To determine the order in which a person's weight would vary based on the given gravity values for each planet, we need to arrange the planets in increasing order of their gravitational acceleration. The person's weight on each planet is proportional to the gravity of that planet, so we will follow the gravity values to rank them accordingly.
The given values are:
1. Mercury: 3.7 m/s²
2. Uranus: 8.9 m/s²
3. Earth: 9.8 m/s²
4. Neptune: 11.2 m/s²
We start with the smallest value and proceed to the largest value. Thus, arranging these planets in increasing order of gravity (and thus, increasing order of a person's weight on the planet) results in:
Mercury < Uranus < Earth < Neptune
So the final arrangement is:
[tex]\[ \text{Mercury} < \text{Uranus} < \text{Earth} < \text{Neptune} \][/tex]
