Answer :
To solve this problem, we need to determine certain parameters for various celestial objects and evaluate whether each object remains within its respective habitable zone. Here is a step-by-step analysis for each planet:
1. Earth:
- Major Axis: [tex]\( 15.209832 \, \text{cm} \)[/tex]
- Eccentricity: [tex]\( 0.017 \)[/tex]
- Scaled Distance Between Foci: [tex]\( 0.258 \, \text{cm} \)[/tex]
- Scaled Habitable Zone Range: [tex]\( 14.21 - 25.07 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? Yes
2. Kepler 79 b:
- Major Axis: [tex]\( 36.056 \, \text{cm} \)[/tex]
- Eccentricity: [tex]\( 0.0291 \)[/tex]
- Scaled Distance Between Foci: [tex]\( 1.049 \, \text{cm} \)[/tex]
- Scaled Habitable Zone Range: [tex]\( 511.98 - 1265.30 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
3. Kepler 442 b:
- Major Axis: [tex]\( 61.19 \, \text{cm} \)[/tex]
- Eccentricity: [tex]\( 0.04 \)[/tex]
- Scaled Distance Between Foci: Not provided
- Scaled Habitable Zone Range: [tex]\( 48.62 - 85.72 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
4. Kepler 432 b:
- Major Axis: [tex]\( 15.01 \, \text{cm} \)[/tex]
- Eccentricity: Not provided
- Scaled Distance Between Foci: [tex]\( 10.184 \, \text{cm} \)[/tex]
- Scaled Habitable Zone Range: [tex]\( 150.15 - 271.72 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
5. Kepler 18 b:
- Major Axis: [tex]\( 6.7 \, \text{cm} \)[/tex]
- Eccentricity: [tex]\( 0.0000 \)[/tex]
- Scaled Distance Between Foci: [tex]\( 0.0000 \, \text{cm} \)[/tex]
- Scaled Habitable Zone Range: [tex]\( 218.86 - 482.75 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
6. Kepler 186 f:
- Major Axis: [tex]\( 6.7184 \, \text{cm} \)[/tex]
- Eccentricity: [tex]\( 0.0769 \)[/tex]
- Scaled Distance Between Foci: Not provided
- Scaled Habitable Zone Range: [tex]\( 3.62 - 6.94 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
7. Trappist 1 b:
- Major Axis: [tex]\( 5.74 \, \text{cm} \)[/tex]
- Eccentricity: Not provided
- Scaled Distance Between Foci: [tex]\( 0.680 \, \text{cm} \)[/tex]
- Scaled Habitable Zone Range: [tex]\( 3.44 - 7.18 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
8. HD 20782 b:
- Major Axis: [tex]\( 5.10 \, \text{cm} \)[/tex]
- Eccentricity: [tex]\( 0.6532 \)[/tex]
- Scaled Distance Between Foci: Not provided
- Scaled Habitable Zone Range: [tex]\( 131.63 - 232.13 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
9. HD 17156:
- Major Axis: [tex]\( 11.89 \, \text{cm} \)[/tex]
- Eccentricity: Not provided
- Scaled Distance Between Foci: [tex]\( 6.047 \, \text{cm} \)[/tex]
- Scaled Habitable Zone Range: [tex]\( 73.75 - 129.11 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
By collating the data from the table, we've determined the specified parameters and whether each object remains within its respective scaled habitable zones. As per the data, only Earth remains within its habitable zone.
1. Earth:
- Major Axis: [tex]\( 15.209832 \, \text{cm} \)[/tex]
- Eccentricity: [tex]\( 0.017 \)[/tex]
- Scaled Distance Between Foci: [tex]\( 0.258 \, \text{cm} \)[/tex]
- Scaled Habitable Zone Range: [tex]\( 14.21 - 25.07 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? Yes
2. Kepler 79 b:
- Major Axis: [tex]\( 36.056 \, \text{cm} \)[/tex]
- Eccentricity: [tex]\( 0.0291 \)[/tex]
- Scaled Distance Between Foci: [tex]\( 1.049 \, \text{cm} \)[/tex]
- Scaled Habitable Zone Range: [tex]\( 511.98 - 1265.30 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
3. Kepler 442 b:
- Major Axis: [tex]\( 61.19 \, \text{cm} \)[/tex]
- Eccentricity: [tex]\( 0.04 \)[/tex]
- Scaled Distance Between Foci: Not provided
- Scaled Habitable Zone Range: [tex]\( 48.62 - 85.72 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
4. Kepler 432 b:
- Major Axis: [tex]\( 15.01 \, \text{cm} \)[/tex]
- Eccentricity: Not provided
- Scaled Distance Between Foci: [tex]\( 10.184 \, \text{cm} \)[/tex]
- Scaled Habitable Zone Range: [tex]\( 150.15 - 271.72 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
5. Kepler 18 b:
- Major Axis: [tex]\( 6.7 \, \text{cm} \)[/tex]
- Eccentricity: [tex]\( 0.0000 \)[/tex]
- Scaled Distance Between Foci: [tex]\( 0.0000 \, \text{cm} \)[/tex]
- Scaled Habitable Zone Range: [tex]\( 218.86 - 482.75 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
6. Kepler 186 f:
- Major Axis: [tex]\( 6.7184 \, \text{cm} \)[/tex]
- Eccentricity: [tex]\( 0.0769 \)[/tex]
- Scaled Distance Between Foci: Not provided
- Scaled Habitable Zone Range: [tex]\( 3.62 - 6.94 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
7. Trappist 1 b:
- Major Axis: [tex]\( 5.74 \, \text{cm} \)[/tex]
- Eccentricity: Not provided
- Scaled Distance Between Foci: [tex]\( 0.680 \, \text{cm} \)[/tex]
- Scaled Habitable Zone Range: [tex]\( 3.44 - 7.18 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
8. HD 20782 b:
- Major Axis: [tex]\( 5.10 \, \text{cm} \)[/tex]
- Eccentricity: [tex]\( 0.6532 \)[/tex]
- Scaled Distance Between Foci: Not provided
- Scaled Habitable Zone Range: [tex]\( 131.63 - 232.13 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
9. HD 17156:
- Major Axis: [tex]\( 11.89 \, \text{cm} \)[/tex]
- Eccentricity: Not provided
- Scaled Distance Between Foci: [tex]\( 6.047 \, \text{cm} \)[/tex]
- Scaled Habitable Zone Range: [tex]\( 73.75 - 129.11 \, \text{cm} \)[/tex]
- Does the planet stay within the habitable zone? No
By collating the data from the table, we've determined the specified parameters and whether each object remains within its respective scaled habitable zones. As per the data, only Earth remains within its habitable zone.
