What if Earth slowed down in its orbit?

Earth zooms around the Sun. The Sun's pull keeps it going round.

What if Earth slowed down? Would it go round more slowly, or would something else happen?

You might guess that a slower Earth would simply take longer to go around the same circle. But orbits are trickier than that. Earth stays the same distance from the Sun only because its sideways speed exactly matches the Sun's pull.

So what happens if Earth is suddenly moving too slowly for a circle? In this lab you can slow Earth down in a model and watch the shape of its path change.

For a given distance r there is exactly one speed, v_c = √(GM/r), that gives a circular orbit. A slower body cannot hold its distance: gravity wins, and the body begins to fall inward, yet its sideways motion means it does not fall straight in.

This lab asks what path results, how close and how fast the planet gets, how long its year becomes, and how the same physics shapes the real orbits of planets and comets.

Earth's path around the Sun is almost a circle.

Sometimes Earth is a tiny bit closer to the Sun. Sometimes it is a tiny bit farther away.

Earth's real orbit is very nearly a circle, but not quite. Its closest point to the Sun, called perihelion, is about 147 million kilometers away, and its farthest, aphelion, about 152 million. Earth moves a little faster near perihelion, about 30.3 kilometers per second, and a little slower near aphelion, about 29.3.

In the model, Earth starts with exactly the speed for a circle, 29.8 kilometers per second, so its distance never changes and its year is 365.26 days.

NASA's Earth fact sheet gives perihelion 147.095 and aphelion 152.100 million km (eccentricity 0.0167), with orbital speed ranging from 29.29 to 30.29 km/s, faster when closer, as Kepler's second law requires.

The model's start is an idealized circle: r = 1 AU, v = v_c = 29.785 km/s, period 365.26 days. Every slower start in this lab begins from that same point, moving in the same direction, only with less speed.

In our pretend lab, Olly slows Earth down.

Earth starts to fall toward the Sun! It gets closer and closer, goes faster and faster, then swings around and back out. It makes a squashed loop.

Choose 'slower', 70 percent of today's speed. Earth can no longer hold its distance, so it starts falling toward the Sun. But it is still moving sideways, so it misses, swooping around the Sun at about 48.5 million kilometers, closer than Mercury's average distance. At that moment it is racing at about 64 kilometers per second, about three times the speed it started with.

Then it climbs back out to where it began, slowing down again. The whole oval trip takes only about 197 days, so a year would be a little over half as long.

At v = 0.7 v_c (20.85 km/s) vis-viva gives a = 0.6623 AU. The start becomes aphelion; perihelion is 2a − r = 48.5 million km (0.325 AU), reached after half a period, and T = 196.85 days. Angular momentum conservation, r_a v_a = r_p v_p, gives v_p ≈ 64.3 km/s, matching the integrated peak of 64.25 km/s.

Gentler slowing gives gentler ovals: 0.85 v_c reaches 84.6 million km with T = 253.0 days; 0.5 v_c dives to 21.4 million km with T = 157.8 days. Starts much slower than half speed carry Earth so close to the Sun that the model's fixed time steps stop being accurate, so this lab quotes no numbers for them.

When Earth is too slow, the Sun's pull wins, and Earth falls inward. Falling makes it go faster.

By the time it is close, it is going so fast that it whooshes past the Sun and swings back out.

The Sun's pull bends Earth's path. At the right speed, the bending makes a circle. Too slow, and the pull bends the path more sharply inward, so Earth falls toward the Sun. Falling speeds it up, just as a ball speeds up when you drop it.

By the time Earth is close, it is moving so fast sideways that it overshoots and swings back out, slowing as it climbs. That back-and-forth makes an oval, an ellipse. Johannes Kepler discovered that real planets move on ellipses like this, fastest when closest to the Sun.

A slower start lowers the total energy, E = ½v² − μ/r, which shrinks the semimajor axis a = −μ/2E, and by Kepler's third law (T² ∝ a³) shortens the period. The start point becomes aphelion because the velocity is perpendicular to the radius there and below v_c.

Kepler's second law, equal areas in equal times, is angular momentum conservation, so speed varies inversely with distance at the ends of the orbit. The model's limits: two point bodies, Newtonian gravity, no other planets, and an instantaneous slowing that no real process could produce.

Comets move on very long, stretched ovals. They creep slowly far away, then zoom past the Sun.

Halley's Comet comes back about every 76 years.

Real planets and comets follow ovals too. Comets have the most stretched paths of all. Halley's Comet takes about 76 years per orbit. In 1948, far out beyond Neptune's distance, it crept along at under 1 kilometer per second. In 1986 it swept within about 88 million kilometers of the Sun, well inside Venus's orbit.

Earth's slowed orbit in the model would bring it much closer to the Sun. The idea of what would happen to Earth's climate is not in the model, but scientists know sunlight grows stronger quickly closer in: at a third of the distance, it is about nine times as strong.

NASA's Halley page records the comet at 35.25 AU in 1948, moving 0.91 km/s, and at perihelion on 9 February 1986 at 0.5871 AU (87.8 million km), well inside Venus's orbit; its period averages 76 years, varying from 74.42 to 79.25 because of planetary perturbations.

By the inverse-square law (OpenStax), sunlight at the model's perihelion of 0.325 AU would be about 1/0.325² ≈ 9.5 times as intense as at 1 AU. What that would do to a real Earth's climate is an idea the orbit model cannot test.