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Table 1
Multipole coefficients of Kleopatra’s gravitational field using the ADAM model and constant density.
| C00 | 1.00000000 | ||
| C10 | 0.00000000 | ||
| C11 | 0.00000000 | S11 | 0.00000000 |
| C20 | − 7.65106929 × 10−1 | ||
| C21 | 3.98110264 × 10−4 | S21 | − 3.07876838 × 10−4 |
| C22 | 3.59335850 × 10−1 | S22 | − 8.65906339 × 10−5 |
| C30 | 1.49466956 × 10−2 | ||
| C31 | − 5.24916471 × 10−2 | S31 | 5.20018496 × 10−4 |
| C32 | − 1.48712568 × 10−3 | S32 | 2.52505000 × 10−3 |
| C33 | 1.17882333 × 10−2 | S33 | − 3.43079734 × 10−4 |
| C40 | 1.30914835 | ||
| C41 | − 1.41497526 × 10−2 | S41 | 7.18145896 × 10−4 |
| C42 | − 1.39568658 × 10−1 | S42 | − 1.72827301 × 10−3 |
| C43 | 3.44681126 × 10−4 | S43 | − 6.95352555 × 10−5 |
| C44 | 1.53908741 × 10−2 | S44 | 5.76718751 × 10−4 |
| C50 | − 3.01286209 × 10−2 | ||
| C51 | 1.39623684 × 10−1 | S51 | − 4.39146849 × 10−5 |
| C52 | 9.49158788 × 10−4 | S52 | − 3.50208422 × 10−3 |
| C53 | − 6.31945029 × 10−3 | S53 | 1.44844074 × 10−6 |
| C54 | 7.63010533 × 10−5 | S54 | 2.87991860 × 10−4 |
| C55 | 7.06444516 × 10−4 | S55 | 9.22871681 × 10−6 |
| C60 | − 2.92621603 | ||
| C61 | 5.01230966 × 10−2 | S61 | − 3.30583966 × 10−3 |
| C62 | 1.41764499 × 10−1 | S62 | 2.29130383 × 10−3 |
| C63 | − 9.12143591 × 10−4 | S63 | 2.24108452 × 10−4 |
| C64 | − 4.29428304 × 10−3 | S64 | − 1.93439069 × 10−4 |
| C65 | 1.33372930 × 10−5 | S65 | − 9.83952170 × 10−6 |
| C66 | 3.04072429 × 10−4 | S66 | 3.14393964 × 10−5 |
| C70 | − 1.49050705 × 10−3 | ||
| C71 | − 4.94081000 × 10−1 | S71 | − 2.54792669 × 10−3 |
| C72 | 1.49282198 × 10−3 | S72 | 6.59185873 × 10−3 |
| C73 | 7.58761100 × 10−3 | S73 | 1.54865702 × 10−5 |
| C74 | − 1.06667828 × 10−4 | S74 | − 2.55582680 × 10−4 |
| C75 | − 2.15423464 × 10−4 | S75 | − 4.16149717 × 10−6 |
| C76 | 5.72095667 × 10−6 | S76 | 1.01143177 × 10−5 |
| C77 | 1.54723186 × 10−5 | S77 | 1.12688336 × 10−6 |
| C80 | 7.61525254 | ||
| C81 | − 1.66415917 × 10−1 | S81 | 1.15002782 × 10−2 |
| C82 | − 2.12136010 × 10−1 | S82 | − 4.07662706 × 10−3 |
| C83 | 2.01880918 × 10−3 | S83 | − 4.60678358 × 10−4 |
| C84 | 3.27454389 × 10−3 | S84 | 1.62346625 × 10−4 |
| C85 | − 2.40746340 × 10−5 | S85 | 1.09881420 × 10−5 |
| C86 | − 6.84753900 × 10−5 | S86 | − 7.21260224 × 10−6 |
| C87 | 3.52331279 × 10−7 | S87 | − 2.79130886 × 10−7 |
| C88 | 3.55651688 × 10−6 | S88 | 7.47645373 × 10−7 |
| C90 | 4.18361848 × 10−1 | ||
| C91 | 1.06717720 | S91 | − 5.47346878 × 10−4 |
| C92 | − 1.15403753 × 10−2 | S92 | − 1.39184073 × 10−2 |
| C93 | − 2.74503944 × 10−2 | S93 | − 1.53156145 × 10−3 |
| C94 | 2.12636564 × 10−4 | S94 | 3.22499931 × 10−4 |
| C95 | 1.74908520 × 10−4 | S95 | 3.27374899 × 10−6 |
| C96 | − 4.45393947 × 10−6 | S96 | − 6.47023483 × 10−6 |
| C97 | − 3.52023978 × 10−6 | S97 | − 2.27651271 × 10−7 |
| C98 | 1.20584507 × 10−7 | S98 | 1.64507039 × 10−7 |
| C99 | 1.83429337 × 10−7 | S99 | 3.05515155 × 10−8 |
| C10,0 | − 2.21145150 × 101 | ||
| C10,1 | 5.03865729 × 10−1 | S10,1 | − 3.33850136 × 10−2 |
| C10,2 | 4.00901809 × 10−1 | S10,2 | 9.98417914 × 10−3 |
| C10,3 | − 4.78661768 × 10−3 | S10,3 | 9.35952923 × 10−4 |
| C10,4 | − 3.83595725 × 10−3 | S10,4 | − 2.25073571 × 10−4 |
| C10,5 | 4.13709990 × 10−5 | S10,5 | − 1.37689312 × 10−5 |
| C10,6 | 4.30269516 × 10−5 | S10,6 | 4.84072887 × 10−6 |
| C10,7 | − 4.17610659 × 10−7 | S10,7 | 1.86498646 × 10−7 |
| C10,8 | − 6.83864198 × 10−7 | S10,8 | − 1.39471718 × 10−7 |
| C10,9 | 6.37173159 × 10−9 | S10,9 | − 2.88792150 × 10−9 |
| C10,10 | 2.80465119 × 10−8 | S10,10 | 1.02591965 × 10−8 |
Notes. The normalisation is given by Eq. (8). The reference radius is R = 59.633 km.
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