Visual guide to the solar system showing planets and their orbital periods around the Sun.

Problem Description:

The image provides information about the solar system, including the planets and their orbital periods around the Sun. The task is to analyze the data and explain the relationship between a planet's distance from the Sun and its orbital period.

Solution Explanation:

#### Step 1: Understanding the Key Information
- Solar System Overview: The solar system consists of the Sun and the planets that orbit it. The planets are listed in order from the Sun: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.
- Orbital Periods: The time it takes for a planet to complete one orbit around the Sun is called its orbital period or year. This period varies depending on the planet's distance from the Sun.
- Distance and Orbital Period Relationship: The farther a planet is from the Sun, the longer it takes to complete one orbit. This relationship is a fundamental principle in astronomy, described by Kepler's Third Law of Planetary Motion.

#### Step 2: Analyzing the Data
The image provides the orbital periods of each planet in Earth years or days:
- Mercury: 88 days
- Venus: 224 days
- Earth: 365 days
- Mars: 687 days
- Jupiter: 11.8 years
- Saturn: 29.8 years
- Uranus: 84.3 years
- Neptune: 165 years

#### Step 3: Observing the Pattern
From the data:
- Closer Planets (Mercury, Venus, Earth, Mars): These planets are closer to the Sun and have shorter orbital periods. For example, Mercury, being the closest planet, has the shortest orbital period (88 days).
- Farther Planets (Jupiter, Saturn, Uranus, Neptune): These planets are farther from the Sun and have much longer orbital periods. For example, Neptune, being the farthest planet, has the longest orbital period (165 years).

#### Step 4: Explaining the Relationship
The relationship between a planet's distance from the Sun and its orbital period can be explained using Kepler's Third Law of Planetary Motion. This law states that the square of the orbital period (\(T\)) of a planet is proportional to the cube of the semi-major axis (\(a\)) of its orbit:
\[
T^2 \propto a^3
\]
In simpler terms:
- A planet farther from the Sun has a larger orbit (larger \(a\)).
- A larger orbit means the planet must travel a greater distance to complete one orbit.
- Since the gravitational force from the Sun decreases with distance, the planet moves more slowly in its orbit.
- As a result, the farther a planet is from the Sun, the longer it takes to complete one orbit.

#### Step 5: Conclusion
The data and the observed pattern confirm that the farther a planet is from the Sun, the longer it takes to orbit the Sun. This is consistent with Kepler's Third Law of Planetary Motion, which mathematically describes this relationship.

Final Answer:

\[
\boxed{\text{The farther a planet is from the Sun, the longer it takes for it to orbit the Sun.}}
\]