Kepler's Laws: Orbits in Motion

A planet on an adjustable ellipse round a star, timed by Kepler's equation. The orbit is cut into sectors that each take the same time to sweep, and every sector has the same area (second law). The star sits at one focus of the ellipse (first law), and the period depends only on the semi-major axis and the star's mass: T2 = 4π2a3/(GM) (third law). The log–log chart puts the eight planets and your orbit on one straight line of slope 1.5.

custom orbit
Orbital period  T = 2π sqrt(a3/GM)
1.000 years
= 365.3 days
Kepler's third law  T2/a3
1.000 yr2/AU3
same for every orbit round a 1.0 solar-mass star
First law: the ellipse
Perihelion q = a(1 − e)0.5000 AU
Aphelion Q = a(1 + e)1.500 AU
Semi-minor axis b0.8660 AU
Star to centre c = ae0.5000 AU
Speeds (vis-viva)
At perihelion vp51.59 km/s
At aphelion va17.20 km/s
Ratio vp/va3.000
= aphelion / perihelion distance
Second law: equal areas  πab/n
Each sector0.3401 AU2 each
8 sectors, each swept in 45.66 days
Areal rate  πab/T2.721 AU2 per year
Semi-major axis a1.000 AU
Eccentricity e0.5000
Star mass M1.0 solar masses
Equal-time sectors8
Animation speed1× · one orbit per 10 s
Tip: drag the eccentricity from 0 to 0.9 and watch the period: it never changes. Only the semi-major axis and the star's mass set T.
Load a real orbit (JPL)
Right now (live)
Distance from the star r0.5000 AU
Speed v51.59 km/s
Angle from perihelion0.0°
0.000 T after perihelion
The star sits at one focus; the other focus is empty.
Constants: GM of the Sun 1.3271244 × 1020 m3/s2 (IAU 2015 nominal) · 1 AU = 149,597,870,700 m · 1 year = 365.25 days. Two bodies only, the planet's own mass ignored; each orbit is drawn in its own plane. Planet elements from JPL's Table 1 (J2000, a 1800–2050 fit); "Earth" is JPL's Earth–Moon barycentre row. Every orbit plays in the same screen time; the real period is the readout.