{"id":200895,"date":"2025-03-14T05:15:21","date_gmt":"2025-03-14T05:15:21","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=200895"},"modified":"2025-03-14T05:15:23","modified_gmt":"2025-03-14T05:15:23","slug":"the-mean-distance-of-mars-from-the-sun-is-142-million-miles","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/14\/the-mean-distance-of-mars-from-the-sun-is-142-million-miles\/","title":{"rendered":"The mean distance of Mars from the Sun is 142 million miles"},"content":{"rendered":"\n

The mean distance of Mars from the Sun is 142 million miles. If the perihelion of Mars is 128.5 million miles, what is the aphelion? Find an equation for the orbit of Mars about the Sun.<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

Mars’s orbit around the Sun is elliptical, characterized by two key distances: perihelion (closest approach) and aphelion (farthest point). The mean distance from Mars to the Sun is approximately 142 million miles, which represents the semi-major axis of its elliptical orbit. Given that the perihelion distance is 128.5 million miles, we can calculate the aphelion distance using the relationship:<\/p>\n\n\n\n

Aphelion Distance (r_max) = 2 \u00d7 Semi-Major Axis (a) – Perihelion Distance (r_min)<\/strong><\/p>\n\n\n\n

Applying the provided values:<\/p>\n\n\n\n

r_max = 2 \u00d7 142 million miles – 128.5 million miles = 155.5 million miles<\/strong><\/p>\n\n\n\n

This calculation indicates that Mars’s aphelion distance is 155.5 million miles.<\/p>\n\n\n\n

To derive an equation for Mars’s orbit, we utilize the standard form of the equation for an elliptical orbit in polar coordinates:<\/p>\n\n\n\n

r(\u03b8) = (p) \/ (1 + \u03b5 \u00d7 cos(\u03b8))<\/strong>\ue206<\/p>\n\n\n\n

Where:<\/p>\n\n\n\n