In astronomy, a planet's elongation is the angular separation between the Sun and the planet, with Earth as the reference point. The greatest elongation of a given inferior planet occurs when this planet's position, in its orbital path around the Sun, is at tangent to the observer on Earth. Since an inferior planet is well within the area of Earth's orbit around the Sun, observation of its elongation should not pose that much a challenge (compared to deep-sky objects, for example). When a planet is at its greatest elongation, it appears farthest from the Sun as viewed from Earth, so its apparition is also best at that point.
An angle ε is drawn between two straight lines from Earth to the Sun, and from Earth to the planet. This is demonstrated for different positions along circular orbits, both for planets closer to the Sun (where the angle is always less than 90°), and for outer planets (for which the angle can range from 0° to 180°), while distinguishing east and west sides.
This diagram shows various possible elongations (ε), each of which is the angular distance between a planet and the Sun from Earth's perspective.
When an inferior planet is visible after sunset, it is near its greatest eastern elongation. When an inferior planet is visible before sunrise, it is near its greatest western elongation. The angle of the maximum elongation (east or west) for Mercury is between 18° and 28°, while that for Venus is between 45° and 47°. These values vary because the planetary orbits are elliptical rather than perfectly circular. Another factor contributing to this inconsistency is orbital inclination, in which each planet's orbital plane is slightly tilted relative to a reference plane, like the ecliptic and invariable planes.
Astronomical tables and websites, such as Heavens-Above, forecast when and where the planets reach their next maximum elongations.