Venus rotates in a nearly circular orbit around the sun. The...

Venus rotates in a nearly circular orbit around the sun. The largest angle formed by Venus, Earth, and the sun is $46.5^{\circ} .$ The distance from Earth to the sun is approximately 149,000,000 kilometers. What is the orbital radius $r$ of Venus? Round to the nearest million kilometers. $108,000,000 \mathrm{km}$. (FIGURE CAN'T COPY)

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Maximum Elongation of Inferior Planets

Maximum elongation refers to the greatest angular separation between an inferior planet and the sun as seen from Earth. This specific angular measurement serves as a key observational parameter that, under the assumption of circular orbits, helps in calculating the orbital radius of the planet using trigonometric relationships.

Trigonometric Relationships in Astronomy

Trigonometry is essential in relating observed angular measurements to actual distances in celestial mechanics. In problems like these, functions such as sine are used to express the proportional relationships in a right triangle, where the known angle and distance from one object (such as Earth) help determine the unknown orbital radius of another object.

Circular Orbit Approximation

This concept involves assuming that a planet's orbit around the sun is a perfect circle. Such an approximation simplifies calculations by treating the distance between the planet and the sun as constant, allowing for the use of simple geometric and trigonometric techniques to solve for orbital parameters.

Transcript

Please give Ace some feedback