The companion pulls the star as well as the planet
Picture a planet circling one star, with another star far outside its orbit. The distant star attracts both members of the inner system. Much of that attraction moves them together. What changes the planet’s orbit around its own star is the small difference between the two pulls.
That difference depends on where the planet is and how its orbit is tilted. Over one fast revolution, many small changes cancel. Some survive the average and keep acting on the orbit’s shape and orientation. Astronomers call this slow evolution secular motion. “Slow” can mean hundreds or thousands of the planet’s own years.
An ordinary ellipse has two separate properties here. Its eccentricity describes how stretched it is; its inclination describes the angle between its plane and the companion’s orbit plane. A tilted outer companion can connect those properties through a gravitational torque, a twist that changes orbital motion.
Reading: Tremaine & Yavetz, Why do Earth satellites stay up?, arXiv:1309.5244v1 · Liu, Muñoz & Lai, Short-range forces in triple systems, arXiv:1409.6717v2
An orbit can stretch without shrinking its middle scale
In the simplest slow-motion model, the inner orbit keeps the same semimajor axis, half the length of the ellipse’s long direction. As eccentricity grows, its nearest point moves inward and its farthest point moves outward. The planet can therefore make a very close stellar passage while retaining the same orbital energy in that averaged model.
Angular momentum supplies the connection to tilt. It has a size and a direction: the direction is perpendicular to the orbit plane, and the size measures how much sideways orbital motion the planet carries. A highly stretched orbit has less angular momentum than a circle with the same semimajor axis. In the simplest model, the component along the companion’s orbit axis stays fixed.
For a prograde orbit, losing angular-momentum size while keeping that component forces its direction closer to the outer axis. Eccentricity rises as inclination falls. The reverse happens during the other part of the cycle. The planet’s ellipse and its plane move together.
Reading: Tremaine & Yavetz, Why do Earth satellites stay up?, arXiv:1309.5244v1
A large initial tilt makes room for a large change
A nearly coplanar orbit already puts most of its angular momentum along the outer axis. Keeping that component leaves little room to reduce the total. Its eccentricity stays modest. A strongly tilted orbit starts with a much smaller axial component, which allows a much more elongated shape.
The detailed dynamics puts the familiar threshold near forty degrees for an initially almost circular test particle and a distant circular companion. That number comes from the gravitational potential as well as the geometry. Starting closer to a right angle can produce stronger excursions, until a close encounter or another physical effect changes the problem.
Lidov and Kozai developed this mechanism in 1962. It first arose in the study of perturbed orbits, and it now appears in discussions of irregular moons, stellar triples and eccentric planets. The same slow-torque idea works across very different lengths and times because its simplest form depends on ratios and angles.
Reading: Tremaine & Yavetz, Why do Earth satellites stay up?, arXiv:1309.5244v1 · Liu, Muñoz & Lai, Short-range forces in triple systems, arXiv:1409.6717v2
Fast motion still matters near a close passage
Averaging works when the orbit changes only a little during each revolution of both the planet and its companion. As the inner orbit becomes extremely stretched, its angular momentum can be small enough that one outer-orbit passage changes it appreciably. Those short episodes can alter the next cycle’s timing and closest approach.
A direct three-dimensional integration keeps the positions and velocities through those episodes. Comparing it with an averaged calculation tells us when the slow description has become inaccurate. Numerical accuracy needs a separate check: making the integration more precise tests the calculation, whereas changing the physical approximation tests the model.
Relativity and the deformation of real bodies also turn the direction of an ellipse’s nearest point. Those effects can interrupt the simple exchange. Their interaction with fast perturbations is still an active research problem, particularly when a very small closest approach determines whether a planet survives.
Reading: Liu, Muñoz & Lai, Short-range forces in triple systems, arXiv:1409.6717v2 · Klein & Hamilton, Short-range forces beyond double averaging, arXiv:2606.19456v1
How a close passage could lead toward a hot Jupiter
A stretched orbit alone does not remove the energy needed to make a tight circular orbit. Tidal deformation can supply that next step. During repeated close passages, energy can move from orbital motion into heat and internal motion. The semimajor axis then falls, and the planet can eventually become a short-period giant.
Gupta and colleagues reported one informative candidate in 2024: TIC 241249530 b, a warm giant planet with an eccentricity near 0.94. Transit and radial-velocity measurements establish its present orbit. A companion star makes a history of slow gravitational torques plausible, and the paper explores an illustrative tidal-evolution scenario.
That history remains an inference from a present-day system. Observing one planet does not reveal every turn of its past orbit, and other formation channels can produce eccentric giants. The useful question is which measurements and physical assumptions distinguish those histories. A slow-torque experiment gives us a place to begin asking it.
Reading: Gupta et al., A hot-Jupiter progenitor on a super-eccentric retrograde orbit, Nature 632 (2024)