2
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Retrograde motion is:

The apparent motion of the planets when they appear to move backward (from east to west) from the direction that they move ordinarily with respect to the stars.

Can planets inside the Earth's orbit around the Sun appear to undergo retrograde motion?

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5
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Both Mercury and Venus undergo retrograde motion, but are visually close to the Sun when this happens, so we don't notice it.

Below is Mercury's right ascension from May 15 to July 15 of this year. Note that it starts off increasing, then decreases (retrograde motion) and then increases again.

*******************************************************************************
Ephemeris / WWW_USER Thu Feb 19 08:02:41 2015 Pasadena, USA      / Horizons    
*******************************************************************************
Target body name: Mercury (199)                   {source: DE-0431LE-0431}
Center body name: Earth (399)                     {source: DE-0431LE-0431}
Center-site name: GEOCENTRIC
*******************************************************************************
Start time      : A.D. 2015-May-15 00:00:00.0000 UT      
Stop  time      : A.D. 2015-Jul-15 00:00:00.0000 UT      
Step-size       : 1440 minutes
*******************************************************************************
Target pole/equ : IAU_MERCURY                     {East-longitude -}
Target radii    : 2439.7 x 2439.7 x 2439.7 km     {Equator, meridian, pole}    
Center geodetic : 0.00000000,0.00000000,0.0000000 {E-lon(deg),Lat(deg),Alt(km)}
Center cylindric: 0.00000000,0.00000000,0.0000000 {E-lon(deg),Dxy(km),Dz(km)}
Center pole/equ : High-precision EOP model        {East-longitude +}
Center radii    : 6378.1 x 6378.1 x 6356.8 km     {Equator, meridian, pole}    
Target primary  : Sun
Vis. interferer : MOON (R_eq= 1737.400) km        {source: DE-0431LE-0431}
Rel. light bend : Sun, EARTH                      {source: DE-0431LE-0431}
Rel. lght bnd GM: 1.3271E+11, 3.9860E+05 km^3/s^2                              
Atmos refraction: NO (AIRLESS)
RA format       : HMS
Time format     : CAL 
EOP file        : eop.150218.p150512                                           
EOP coverage    : DATA-BASED 1962-JAN-20 TO 2015-FEB-18. PREDICTS-> 2015-MAY-11
Units conversion: 1 au= 149597870.700 km, c= 299792.458 km/s, 1 day= 86400.0 s 
Table cut-offs 1: Elevation (-90.0deg=NO ),Airmass (>38.000=NO), Daylight (NO )
Table cut-offs 2: Solar Elongation (  0.0,180.0=NO ),Local Hour Angle( 0.0=NO )
**************************************************************************************************************
 Date__(UT)__HR:MN     R.A._(ICRF/J2000.0)_DEC  APmag  S-brt            delta      deldot    S-O-T /r    S-T-O
**************************************************************************************************************
$$SOE
     2015-May-15 00:00     04 42 01.78 +24 08 32.2   1.53   4.36 0.69142867651373 -28.9445515  18.6988 /T 129.3762
     2015-May-16 00:00     04 43 23.87 +24 00 54.9   1.74   4.49 0.67512627148213 -27.4926615  18.0144 /T 132.4768
     2015-May-17 00:00     04 44 24.75 +23 51 35.3   1.96   4.63 0.65967892310678 -25.9844651  17.2466 /T 135.5875
     2015-May-18 00:00     04 45 04.61 +23 40 37.1   2.21   4.77 0.64511881456032 -24.4211059  16.3963 /T 138.7127
     2015-May-19 00:00     04 45 23.80 +23 28 04.3   2.47   4.91 0.63147747327791 -22.8037380  15.4651 /T 141.8554
     2015-May-20 00:00     04 45 22.86 +23 14 01.5   2.75   5.06 0.61878570842679 -21.1337209  14.4555 /T 145.0181
     2015-May-21 00:00     04 45 02.49 +22 58 33.7   3.05   5.20 0.60707343838108 -19.4128031  13.3707 /T 148.2014
     2015-May-22 00:00     04 44 23.61 +22 41 46.8   3.37   5.33 0.59636941752453 -17.6432855  12.2149 /T 151.4048
     2015-May-23 00:00     04 43 27.36 +22 23 47.7   3.71   5.45 0.58670087720487 -15.8281545  10.9939 /T 154.6255
     2015-May-24 00:00     04 42 15.08 +22 04 44.1   4.07   5.56 0.57809309959244 -13.9711803   9.7148 /T 157.8583
     2015-May-25 00:00     04 40 48.34 +21 44 44.8   4.46   5.63 0.57056894619759 -12.0769753   8.3871 /T 161.0937
     2015-May-26 00:00     04 39 08.89 +21 23 59.8   4.87   5.66 0.56414836550867 -10.1510071   7.0239 /T 164.3154
     2015-May-27 00:00     04 37 18.70 +21 02 40.1   5.29   5.62 0.55884790663755  -8.1995645   5.6456 /T 167.4924
     2015-May-28 00:00     04 35 19.87 +20 40 57.9   n.a.   n.a. 0.55468026744915  -6.2296724   4.2893 /T 170.5572
     2015-May-29 00:00     04 33 14.63 +20 19 06.0   n.a.   n.a. 0.55165390565664  -4.2489596   3.0439 /T 173.3313
     2015-May-30 00:00     04 31 05.30 +19 57 18.0   n.a.   n.a. 0.54977273920552  -2.2654833   2.1722 /T 175.2574
     2015-May-31 00:00     04 28 54.24 +19 35 48.1   n.a.   n.a. 0.54903595776444  -0.2875219   2.2105 /L 175.1837
     2015-Jun-01 00:00     04 26 43.78 +19 14 50.1   n.a.   n.a. 0.54943796056976   1.6766529   3.1266 /L 173.1900
     2015-Jun-02 00:00     04 24 36.24 +18 54 38.3   n.a.   n.a. 0.55096842790710   3.6190086   4.3897 /L 170.4268
     2015-Jun-03 00:00     04 22 33.81 +18 35 25.8   5.29   5.65 0.55361252502737   5.5319758   5.7564 /L 167.4122
     2015-Jun-04 00:00     04 20 38.57 +18 17 25.2   4.88   5.70 0.55735122910170   7.4086481   7.1443 /L 164.3125
     2015-Jun-05 00:00     04 18 52.42 +18 00 48.1   4.49   5.68 0.56216176249744   9.2429487   8.5180 /L 161.1913
     2015-Jun-06 00:00     04 17 17.09 +17 45 44.4   4.12   5.62 0.56801810956371  11.0297524   9.8584 /L 158.0785
     2015-Jun-07 00:00     04 15 54.09 +17 32 22.7   3.77   5.53 0.57489158958468  12.7649573  11.1530 /L 154.9902
     2015-Jun-08 00:00     04 14 44.76 +17 20 50.1   3.45   5.42 0.58275145605987  14.4455044  12.3929 /L 151.9356
     2015-Jun-09 00:00     04 13 50.19 +17 11 11.8   3.15   5.31 0.59156549247635  16.0693469  13.5713 /L 148.9204
     2015-Jun-10 00:00     04 13 11.32 +17 03 31.6   2.87   5.18 0.60130057734526  17.6353760  14.6833 /L 145.9474
     2015-Jun-11 00:00     04 12 48.85 +16 57 51.6   2.61   5.06 0.61192319592983  19.1433125  15.7250 /L 143.0178
     2015-Jun-12 00:00     04 12 43.37 +16 54 12.5   2.37   4.94 0.62339988172426  20.5935736  16.6938 /L 140.1313
     2015-Jun-13 00:00     04 12 55.28 +16 52 33.7   2.15   4.81 0.63569757625371  21.9871244  17.5876 /L 137.2863
     2015-Jun-14 00:00     04 13 24.86 +16 52 53.2   1.94   4.69 0.64878390050511  23.3253217  18.4055 /L 134.4805
     2015-Jun-15 00:00     04 14 12.31 +16 55 08.3   1.75   4.58 0.66262733523404  24.6097559  19.1469 /L 131.7103
     2015-Jun-16 00:00     04 15 17.69 +16 59 15.2   1.57   4.46 0.67719731085661  25.8420965  19.8117 /L 128.9719
     2015-Jun-17 00:00     04 16 41.05 +17 05 09.2   1.40   4.35 0.69246421084326  27.0239479  20.4002 /L 126.2604
     2015-Jun-18 00:00     04 18 22.35 +17 12 45.4   1.25   4.24 0.70839929524826  28.1567176  20.9133 /L 123.5707
     2015-Jun-19 00:00     04 20 21.53 +17 21 57.8   1.10   4.14 0.72497455264057  29.2415000  21.3516 /L 120.8972
     2015-Jun-20 00:00     04 22 38.49 +17 32 40.5   0.96   4.04 0.74216248879516  30.2789728  21.7164 /L 118.2337
     2015-Jun-21 00:00     04 25 13.15 +17 44 46.7   0.83   3.94 0.75993585914434  31.2693054  22.0086 /L 115.5738
     2015-Jun-22 00:00     04 28 05.39 +17 58 09.6   0.71   3.84 0.77826734979511  32.2120717  22.2296 /L 112.9109
     2015-Jun-23 00:00     04 31 15.13 +18 12 42.2   0.59   3.75 0.79712920966069  33.1061670  22.3805 /L 110.2380
     2015-Jun-24 00:00     04 34 42.27 +18 28 17.0   0.48   3.65 0.81649283449812  33.9497246  22.4625 /L 107.5478
     2015-Jun-25 00:00     04 38 26.75 +18 44 46.2   0.37   3.56 0.83632830264123  34.7400316  22.4769 /L 104.8329
     2015-Jun-26 00:00     04 42 28.49 +19 02 02.2   0.27   3.47 0.85660386201288  35.4734443  22.4247 /L 102.0858
     2015-Jun-27 00:00     04 46 47.47 +19 19 56.7   0.17   3.38 0.87728536859778  36.1453054  22.3070 /L  99.2988
     2015-Jun-28 00:00     04 51 23.65 +19 38 21.2   0.07   3.30 0.89833567803594  36.7498651  22.1247 /L  96.4642
     2015-Jun-29 00:00     04 56 17.02 +19 57 07.2  -0.02   3.21 0.91971399456822  37.2802130  21.8789 /L  93.5742
     2015-Jun-30 00:00     05 01 27.57 +20 16 05.6  -0.12   3.13 0.94137518555319  37.7282290  21.5704 /L  90.6210
     2015-Jul-01 00:00     05 06 55.30 +20 35 07.1  -0.20   3.05 0.96326907552925  38.0845640  21.2001 /L  87.5974
     2015-Jul-02 00:00     05 12 40.17 +20 54 01.8  -0.29   2.96 0.98533974152847  38.3386660  20.7688 /L  84.4961
     2015-Jul-03 00:00     05 18 42.16 +21 12 39.8  -0.38   2.88 1.00752484088954  38.4788698  20.2775 /L  81.3104
     2015-Jul-04 00:00     05 25 01.19 +21 30 50.5  -0.46   2.80 1.02975501346900  38.4925685  19.7269 /L  78.0344
     2015-Jul-05 00:00     05 31 37.13 +21 48 23.0  -0.54   2.73 1.05195341081967  38.3664848  19.1182 /L  74.6631
     2015-Jul-06 00:00     05 38 29.80 +22 05 05.9  -0.63   2.65 1.07403541451894  38.0870574  18.4526 /L  71.1926
     2015-Jul-07 00:00     05 45 38.91 +22 20 47.8  -0.71   2.57 1.09590861358459  37.6409536  17.7315 /L  67.6206
     2015-Jul-08 00:00     05 53 04.08 +22 35 16.7  -0.79   2.49 1.11747311584451  37.0157141  16.9564 /L  63.9467
     2015-Jul-09 00:00     06 00 44.78 +22 48 20.6  -0.87   2.41 1.13862226817234  36.2005225  16.1294 /L  60.1725
     2015-Jul-10 00:00     06 08 40.36 +22 59 47.7  -0.95   2.34 1.15924385212199  35.1870766  15.2529 /L  56.3023
     2015-Jul-11 00:00     06 16 49.99 +23 09 26.1  -1.03   2.26 1.17922180051076  33.9705111  14.3295 /L  52.3431
     2015-Jul-12 00:00     06 25 12.69 +23 17 04.6  -1.11   2.17 1.19843844390623  32.5502953  13.3626 /L  48.3050
     2015-Jul-13 00:00     06 33 47.27 +23 22 32.8  -1.19   2.09 1.21677724378686  30.9310023  12.3560 /L  44.2011
     2015-Jul-14 00:00     06 42 32.40 +23 25 41.0  -1.28   2.00 1.23412590569533  29.1228358  11.3140 /L  40.0476
     2015-Jul-15 00:00     06 51 26.58 +23 26 21.1  -1.37   1.91 1.25037969990154  27.1418048  10.2415 /L  35.8640
    $$EOE
**************************************************************************************************************
Column meaning:

TIME

  Prior to 1962, times are UT1. Dates thereafter are UTC. Any 'b' symbol in
the 1st-column denotes a B.C. date. First-column blank (" ") denotes an A.D.
date. Calendar dates prior to 1582-Oct-15 are in the Julian calendar system.
Later calendar dates are in the Gregorian system.

  Time tags refer to the same instant throughout the universe, regardless of
where the observer is located.

  The dynamical Coordinate Time scale is used internally. It is equivalent to
the current IAU definition of "TDB". Conversion between CT and the selected
non-uniform UT output scale has not been determined for UTC times after the
next July or January 1st.  The last known leap-second is used over any future
interval.

  NOTE: "n.a." in output means quantity "not available" at the print-time.

 R.A._(ICRF/J2000.0)_DEC =
   J2000.0 astrometric right ascension and declination of target center.
Adjusted for light-time. Units: HMS (HH MM SS.ff) and DMS (DD MM SS.f)

 APmag S-brt =
   Target's approximate apparent visual magnitude & surface brightness. For
planets and satellites, values are available only for solar phase angles in the
range generally visible from Earth. This is to avoid extrapolation of models
beyond their valid (data-based) limits.
   Units: MAGNITUDE & VISUAL MAGNITUDES PER SQUARE ARCSECOND

 delta  deldot =
   Range ("delta") and range-rate ("delta-dot") of target center with respect
to the observer at the instant light seen by the observer at print-time would
have left the target center (print-time minus down-leg light-time); the
distance traveled by a light ray emanating from the center of the target and
recorded by the observer at print-time. "deldot" is a projection of the
velocity vector along this ray, the light-time-corrected line-of-sight from the
coordinate center, and indicates relative motion. A positive "deldot" means the
target center is moving away from the observer (coordinate center). A negative
"deldot" means the target center is moving toward the observer.
Units: AU and KM/S

 S-O-T /r =
    Sun-Observer-Target angle; target's apparent solar elongation seen from
observer location at print-time. If negative, the target center is behind
the Sun. Angular units: DEGREES.

    The '/r' column is a Sun-relative code, output for observing sites
with defined rotation models only.

         /T indicates target trails Sun (evening sky)
         /L indicates target leads Sun  (morning sky)

    NOTE: The S-O-T solar elongation angle is the total separation in any
direction. It does not indicate the angle of Sun leading or trailing.

 S-T-O =
   "S-T-O" is the Sun->Target->Observer angle; the interior vertex angle at
target center formed by a vector to the apparent center of the Sun at
reflection time on the target and the apparent vector to the observer at
print-time. Slightly different from true PHASE ANGLE (requestable separately)
at the few arcsecond level in that it includes stellar aberration on the
down-leg from target to observer.  Units: DEGREES


 Computations by ...
     Solar System Dynamics Group, Horizons On-Line Ephemeris System
     4800 Oak Grove Drive, Jet Propulsion Laboratory
     Pasadena, CA  91109   USA
     Information: http://ssd.jpl.nasa.gov/
     Connect    : telnet://ssd.jpl.nasa.gov:6775  (via browser)
                  telnet ssd.jpl.nasa.gov 6775    (via command-line)
     Author     : Jon.Giorgini@jpl.nasa.gov

**************************************************************************************************************
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  • $\begingroup$ By "visually close to the Sun" do you mean we can't see it because the Sun is too bright, and not that Mercury/Venus are behind the Sun? $\endgroup$ – Allure Jan 24 at 20:13
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You would need to have a planet orbit very slowly around the star. A planet moves retrograde because the planet is passing the other in its orbit so that the slower planet appears to be going backwards.

So in order for this to happen you would need a planet having an orbit such that the outer planet passes the inner planet. But I think that this would result in an unstable orbit for one of the two planets. Either the inner one would fall into the orbiting star or the outer one would escape.

The inner planets have a smaller orbit so they move "faster" in order to not fall into the sun. So they are always "passing" the planets in orbits that are outside of their orbit.

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TL;DR Not for planets, but for other stuff yes.

As explained in an earlier answer, planets are on circular orbits (quasi-circular actually but that's a detail). The closer to the star, the faster the planet is on its orbit. So, the retrograde motion observed for Mars cannot happen for Venus for instance. At most you could see Venus going retrograde when it actually turns around the sun, but you would clearly understand that the planet is just on the other side of the solar system -- which I think is not what you were wondering about.

But there's another type of situation where you see a retrograde orbit for an inner body: if the orbit is not circular but a nice ellipse! The orbit would have to be very eccentric though (very narrow). Planets do not have eccentric orbits (in the solar system at least) because, in short, the formation of planets favors circular orbits in the long term. But some asteroids are in this situation (for example many in the Aten family).

If the perihelion (closest point) is very close to the sun and the aphelion (farthest point) is much further, then even if the asteroid remains in the interior of the Earth's orbit you would see it going backwards near aphelion. What happens is that speed on a eccentric (elliptic) orbit is slower at the apoapse. For instance, if your perihelion was grazing the surface of the sun, you would have a speed of almost 0 at your aphelion. And you would see it drifting backward because of Earth's motion.

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Unsure where the original poster obtained an idea that objects inside the Earth’s orbit, as seen from Earth, “move ordinarily with respect to the stars” from west to east.

First of all, of which “west” and “east” do we speak? To be specific, let’s understand these for the region of sky not far from the meridian. That is, when the object X culminates, then nearby objects having the right ascension greater than RA(X) are on the east from the meridian (not yet culminated), whereas those having RA < RA(X) are on the west from the meridian (already culminated).

For the Sun itself, every educated person can remember that its diurnal motion is slightly slower than diurnal motion of the inertial celestial sphere (fixed stars) – that is, with respect to those stars Sun goes from west to east. Its right ascension increases monotonically. For other objects inside the Earth’s orbit, their right ascension is within 90° of the Sun’s, hence in average they move “from west to east” as well, and quicker do it when are behind the Sun.

But definitely the terrestrial picture is opposite for e.g. Venus when it overtakes Earth in their orbital motions near the inferior conjunction.

Venus and Earth orbit the Sun

During this part of the orbit the right ascension of Venus decreases – seen on this animation near the end of cycle. “Experts” asserting that it’s impossible to see mistake – Venus is not very close to Sun during it, and anyway perfectly observable (albeit rare) during Venus’s transits before the Sun.

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  • $\begingroup$ Sorry, but you made a simple answer ("Yes, inferior planets also show retrograde motion") very complicated with extraneous information. About the animation, I do not understand how it demonstrates the retrograde motion. To me, it shows all of the planets continuing to move in the same direction. A figure or animation of Venus' position on a sky chart would be infinitely more useful. $\endgroup$ – JohnHoltz May 29 at 13:13
  • $\begingroup$ @JohnHoltz: the picture requires a mild geometric imagination (namely, ability to construct segments in mind) to understand. RA increases counter-cw here, but one sees that the Earth–Venus vector rotates clockwise near the inf.conj. JohnHoltz thinks one way but more mathematical users, probably, think other way. As for extraneous information, Ī̲ deem it useful to disprove “a planet moves retrograde because is passing the other in its orbit so that the slower planet appears to be going backwards” bollocks where phenomena of outer planets are thoughtlessly extrapolated to interior planets. $\endgroup$ – Incnis Mrsi May 29 at 17:30

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