(451) Patientia
ephemeris	date	magn	radius	delta	ra	dec	elong	phase
Today	20 Jun 2019	12.6	3.167 AU	3.172 AU	11h41m	+18°26'	80.5°	18.4°
Opposition	24 May 2020	11.3	3.292 AU	2.290 AU	16h13m	-11°12'	170.2°	3.0°

The interactive orbit chart above shows the body's path through the solar system and its position at the given date. Green and blue lines are shown perpendicular to the ecliptic plane: Green if the path is above the ecliptic plane, blue if it is below. (Left-click and drag to rotate the view; Right-click and drag to move the view; Use scroll wheel to zoom in our out.)

The lightcurve chart below shows the estimated development of the minor planet's magnitude.

The all-sky chart below shows the path of of the minor planet over the same period as the lightcurve. The current position is marked yellow.

The following chart shows the path of the minor planet in the next few days. The field of view is optimized for (~10x50) binoculars and finderscopes. A more printer-friendly version of the same chart can be found below.

    Terminology:
            
    delta:  distance between minor planet and earth in AU
    radius: distance between minor planet and sun in AU
    magn:   magnitude (brightness) estimate    
    ra:     right ascension in hours (24h = 360deg)
    dec:    declination in degrees
    elong:  elongation in degrees (angle sun-earth-minor planet)    
    phase:  phase angle in degrees (angle sun-minor planet-earth)        
    AU:     Astronomical Unit (mean distance between earth and sun: 149597870.7 km
    

Orbital elements provided by MPC (Minor Planet Center)
Calculations by a modified version of AAPlus, a C# implementation of the AA+ project by PJ Naughter from the algorithms presented in the book "Astronomical Algorithms" by Jean Meeus.
NGC2000 dso catalog and star labels from VizieR as provided by the Strasbourg astronomical Data Center.
Tycho2 catalog from the ESO archive.