To solve the problem of arranging the planets in increasing order based on their gravitational forces, we start with the provided table of planetary gravities:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Planet} & \text{Gravity} \left( \text{m}/\text{s}^2 \right) \\
\hline
\text{Earth} & 9.8 \\
\text{Mercury} & 3.7 \\
\text{Neptune} & 11.2 \\
\text{Uranus} & 8.9 \\
\hline
\end{array}
\][/tex]
Step-by-Step Solution:
1. Extract the Gravity Values and Corresponding Planets:
- Earth: \( 9.8 \, \text{m}/\text{s}^2 \)
- Mercury: \( 3.7 \, \text{m}/\text{s}^2 \)
- Neptune: \( 11.2 \, \text{m}/\text{s}^2 \)
- Uranus: \( 8.9 \, \text{m}/\text{s}^2 \)
2. List the Gravity Values in Numerical Order:
- 3.7 (Mercury)
- 8.9 (Uranus)
- 9.8 (Earth)
- 11.2 (Neptune)
3. Match the Ordered Gravity Values to Their Planets:
- 3.7 \( \rightarrow \) Mercury
- 8.9 \( \rightarrow \) Uranus
- 9.8 \( \rightarrow \) Earth
- 11.2 \( \rightarrow \) Neptune
4. Write the Planets in Increasing Order of Their Gravities:
- Mercury
- Uranus
- Earth
- Neptune
Thus, the planets arranged in increasing order based on a person's weight (which is directly proportional to the gravitational force) are:
Mercury, Uranus, Earth, Neptune.
