Searching for Orbits for a Mission to the Asteroid 2001SN263 Considering Errors in the Physical Parameters
Abstract
1. Introduction
2. The Triple Asteroid 2001SN263
3. Description of the Problem
4. Equations of Motion
5. Results
5.1. A Good Option to Observe Alpha and Gamma
5.2. A Good Option to Observe Beta
5.3. An Option to Observe All the Three Bodies of the System
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Body | Central Body | a | e | i | Period | Radius (km) | Mass (× 1010 kg) [33] |
---|---|---|---|---|---|---|---|
Alpha | Sun | 1.99 AU | 0.48 | 6.7° | 2.80 years | 1.30 | |
Beta | Alpha | 16.633 km | 0.015 | 0.00° | 6.23 days | 0.39 | |
Gamma | Alpha | 3.804 km | 0.016 | 13.87° | 0.69 days | 0.29 |
Scenario | Symbol | Nomenclature |
---|---|---|
1 | (+) (+) | mβ + error, mγ + error |
2 | (+) (0) | mβ + error, mγ without error |
3 | (+) (−) | mβ + error, mγ − error |
4 | (0) (+) | mβ without error, mγ + error |
5 | (0) (0) | mβ without error, mγ without error |
6 | (0) (−) | mβ without error, mγ − error |
7 | (−) (+) | mβ − error, mγ + error |
8 | (−) (0) | mβ − error, mγ without error |
9 | (−) (−) | mβ − error, mγ − error |
Orbits with the Spacecraft Starting in the Periapsis (Same Side Orbits) |
---|
-2: Orbit internal to Gamma in resonance 3:4 |
-3: Orbit internal to Gamma in resonance 4:5 |
-4: Orbit external to Gamma in resonance 3:1 |
Orbits with the spacecraft starting in the apoapsis (same side orbits) |
-5: Orbit internal to Beta in resonance 1:2 |
-12: Orbit external to Gamma in resonance 4:3 |
-15: Orbit external to Gamma in resonance 7:5 |
Orbit with the spacecraft starting in the periapsis (opposite side orbits) |
-18: Orbit internal to Gamma in resonance 5:6 |
Orbit with the spacecraft starting in the apoapsis (opposite side orbits) |
-20: Orbit external to Gamma in resonance 6:5 |
Orbit with the spacecraft starting in the periapsis (same side orbits with i = 13.87°) |
-22: Orbit internal to Gamma in resonance 3:4 |
Orbits with the spacecraft starting in the apoapsis (same side orbits with i = 13.87°) |
-25: Orbit internal to Beta in resonance 1:2 |
-27: Orbit internal to Beta in resonance 3:5 |
-31: Orbit external to Gamma in resonance 7:2 |
Orbit with the spacecraft starting in the periapsis (same side orbits with i = 90°) |
-38: Orbit internal to Gamma in resonance 3:4 |
Orbit with the spacecraft starting in the apoapsis (same side orbits with i = 90°) |
-42: Orbit internal to Beta in resonance 2:3 |
-52: Orbit external to Gamma in resonance 8:5 |
Orbits with the spacecraft starting in the apoapsis (same side orbits with i = 180°) |
-59: Orbit internal to Beta in resonance 3:5 |
-60: Orbit internal to Beta in resonance 4:7 |
-61: Orbit internal to Beta in resonance 5:9 |
Family 1—Positive Errors in the Mass of Beta | ||||||
---|---|---|---|---|---|---|
Observation Times (Days) | ||||||
Positive Errors in the Mass of Gamma | No Errors in the Mass of Gamma | Negative Errors in the Mass of Gamma | ||||
Orbit | True Anomaly 0° | True Anomaly 180° | True Anomaly 0° | True Anomaly 180° | True Anomaly 0° | True Anomaly 180° |
2 | ||||||
R1 | 6.95 | 9.62 | 18.57 | 18.57 | 10.23 | 10.23 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 5.88 | 8.47 | 13.20 | 13.20 | 6.98 | 6.98 |
3 | ||||||
R1 | 3.53 | 6.72 | 62.50 | 62.50 | 10.44 | 14.76 |
R2 | 1.49 | 0.84 | 0 | 0 | 0 | 0 |
R3 | 7.21 | 5.67 | 43.07 | 43.06 | 8.06 | 12.72 |
4 | ||||||
R1 | 6.50 | 6.48 | 4.94 | 6.02 | 13.34 | 4.72 |
R2 | 0 | 0 | 0 | 1.36 | 0 | 0.62 |
R3 | 7.87 | 5.62 | 6.74 | 6.99 | 15.84 | 5.93 |
5 | ||||||
R1 | 0 | 0 | 0 | 0 | 0 | 0 |
R2 | 62.50 | 62.50 | 62.50 | 62.50 | 62.50 | 62.50 |
R3 | 0 | 0 | 0 | 0 | 0 | 0 |
12 | ||||||
R1 | 3.55 | 3.61 | 25.86 | 25.87 | 12.62 | 16.51 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 4.65 | 4.96 | 30.07 | 30.07 | 13.85 | 18.22 |
15 | ||||||
R1 | 6.34 | 7.19 | 18.65 | 15.36 | 6.16 | 13.41 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 6.64 | 5.60 | 21.73 | 18.28 | 6.70 | 9.60 |
18 | ||||||
R1 | 28.54 | 25.41 | 11.83 | 12.44 | 20.68 | 17.55 |
R2 | 0.87 | 0 | 0 | 0 | 0 | 0 |
R3 | 9.25 | 8.46 | 8.13 | 8.45 | 17.10 | 11.56 |
20 | ||||||
R1 | 52.40 | 52.41 | 51.78 | 51.71 | 14.55 | 14.55 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 12.77 | 12.76 | 15.32 | 15.36 | 5.51 | 5.50 |
22 | ||||||
R1 | 1.86 | 1.86 | 62.50 | 62.50 | 6.03 | 6.03 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 1.45 | 1.45 | 43.31 | 43.33 | 4.04 | 4.04 |
25 | ||||||
R1 | 0 | 0 | 7.50 | 1.65 | 0.09 | 0 |
R2 | 1.84 | 1.84 | 2.65 | 2.66 | 2.48 | 2.77 |
R3 | 0 | 0 | 7.71 | 0.46 | 0.41 | 0.48 |
27 | ||||||
R1 | 10.56 | 7.06 | 1.87 | 13.37 | 11.29 | 1.66 |
R2 | 1.48 | 4.33 | 2.65 | 1.75 | 2.21 | 5.65 |
R3 | 9.93 | 7.94 | 2.79 | 14.84 | 11.85 | 2.55 |
31 | ||||||
R1 | 0 | 0 | 0 | 1.33 | 0.09 | 0.09 |
R2 | 2.01 | 2.01 | 6.68 | 6.32 | 1.92 | 1.92 |
R3 | 3.16 | 3.17 | 1.33 | 2.35 | 1.21 | 1.21 |
38 | ||||||
R1 | 5.78 | 5.78 | 7.07 | 7.07 | 6.32 | 6.32 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 2.64 | 2.64 | 3.23 | 3.23 | 3.36 | 3.36 |
42 | ||||||
R1 | 0.90 | 0.93 | 1.91 | 1.66 | 1.62 | 1.61 |
R2 | 0.71 | 0.31 | 0.46 | 0.30 | 0.33 | 0.34 |
R3 | 1.16 | 1.95 | 1.95 | 1.59 | 1.46 | 1.38 |
52 | ||||||
R1 | 8.09 | 11.34 | 12.86 | 13.03 | 14.36 | 12.06 |
R2 | 0.78 | 0 | 0.49 | 0.47 | 0.16 | 0.43 |
R3 | 6.94 | 9.56 | 10.41 | 10.08 | 10.78 | 9.79 |
59 | ||||||
R1 | 0.79 | 0.79 | 1.16 | 1.16 | 0.66 | 0.69 |
R2 | 0.97 | 0.99 | 0.88 | 0.88 | 1.00 | 1.00 |
R3 | 0.71 | 0.57 | 1.32 | 0.95 | 0.70 | 0.60 |
60 | ||||||
R1 | 0.11 | 0.11 | 0.10 | 0.10 | 0.09 | 0.09 |
R2 | 0.17 | 0.17 | 0.16 | 0.16 | 0.17 | 0.17 |
R3 | 0.24 | 0.24 | 0.24 | 0.24 | 0.24 | 0.24 |
61 | ||||||
R1 | 0.14 | 0.14 | 0.14 | 0.14 | 0.13 | 0.13 |
R2 | 0.16 | 0.16 | 0.16 | 0.16 | 0.16 | 0.16 |
R3 | 0.24 | 0.24 | 0.24 | 0.24 | 0.24 | 0.24 |
Family 2—No Errors in the Mass of Beta | ||||||
---|---|---|---|---|---|---|
Observation Times (Days) | ||||||
Positive Errors in the Mass of Gamma | No Errors in the Mass of Gamma | Negative Errors in the Mass of Gamma | ||||
Orbit | True Anomaly 0° | True Anomaly 180° | True Anomaly 0° | True Anomaly 180° | True Anomaly 0° | True Anomaly 180° |
2 | ||||||
R1 | 3.52 | 2.91 | 25.13 | 40.69 | 10.22 | 10.22 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 3.75 | 3.02 | 18.50 | 25.02 | 6.97 | 6.97 |
3 | ||||||
R1 | 3.42 | 3.41 | 62.50 | 62.50 | 4.43 | 4.43 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 3.51 | 3.22 | 43.07 | 43.07 | 2.66 | 2.66 |
4 | ||||||
R1 | 21.18 | 6.60 | 6.86 | 18.00 | 1.53 | 1.53 |
R2 | 0 | 0 | 0 | 0 | 2.27 | 2.63 |
R3 | 20.63 | 7.60 | 5.92 | 20.61 | 1.98 | 1.98 |
5 | ||||||
R1 | 0 | 0 | 0 | 0 | 0 | 0 |
R2 | 62.50 | 62.50 | 62.50 | 62.50 | 62.50 | 62.50 |
R3 | 0 | 0 | 0 | 0 | 0 | 0 |
12 | ||||||
R1 | 2.74 | 3.02 | 25.83 | 25.82 | 7.26 | 8.80 |
R2 | 0 | 1.14 | 0 | 0 | 0 | 0 |
R3 | 4.67 | 5.04 | 30.39 | 30.40 | 7.05 | 8.59 |
15 | ||||||
R1 | 5.96 | 9.52 | 24.27 | 24.26 | 11.90 | 42.46 |
R2 | 0 | 0 | 0 | 0 | 0.24 | 0 |
R3 | 5.03 | 7.56 | 27.15 | 27.15 | 12.79 | 31.33 |
18 | ||||||
R1 | 9.66 | 12.08 | 35.73 | 11.36 | 6.19 | 6.19 |
R2 | 0 | 0 | 0.69 | 0 | 0 | 0 |
R3 | 5.36 | 5.83 | 16.51 | 5.99 | 2.64 | 2.64 |
20 | ||||||
R1 | 52.19 | 52.20 | 36.18 | 35.00 | 32.56 | 24.10 |
R2 | 0 | 0 | 0.43 | 0 | 0 | 0 |
R3 | 12.33 | 12.32 | 12.61 | 11.63 | 12.65 | 12.39 |
22 | ||||||
R1 | 1.86 | 1.86 | 62.50 | 62.50 | 6.03 | 6.03 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 1.46 | 1.46 | 43.03 | 43.02 | 4.06 | 4.05 |
25 | ||||||
R1 | 2.71 | 2.73 | 6.86 | 2.40 | 2.36 | 2.33 |
R2 | 1.42 | 0.99 | 0.88 | 0 | 0.55 | 0.55 |
R3 | 1.48 | 1.43 | 7.58 | 1.71 | 1.25 | 2.68 |
27 | ||||||
R1 | 0 | 0 | 5.51 | 5.64 | 0 | 0 |
R2 | 2.22 | 2.20 | 4.58 | 4.55 | 2.32 | 2.32 |
R3 | 0.51 | 0.50 | 4.27 | 5.06 | 0.32 | 0.32 |
31 | ||||||
R1 | 4.55 | 10.91 | 4.32 | 5.39 | 1.62 | 11.24 |
R2 | 5.80 | 1.15 | 1.59 | 2.23 | 4.48 | 1.38 |
R3 | 5.08 | 8.69 | 5.17 | 5.65 | 3.31 | 11.43 |
38 | ||||||
R1 | 6.61 | 6.61 | 8.12 | 8.13 | 6.71 | 6.71 |
R2 | 0 | 0 | 0.32 | 0.37 | 0 | 0 |
R3 | 3.05 | 3.05 | 4.43 | 4.40 | 3.81 | 3.80 |
42 | ||||||
R1 | 1.87 | 1.87 | 2.16 | 2.18 | 1.88 | 1.88 |
R2 | 0.69 | 0.69 | 0.34 | 0.34 | 0.78 | 0.78 |
R3 | 1.06 | 1.04 | 0.88 | 1.01 | 1.34 | 1.34 |
52 | ||||||
R1 | 6.53 | 5.57 | 9.15 | 5.00 | 13.73 | 11.90 |
R2 | 0.34 | 0.44 | 0 | 0 | 0 | 0.31 |
R3 | 4.57 | 4.31 | 8.23 | 4.03 | 9.84 | 9.57 |
59 | ||||||
R1 | 2.39 | 2.39 | 1.88 | 1.86 | 2.14 | 2.14 |
R2 | 2.55 | 2.56 | 2.68 | 2.68 | 2.89 | 2.93 |
R3 | 2.83 | 2.83 | 2.62 | 2.61 | 3.57 | 3.55 |
60 | ||||||
R1 | 2.65 | 2.67 | 2.27 | 1.65 | 0.69 | 0.69 |
R2 | 1.01 | 0.64 | 1.53 | 1.07 | 0.35 | 0.35 |
R3 | 2.08 | 1.97 | 2.35 | 1.34 | 0.54 | 0.54 |
61 | ||||||
R1 | 0.69 | 0.80 | 2.48 | 2.52 | 0.15 | 0.15 |
R2 | 2.58 | 2.66 | 1.39 | 1.33 | 0.17 | 0.17 |
R3 | 2.79 | 2.75 | 1.52 | 1.90 | 0.25 | 0.25 |
Family 3—Negative Errors in the Mass of Beta | ||||||
---|---|---|---|---|---|---|
Observation Times (Days) | ||||||
Positive Errors in the Mass of Gamma | No Errors in the Mass of Gamma | Negative Errors in the Mass of Gamma | ||||
Orbit | True Anomaly 0° | True Anomaly 180° | True Anomaly 0° | True Anomaly 180° | True Anomaly 0° | True Anomaly 180° |
2 | ||||||
R1 | 2.85 | 2.98 | 18.55 | 18.55 | 10.22 | 10.22 |
R2 | 0.65 | 0.72 | 0 | 0 | 0 | 0 |
R3 | 2.46 | 2.49 | 13.17 | 13.17 | 6.97 | 6.96 |
3 | ||||||
R1 | 5.59 | 3.82 | 62.50 | 62.50 | 4.42 | 4.41 |
R2 | 1.44 | 0 | 0 | 0 | 0 | 0 |
R3 | 5.61 | 3.95 | 43.06 | 43.07 | 2.65 | 2.64 |
4 | ||||||
R1 | 2.59 | 24.33 | 22.45 | 3.60 | 5.97 | 4.85 |
R2 | 0 | 0 | 0 | 0.68 | 0.51 | 0.57 |
R3 | 3.10 | 23.88 | 22.49 | 5.25 | 5.53 | 5.24 |
5 | ||||||
R1 | 0 | 0 | 0 | 0 | 0 | 0 |
R2 | 62.50 | 62.50 | 62.50 | 62.50 | 62.50 | 62.50 |
R3 | 0 | 0 | 0 | 0 | 0 | 0 |
12 | ||||||
R1 | 1.97 | 3.05 | 25.80 | 25.78 | 22.53 | 4.16 |
R2 | 0.49 | 0.49 | 0 | 0 | 0 | 1.65 |
R3 | 3.22 | 5.37 | 30.39 | 30.37 | 23.71 | 5.23 |
15 | ||||||
R1 | 3.84 | 3.84 | 23.95 | 23.95 | 18.00 | 17.38 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 4.08 | 4.08 | 26.53 | 26.53 | 17.25 | 17.99 |
18 | ||||||
R1 | 7.27 | 6.48 | 10.67 | 27.67 | 45.54 | 9.66 |
R2 | 0 | 0 | 0.24 | 0 | 0 | 0 |
R3 | 3.76 | 2.98 | 5.98 | 18.11 | 20.09 | 5.58 |
20 | ||||||
R1 | 52.27 | 52.27 | 51.56 | 51.57 | 52.55 | 51.72 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 12.79 | 12.80 | 14.95 | 14.95 | 17.37 | 18.03 |
22 | ||||||
R1 | 1.86 | 1.86 | 62.50 | 62.50 | 6.02 | 6.02 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 1.46 | 1.46 | 42.82 | 42.83 | 4.10 | 4.09 |
25 | ||||||
R1 | 0.39 | 0.75 | 1.87 | 2.21 | 0.99 | 1.04 |
R2 | 1.60 | 1.89 | 0.62 | 0.45 | 2.44 | 2.47 |
R3 | 1.89 | 1.95 | 2.55 | 2.28 | 1.65 | 1.66 |
27 | ||||||
R1 | 0 | 0 | 0 | 0 | 0 | 0 |
R2 | 1.68 | 2.11 | 1.62 | 1.62 | 1.34 | 1.34 |
R3 | 0.43 | 0.43 | 0.36 | 0.36 | 0.35 | 0.35 |
31 | ||||||
R1 | 0.99 | 2.45 | 7.28 | 6.89 | 7.26 | 7.26 |
R2 | 0.57 | 2.12 | 2.13 | 4.45 | 1.40 | 1.40 |
R3 | 1.60 | 2.33 | 5.30 | 5.31 | 4.40 | 4.40 |
38 | ||||||
R1 | 7.97 | 7.97 | 8.49 | 8.27 | 8.14 | 8.14 |
R2 | 0 | 0 | 0.09 | 0 | 0 | 0 |
R3 | 4.38 | 4.38 | 4.27 | 4.02 | 5.02 | 5.03 |
42 | ||||||
R1 | 1.79 | 1.78 | 2.20 | 2.42 | 1.58 | 1.58 |
R2 | 1.45 | 1.44 | 0.69 | 0.52 | 0.03 | 0.04 |
R3 | 0.70 | 0.85 | 1.01 | 0.94 | 0.11 | 0.11 |
52 | ||||||
R1 | 1.81 | 1.81 | 7.33 | 5.76 | 18.28 | 18.36 |
R2 | 0 | 0 | 0 | 0 | 0 | 0 |
R3 | 1.68 | 1.68 | 7.53 | 5.46 | 13.27 | 13.98 |
59 | ||||||
R1 | 0.78 | 0.77 | 0.31 | 0.31 | 0.25 | 0.25 |
R2 | 3.05 | 3.05 | 2.84 | 2.84 | 2.68 | 2.68 |
R3 | 2.96 | 2.97 | 2.93 | 2.93 | 2.76 | 2.76 |
60 | ||||||
R1 | 3.11 | 3.21 | 3.11 | 3.02 | 2.65 | 2.64 |
R2 | 2.97 | 2.82 | 2.99 | 2.92 | 3.13 | 3.14 |
R3 | 2.85 | 2.99 | 3.17 | 3.11 | 2.99 | 2.99 |
61 | ||||||
R1 | 3.14 | 3.15 | 2.55 | 2.51 | 2.82 | 2.82 |
R2 | 1.62 | 1.48 | 1.61 | 1.71 | 2.09 | 2.08 |
R3 | 2.80 | 2.86 | 2.41 | 2.40 | 2.40 | 2.58 |
Scenario | Observational Times (Days) | ||
---|---|---|---|
True Anomaly 0° | True Anomaly 180° | ||
(+) (+) | R1 | 52.40 | 52.41 |
R3 | 12.77 | 12.76 | |
(+) (0) | R1 | 51.78 | 51.71 |
R3 | 15.32 | 15.36 | |
(+) (−) | R1 | 14.55 | 14.55 |
R3 | 5.51 | 5.50 | |
(0) (+) | R1 | 52.19 | 52.20 |
R3 | 12.33 | 12.32 | |
(0) (0) | R1 | 36.18 | 35.00 |
R3 | 12.61 | 11.63 | |
(0) (−) | R1 | 32.56 | 24.10 |
R3 | 12.65 | 12.39 | |
(−) (+) | R1 | 52.27 | 52.27 |
R3 | 12.79 | 12.80 | |
(−) (0) | R1 | 51.56 | 51.57 |
R3 | 14.95 | 14.95 | |
(−) (−) | R1 | 52.55 | 51.72 |
R3 | 17.37 | 18.03 |
Scenario (+) (+) | R1 | 0.79 | 0.79 |
R2 | 0.97 | 0.99 | |
R3 | 0.71 | 0.57 | |
Scenario (+) (0) | R1 | 1.16 | 1.16 |
R2 | 0.88 | 0.88 | |
R3 | 1.32 | 0.95 | |
Scenario (+) (−) | R1 | 0.66 | 0.69 |
R2 | 1.00 | 1.00 | |
R3 | 0.70 | 0.60 | |
Scenario (0) (+) | R1 | 2.39 | 2.39 |
R2 | 2.55 | 2.56 | |
R3 | 2.83 | 2.83 | |
Scenario (0) (−) | R1 | 2.14 | 2.14 |
R2 | 2.89 | 2.93 | |
R3 | 3.57 | 3.55 | |
Scenario (−) (+) | R1 | 0.78 | 0.77 |
R2 | 3.05 | 3.05 | |
R3 | 2.96 | 2.97 | |
Scenario (−) (0) | R1 | 0.31 | 0.31 |
R2 | 2.84 | 2.84 | |
R3 | 2.93 | 2.93 | |
Scenario (−) (−) | R1 | 0.25 | 0.25 |
R2 | 2.68 | 2.68 | |
R3 | 2.76 | 2.76 |
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de Almeida Junior, A.K.; Mescolotti, B.Y.P.M.; Chiaradia, A.P.M.; Gomes, V.M.; de Almeida Prado, A.F.B. Searching for Orbits for a Mission to the Asteroid 2001SN263 Considering Errors in the Physical Parameters. Symmetry 2022, 14, 1789. https://doi.org/10.3390/sym14091789
de Almeida Junior AK, Mescolotti BYPM, Chiaradia APM, Gomes VM, de Almeida Prado AFB. Searching for Orbits for a Mission to the Asteroid 2001SN263 Considering Errors in the Physical Parameters. Symmetry. 2022; 14(9):1789. https://doi.org/10.3390/sym14091789
Chicago/Turabian Stylede Almeida Junior, Allan Kardec, Bruna Yukiko Pinheiro Masago Mescolotti, Ana Paula Marins Chiaradia, Vivian M. Gomes, and Antonio Fernando Bertachini de Almeida Prado. 2022. "Searching for Orbits for a Mission to the Asteroid 2001SN263 Considering Errors in the Physical Parameters" Symmetry 14, no. 9: 1789. https://doi.org/10.3390/sym14091789
APA Stylede Almeida Junior, A. K., Mescolotti, B. Y. P. M., Chiaradia, A. P. M., Gomes, V. M., & de Almeida Prado, A. F. B. (2022). Searching for Orbits for a Mission to the Asteroid 2001SN263 Considering Errors in the Physical Parameters. Symmetry, 14(9), 1789. https://doi.org/10.3390/sym14091789