To determine the order of the planets based on a person's weight, we first consider that a person's weight on a planet is directly proportional to the acceleration due to gravity on that planet. Therefore, the greater the gravity, the more a person would weigh.
Given the gravity values for the planets:
- Mercury: [tex]\(3.7 \, m/s^2\)[/tex]
- Earth: [tex]\(9.8 \, m/s^2\)[/tex]
- Neptune: [tex]\(11.2 \, m/s^2\)[/tex]
- Uranus: [tex]\(8.9 \, m/s^2\)[/tex]
We need to arrange these planets in increasing order of gravity, and thus, in increasing order of weight.
1. Mercury: [tex]\(3.7 \, m/s^2\)[/tex]
2. Uranus: [tex]\(8.9 \, m/s^2\)[/tex]
3. Earth: [tex]\(9.8 \, m/s^2\)[/tex]
4. Neptune: [tex]\(11.2 \, m/s^2\)[/tex]
So, if we arrange the planets in increasing order based on a person's weight, the order will be:
[tex]\[ \text{Mercury} < \text{Uranus} < \text{Earth} < \text{Neptune} \][/tex]
