# Venus' magnitude during inferior conjunction

I was doing an assignment on Stellarium when I observed Venus to have an apparent magnitude that didn't become less negative than -3, even at inferior conjunctions when we faced the dark side of Venus.

As far as I understand, apparent magnitude is subjective to an observer on earth, and that observer does not see Venus at all during an inferior conjunctions, so the magnitude should rise above zero.

I checked for other inferior and exterior planets and the moon on Stellarium; they all supported my theory. I thought it was some sort of bug, but apparently it's a scientific fact. I couldn't find any explanation online.

Did I understand something wrong?

• Out of curiosity, have you checked the magnitude of Venus during the inferior conjunction of June 2012? What was it during that conjunction? Maybe the difference is that Venus IS visible during some inferior conjunctions but not others. – JohnHoltz Oct 29 '19 at 12:31
• It would be great if you could post some specific dates, planets and magnitudes if you wanted them independently double-checked by other methods. – uhoh Oct 30 '19 at 1:08
• @JohnHoltz The magnitude was around -4, still pretty high for a planet during inferior conjunction. I monitored Venus' magnitude and ran the simulation for 100 years back and forth, the magnitude did not rise above -3.8 in either case. I understand Venus is sometimes not visible, but what I don't understand is, why is its magnitude so high (negative) all the time? – Diaa Eldin Malek Nov 2 '19 at 12:38

I found references which indicate that Venus usually goes dark. Check out the graphs in this paper for one example.

The exceptions happen when Venus' orbit, which is slightly out of the ecliptic, brings it to inferior conjunction when projected onto our (Earth's) orbital plane, but Venus remains at a slight angle relative to our viewing lines.

From UniverseToday,

Not all inferior conjunctions of Venus are created equal. The planet’s orbit is tilted 3 degrees with respect to our own and can thus pass a maximum of eight degrees north or south of the Sun. Venus last did this on inferior conjunction in 2009 and will once again pass a maximum distance north of the Sun in 2017. For the southern hemisphere, the red letter years are 2007, and next year in 2015.

• Problem is that the magnitude of Venus is -3.8 at its darkest, which is pretty bright. Can this be explained by orbital inclination alone? I mean, mercury has a 7 degrees inclination, yet its magnitude can go up to 5 during inferior conjunctions. One other thing, I checked for 2012's Venus transit, and it STILL had a really low magnitude (~ -3.8), even though mercury during transit (11 Nov. 2019) shows a very high magnitude (6.7). – Diaa Eldin Malek Nov 2 '19 at 13:32
• @DiaaEldinMalek I recommend reading the entire article and tracking down references, etc. – Carl Witthoft Nov 4 '19 at 13:23
• I will do that, thank you! – Diaa Eldin Malek Nov 4 '19 at 22:08

As the phase angle of Venus changes, so does its distance to Earth. More about modeling the phase angle dependence of apparent magnitude can be found in this answer to Calculating the apparent magnitude of a satellite. For more on that subject, see What is the difference between albedo, absolute magnitude or apparent magnitude? and also these: 1, 2, 3.

When it is closest to us, the smallest fraction of the disk is illuminated, and when it's farthest, nearly the whole disk is illuminated. This cancellation results in a compression of the range of apparent magnitudes throughout the Earth-Venus synodic cycle.

Remarkably, Venus' apparent brightness stays within roughly a 1.2 magnitude range throughout its synodic cycle!

I've dropped out a few data points where apparent magnitude was reported as n.a. but those likely represent geometries where they have less confidence on the model. Looking at the images of Venus below you can see that close to inferior conjunction the light from venus is strongly forward-scattered and so details of the atmospheric optical properties will strongly affect the apparent brightness.

The image below is from the question How (the heck) was this photo of Venus at inferior conjunction (between us and the Sun) taken?

above: Phases of Venus, from here.

Below I've used predictions from JPL's Horizons web interface using the setup below.

Python script for plotting:

import numpy as np
import matplotlib.pyplot as plt

fname = 'horizons_results Venus magnitude 01.txt'

with open(fname, 'r') as infile:

lines = lines[0].splitlines()

iSOE  = [i for i, line in enumerate(lines) if "$$SOE" in line][0] iEOE = [i for i, line in enumerate(lines) if "$$EOE" in line][0]

lines = lines[iSOE+1:iEOE]
lines = [line.replace('n.a.', '-42') for line in lines]

years = 2000 + np.arange(len(lines))/365.2564

lines = [line.split()[2:] for line in lines]
[x.pop(9) for x in lines]
lines = [[float(x) for x in line] for line in lines]

data = (np.array(lines).T).copy()
data[data==-42.] = np.nan

aparent_magnitude, surface_brightness, illum_percent, angular_diam = data[0:4]
d_Earth, dd_Earth, d_Sun, dd_Sun = data[4:8]
Sun_Oberver_Target, Sun_Target_Observer = data[8:10]

if True:
plt.figure()
names  = ('Aparent Magnitude (mag)', 'Surface Brightness (mag/arcsec^2)',
'Percent Illuminated (%)', 'Angular Diameter (arcsec)')
things = (aparent_magnitude, surface_brightness,
illum_percent, angular_diam)
for i, (name, thing) in enumerate(zip(names, things)):
plt.subplot(4, 1, i+1)
plt.plot(years, thing)
plt.title(name, fontsize=16)
plt.xlim(2000, 2030)
plt.show()

if True:
plt.figure()
names  = ('Sun-Observer-Target angle (deg)',
'Sun-Target-Observer angle (deg)'  )
things = (Sun_Oberver_Target, Sun_Target_Observer)
for i, (name, thing) in enumerate(zip(names, things)):
plt.subplot(4, 1, i+1)
plt.plot(years, thing)
plt.title(name, fontsize=16)
plt.xlim(2000, 2030)
plt.show()

• This is a great answer, but, if you look at the results more carefully, you'll see that, near inferior conjunction, Venus' apparent magnitude is listed as "n.a." by HORIZONS. The first example (with your settings) starts 2002-Jan-09 00:00 and goes for 11 days (the n.a.'s preceding this starting 2000-Jun-06 00:00 are for a superior conjunction). I realize you cover this case with lines = [line.replace('n.a.', '-42') for line in lines] but I think that's only accurate for superior conjunctions, not inferior ones. This also explains the odd jump in your apparent magnitude graph. – user21 Oct 30 '19 at 12:48
• @barrycarter okay I'll to do some semi-exhaustive, detailed analysis in the morning to see what's going on with their n.a.'s – uhoh Oct 30 '19 at 13:31