C/1988 P1 (Machholz)
| Parameter |
Value |
| Designation |
C/1988 P1 (Machholz) |
| Type |
C |
| Perihelion (tp_cal, UTC) |
1988-09-17T13:37:56.176320Z |
| Orbit solution date (soln_date, UTC) |
2021-04-15T23:29:36Z |
| Obs used |
56 |
| NEO |
- |
| M1 |
- |
| K1 |
- |
| PC |
- |
Osculating Elements
| Parameter |
Value |
| Epoch (epoch_cal, TDB) |
1988-08-19.0000000 |
| e |
0.99999939 |
| q (au) |
0.164552 |
| a (au) |
268133.697775 |
| i (deg) |
40.198656 |
| Ω (om, deg) |
167.727558 |
| ω (w, deg) |
349.037996 |
| M (ma, deg) |
360.000000 |
Magnitude
Scatter + Global Linear
$$
M_a = (7.847 + 2.000\cdot 2.5\log_{10} r) + \epsilon - 2.5\log_{10}\Phi(\theta) + 5\log_{10}\Delta
$$
$$
\theta = 180^\circ - \alpha
$$
$$
\Phi(\theta) = \frac{\delta_{90} D(\theta) + 1}{\delta_{90} + 1},\quad D(\theta) = k\cdot \Phi_{HG}(\theta; g_f) + (1-k)\cdot \Phi_{HG}(\theta; g_b)
$$
$$
\Phi_{HG}(\theta; g) = \left(\frac{1+g^2}{1+g^2-2g\cos\theta}\right)^{3/2},\quad \Phi_{HG}(90^\circ)=1
$$
Model Parameters
| Parameter |
Value |
| H0 |
7.847 |
| n |
2.000 |
| gf |
0.942 |
| gb |
-1.000 |
| k |
0.948 |
| δ90 |
10.000 |
| Parameter |
Symbol |
Range |
Description |
| Absolute magnitude at 1 AU from Sun and Earth |
H0 |
-5 to 20 |
Intrinsic brightness of the comet |
| Photometric slope parameter |
n |
2 to 6 |
Rate of brightness change with heliocentric distance |
| Forward scattering asymmetry factor |
gf |
0.8 to 1 |
Degree of forward scattering |
| Backward scattering asymmetry factor |
gb |
-1 to -0.5 |
Degree of backward scattering |
| Partitioning coefficient |
k |
0.8 to 1 |
Ratio between forward/backward scattering contributions |
| Dust-to-gas brightness ratio |
δ90 |
1 to 10 |
Relative contribution of dust scattering to gas emission |
Reference: EPSC-DPS2025-160
Residuals (Piecewise)
$$\epsilon = a \log_{10} r_{\mathrm{au}} + b$$
| Start (UTC) |
End (UTC) |
a |
b |
| 1988-08-06 |
1988-09-17 |
+1.7150 |
+0.218 |
| 1988-09-24 |
1988-10-17 |
+15.0229 |
+5.774 |
log10 r = log10(heliocentric distance / AU), Δ = geocentric distance (AU)
Ephemeris
| Date/Time (UTC) |
RA (J2000) |
Dec (J2000) |
Nearest HIP |
Dist from HIP (arcmin) |
| 2026-02-03 00:00 |
22:09:40.08 |
-00:01:38.7 |
HIP 109301 |
15.83 |
| 2026-02-03 12:00 |
22:09:41.79 |
-00:01:31.0 |
HIP 109301 |
16.19 |
| 2026-02-04 00:00 |
22:09:43.50 |
-00:01:23.2 |
HIP 109301 |
16.56 |
| 2026-02-04 12:00 |
22:09:45.22 |
-00:01:15.4 |
HIP 109301 |
16.93 |
| 2026-02-05 00:00 |
22:09:46.94 |
-00:01:07.5 |
HIP 109301 |
17.30 |
| 2026-02-05 12:00 |
22:09:48.66 |
-00:00:59.5 |
HIP 109301 |
17.68 |
| 2026-02-06 00:00 |
22:09:50.38 |
-00:00:51.5 |
HIP 109301 |
18.06 |
| 2026-02-06 12:00 |
22:09:52.11 |
-00:00:43.4 |
HIP 109301 |
18.45 |
| 2026-02-07 00:00 |
22:09:53.85 |
-00:00:35.2 |
HIP 109301 |
18.84 |
| 2026-02-07 12:00 |
22:09:55.58 |
-00:00:27.0 |
HIP 109301 |
19.23 |
| 2026-02-08 00:00 |
22:09:57.32 |
-00:00:18.7 |
HIP 109301 |
19.63 |
| 2026-02-08 12:00 |
22:09:59.06 |
-00:00:10.3 |
HIP 109301 |
20.03 |
| 2026-02-09 00:00 |
22:10:00.81 |
-00:00:01.9 |
HIP 109301 |
20.43 |
| 2026-02-09 12:00 |
22:10:02.55 |
+00:00:06.6 |
HIP 109301 |
20.83 |
| 2026-02-10 00:00 |
22:10:04.30 |
+00:00:15.2 |
HIP 109301 |
21.24 |
| 2026-02-10 12:00 |
22:10:06.06 |
+00:00:23.8 |
HIP 109301 |
21.65 |
| 2026-02-11 00:00 |
22:10:07.81 |
+00:00:32.5 |
HIP 109301 |
22.06 |
| 2026-02-11 12:00 |
22:10:09.57 |
+00:00:41.2 |
HIP 109301 |
22.48 |
| 2026-02-12 00:00 |
22:10:11.33 |
+00:00:50.0 |
HIP 109301 |
22.90 |
| 2026-02-12 12:00 |
22:10:13.09 |
+00:00:58.8 |
HIP 109301 |
23.32 |
| 2026-02-13 00:00 |
22:10:14.85 |
+00:01:07.7 |
HIP 109301 |
23.74 |
| 2026-02-13 12:00 |
22:10:16.61 |
+00:01:16.7 |
HIP 109301 |
24.16 |
| 2026-02-14 00:00 |
22:10:18.38 |
+00:01:25.7 |
HIP 109301 |
24.59 |
| 2026-02-14 12:00 |
22:10:20.15 |
+00:01:34.8 |
HIP 109301 |
25.01 |
| 2026-02-15 00:00 |
22:10:21.91 |
+00:01:43.9 |
HIP 109301 |
25.44 |
| 2026-02-15 12:00 |
22:10:23.68 |
+00:01:53.1 |
HIP 109301 |
25.87 |
| 2026-02-16 00:00 |
22:10:25.45 |
+00:02:02.4 |
HIP 109301 |
26.30 |
| 2026-02-16 12:00 |
22:10:27.22 |
+00:02:11.7 |
HIP 109301 |
26.74 |
| 2026-02-17 00:00 |
22:10:29.00 |
+00:02:21.0 |
HIP 109301 |
27.17 |
| 2026-02-17 12:00 |
22:10:30.77 |
+00:02:30.4 |
HIP 109301 |
27.61 |
| 2026-02-18 00:00 |
22:10:32.54 |
+00:02:39.9 |
HIP 109301 |
28.04 |
| 2026-02-18 12:00 |
22:10:34.31 |
+00:02:49.4 |
HIP 109301 |
28.48 |
| 2026-02-19 00:00 |
22:10:36.09 |
+00:02:58.9 |
HIP 109301 |
28.92 |
| 2026-02-19 12:00 |
22:10:37.86 |
+00:03:08.5 |
HIP 109301 |
29.36 |
| 2026-02-20 00:00 |
22:10:39.63 |
+00:03:18.1 |
HIP 109301 |
29.80 |
| 2026-02-20 12:00 |
22:10:41.41 |
+00:03:27.8 |
HIP 109301 |
30.24 |
| 2026-02-21 00:00 |
22:10:43.18 |
+00:03:37.6 |
HIP 109578 |
30.66 |
| 2026-02-21 12:00 |
22:10:44.95 |
+00:03:47.4 |
HIP 109578 |
30.55 |
| 2026-02-22 00:00 |
22:10:46.72 |
+00:03:57.2 |
HIP 109578 |
30.44 |
| 2026-02-22 12:00 |
22:10:48.49 |
+00:04:07.1 |
HIP 109578 |
30.35 |
| 2026-02-23 00:00 |
22:10:50.26 |
+00:04:17.0 |
HIP 109578 |
30.26 |
| 2026-02-23 12:00 |
22:10:52.03 |
+00:04:26.9 |
HIP 109578 |
30.18 |
| 2026-02-24 00:00 |
22:10:53.80 |
+00:04:36.9 |
HIP 109578 |
30.11 |