rvanveshana.com
t = 0.00s
Gravity Force (F_g) Velocity Vector (v) Swept Area

Live Telemetry & Summary

Observe the live orbital values changing in real-time. Perihelion has high velocity, Aphelion has low velocity.

Time:0.00 s
Orbital Period (T):6.28 s
Separation (r):6.00 AU
Planet Velocity (v):152.75 km/s
Kepler Ratio (T²/a³):0.0395

Variable Adjuster

Orbital Radius (a)10AU
515
Eccentricity (e)0.4
00.7

Gravitational Orbits Lab

GRAV

Newton's Law of Gravitation describes the attractive force between masses. In a star-planet system, this force keeps the planet in an elliptical orbit. Kepler's Second Law states that the line joining the planet to the star sweeps out equal areas in equal times, causing the planet to travel faster at perihelion (closest approach) than at aphelion (farthest distance).

F=GMmr2,T2=4π2GMa3F = G \frac{M m}{r^2}, \quad T^2 = \frac{4\pi^2}{GM} a^3

Whiteboard Solver Steps

Step 1

Universal Gravitation & Orbit Shape

Kepler's First Law states that planetary orbits are ellipses with the star at one focus. The eccentricity measures how circular (e=0) or stretched (e approaching 1) the orbit is.

r(θ)=a(1−e2)1+ecos⁡(θ),e=0.4r(\theta) = \frac{a(1 - e^2)}{1 + e \cos(\theta)}, \quad e = 0.4
Step 2

Kepler's Third Law (Harmonic Law)

The square of the orbital period is directly proportional to the cube of the semi-major axis. Here, the period T = 6.28 seconds.

T2∝a3⇒T2a3=4π2GM=0.03948T^2 \propto a^3 \Rightarrow \frac{T^2}{a^3} = \frac{4\pi^2}{GM} = 0.03948