At what time, in days, is Venus at its maximum …

Mathematics Questions
Short Answer
Step by Step Solution
Mathematics Questions

The planet Venus orbits the Sun every 225 days. Because of its elliptical orbit, the distance between Venus and the Sun periodically increases and decreases. The maximum distance of Venus from the Sun is 108.9 million kilometers, and the minimum distance of Venus from the Sun is 107.5 million kilometers. The planet reaches each of its maximum distance and minimum distance from the Sun once every 225 days. The sinusoidal function , given by , models the distance, in millions of kilometers, between Venus and the Sun as a function of time , in days. Based on the function , Venus is at its maximum distance from the Sun at time days.

Short Answer

Venus varies in distance from the Sun between 107.5 million kilometers and 108.9 million kilometers due to its orbital cycle, which takes approximately 225 days. The maximum distance occurs around 56 days into this cycle.

Step-by-Step Solution

Step 1: Understand the Distance Range

The planet Venus has a distinct distance from the Sun that varies. Its maximum distance is 108.9 million kilometers, while its minimum distance is 107.5 million kilometers. This fluctuation in distance occurs due to its orbit around the Sun, leading to its varying proximity.

Step 2: Frequency of Distance Changes

Venus undergoes a complete orbital cycle where it reaches both its maximum and minimum distances from the Sun. This entire cycle takes approximately 225 days. Within this period, the planet reaches its furthest and closest points relative to the Sun.

Step 3: Timing of Maximum Distance

According to the sinusoidal function describing Venus’s orbit, the planet achieves its maximum distance from the Sun at around 56 days into its orbit. This key time indicates when Venus is farthest from the Sun, highlighting an important aspect of its orbital dynamics.

Related Concepts

Distance Range

The differing measurements between the maximum and minimum distance of venus from the sun, specifically 108.9 million kilometers as the maximum and 107.5 million kilometers as the minimum.

Orbital Cycle

The complete journey that venus takes around the sun, which lasts approximately 225 days and includes reaching both its maximum and minimum distances.

Timing Of Maximum Distance

The specific point in venus’s orbit, occurring around 56 days after it begins its cycle, when the planet is farthest from the sun.

Table Of Contents
  1. The planet Venus orbits the Sun every 225 days. Because of its elliptical orbit, the distance between Venus and the Sun periodically increases and decreases. The maximum distance of Venus from the Sun is 108.9 million kilometers, and the minimum distance of Venus from the Sun is 107.5 million kilometers. The planet reaches each of its maximum distance and minimum distance from the Sun once every 225 days. The sinusoidal function , given by , models the distance, in millions of kilometers, between Venus and the Sun as a function of time , in days. Based on the function , Venus is at its maximum distance from the Sun at time days.

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