Roche Lobe
restricted m=0.99 m=0.01 x=-0.61 vy=-s/10
Open in the app The dials and keys named below are the app's.
The setup
A heavy body of mass 0.99 and a light one of 0.01 stand one unit apart in the frame that turns with them. A massless particle starts 0.6 to the left of the heavy body, moving at s/10 the way the frame turns. At the opening value of 7 it orbits the heavy body, swinging out to 0.70 on the far side and back to 0.50; the light body's pull keeps any orbit here from being a perfect circle.
The gate
In the turning frame one quantity keeps: the Jacobi integral, the particle's energy counted with the frame's centrifugal potential. The energy readout shows it, −1.596 at s = 7. Each value fences the particle into the region its energy can reach, and at L1, between the two bodies, the fence has a neck whose level is −1.583. Below that level the neck is shut, and the particle can never leave the heavy body's side, its Roche lobe. The level is crossed at s = 7.19.
Through the neck
An open neck is not yet an escape, since the particle must also arrive at it heading through. From 7.2 to 7.5 it still stays for two minutes. At 7.6 it slips through at 31 s and passes 0.002 from the light body. At 7.8 it is out at 12 s, and at 8 at 5.4 s, flung 7.6 away. In a close pair of stars this neck is where gas from a swollen star spills onto its companion.
History
Carl Jacobi found the integral in 1836. The lobe is named after Édouard Roche, the French astronomer who studied how a companion's pull shapes a body near it.
Try
- Drag s to 7.6 and give it half a minute; Speed 4 shortens the wait to under 8 s.
- Drag s to 8: the particle is through the neck in 5.4 s and thrown far past the light body.
- Drag s down to 3 and raise Trail to 80: the orbit swings between 0.2 and 0.6 from the heavy body and begins a rosette.
- Top in the deck shows the lobe flat, with the light body on the diagonal beyond it.