# Keplers Laws

Hello all!!

I read this post on another physics forum. I thought Keplers laws were accurate for our earth/sun system?

"Keplers law is so easily disproven

Keplers Law states that the planets move in elliptical orbits with the sun at one focus of the ellipse so that a line connecting the sun and a planet will sweep out equal areas in equal times.

An ellipse is a central conic symmetric about a central point so that the major axis passing through the focus bisects the ellipse making the areas of both sides of the bisected ellipse equal.

The perihelion and aphelion are the closest and furthest points from the sun the focus that the Earths orbit intersects the major axis.

By applying Kepler's Law to the Earth's orbit, these points are placed in early January and July. However, the time it takes for the Earth to move between these astronomical points, January to July is 72 hours less than the time it takes to move from July to January, sweeping out equal areas in unequal times. Thus, applying Kepler's Law to determine the perihelion and aphelion of the Earth's orbit disproves Kepler's Law!

The fact that it takes longer for the Earth to move between the summer (June) and winter (December) solstices than it does to move between the winter and summer solstices shows that the sun is moving toward the winter solstice.

Bottom line

Newton based his proof of mass/gravity on historical forces producing Kepler's Law we may have to rethink why objects fall."

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Doc Al
Mentor
Sounds like crackpottery to me.

russ_watters
Mentor
Well, it looks like the 72 hour difference is wrong: http://aa.usno.navy.mil/data/docs/EarthSeasons.php [Broken]

Kepler's laws aren't perfect, but they worked to a pretty high degree of accuracy for early astronomers and Newton's laws still work well today. So I guess that claim is "easily disproven".

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Janus
Staff Emeritus
Gold Member
If you look at the chart given by Russ you will notice that the time between perigees apogees vary from year to year. If you average these times out, you will find that average apogee-perigee time equals average perigee-apogee time quite closely.

The reason they vary at all is due to the fact that the Earth does not orbit the Sun alone. Gravitational interraction between the Earth and other planets at times retards and at other times accelerates the Earth in its orbit.

Meir Achuz
Homework Helper
Gold Member
The fact that it takes longer for the Earth to move between the summer (June) and winter (December) solstices than it does to move between the winter and summer solstices shows that the sun is moving toward the winter solstice.
The solstices have nothing to do with the Earth's orbit.
They are related to the angle the Earth's axis makes with the vector from the Sun to the Earth.

D H
Staff Emeritus
The reason they vary at all is due to the fact that the Earth does not orbit the Sun alone. Gravitational interraction between the Earth and other planets at times retards and at other times accelerates the Earth in its orbit.
You forgot about the moon, which is the biggest perturbing factor in the Earth's orbit around the Sun. Since the Earth's orbit around the Sun is nearly circular, the Earth's orbit around the Earth-Moon center of mass can perturb the Earth's perihelion and apohelion times by a few days. If you look at the data Russ provided, there are indeed years where it takes 3-4 fewer days to travel from perihelion to apohelion than from apohelion to perihelion. The author of this crackpottery omitted the fact that in other years it takes 3-4 more days to travel from perihelion to apohelion than from apohelion to perihelion.

russ_watters
Mentor
I'm not following the logic there, DH - doesn't the earth move so fast around the sun that the moon being on one side or the other would only change the apsis timing by plus or minus an hour or so?

D H
Staff Emeritus

Got it.

The Earth is moving very fast along its orbital path. However, the distance between the Sun and Earth changes very slowly:
$$\dot r = \frac{a(1-\epsilon^2)}{(1+\epsilon\cos\theta)^2}\epsilon\dot\theta\sin\theta$$

This is particularly so near perihelion and apohelion. 1 days before/after perihelion, the radial distance between the Earth and Sun changes by about 8 m/s.

In comparison, if the Moon is half full, the Earth's rotation about the Earth-Moon center of mass changes the Earth-Sun distance by about 11 m/s. This can easily skew the perihelion (or apohelion) timing by more than a day.

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Janus
Staff Emeritus
Gold Member
You forgot about the moon, which is the biggest perturbing factor in the Earth's orbit around the Sun. Since the Earth's orbit around the Sun is nearly circular, the Earth's orbit around the Earth-Moon center of mass can perturb the Earth's perihelion and apohelion times by a few days. If you look at the data Russ provided, there are indeed years where it takes 3-4 fewer days to travel from perihelion to apohelion than from apohelion to perihelion. The author of this crackpottery omitted the fact that in other years it takes 3-4 more days to travel from perihelion to apohelion than from apohelion to perihelion.
The Earth's orbit around the Earth-moon center of gravity is in the neighborhood of 4683 km, givng it a diameter of 9366 km. The Earth's mean orbital velocity is 29 km/sec. At this speed it traverses the Earth's orbit around the center of gravity in 5.36 min. This is the maximum time difference caused by the moon.

Or look at it this way, 3 days is .008 of a year. 0.008 of the Earth's orbital circumference is 7,720,236 km , or about 10 times the diameter of the Moon's orbit.

D H
Staff Emeritus
The Earth's orbit around the Earth-moon center of gravity is in the neighborhood of 4683 km, givng it a diameter of 9366 km. The Earth's mean orbital velocity is 29 km/sec. At this speed it traverses the Earth's orbit around the center of gravity in 5.36 min. This is the maximum time difference caused by the moon.

Or look at it this way, 3 days is .008 of a year. 0.008 of the Earth's orbital circumference is 7,720,236 km , or about 10 times the diameter of the Moon's orbit.
You are comparing the wrong things. That 29 km/sec is almost entirely normal to the Earth-Sun vector. The component along the Earth-Sun vector is very small thanks to the small eccentricity of the Earth's orbit. Perihelion is defined as the time at which the Earth-Sun separation reaches a local minimum. The radial component of the Earth's velocity is much, much smaller than 29 km/sec.

D H
Staff Emeritus
I'm not following the logic there, DH - doesn't the earth move so fast around the sun that the moon being on one side or the other would only change the apsis timing by plus or minus an hour or so?
The time separation between successive periapsis/apoapsis and apoapsis/periapsis varies by 3-4 days. The OP stated the variation is one-sided. Note well: This obviously is not the case. Sometimes it takes longer than average for from periapsis to apoapsis, sometimes shorter. The source of this variation is obviously that Kepler' Laws are a simplification. Y'all posited Jupiter as the cause of this variation; I picked the Moon as the obvious culprit. I never worry about the effects of Jupiter on LEO satellites for rendezvous problems. (People at Goddard who need very precise long-term trajectories may worry about Jupiter, but I don't.) OTOH, I do worry about the Moon.

russ_watters
Mentor
I get it now. I didn't consider that the moon moved the earth enough perpendicular to the orbit to affect the placement of the apsis. I was only considering how much the moon could move the earth forward or backwards in the orbit. I was looking at the problem from the wrong direction (literally).

Janus
Staff Emeritus
Gold Member
Same here.

D H
Staff Emeritus
I just wrote a little Sun/Earth/Moon simulator. To keep things simple I made the orbits lie in the same plane. Over a 100 hundred year interval, the simulation occasionally exhibited a 5+ day disparity between between Earth perihelion-to-apohelion and apohelion-to-perihelion. No pyschoceramics needed, just Newton's Laws.