Kepler's 1st Law

[brave_new_world]

Kepler's 1st law of planetary motion states:

 

Planets move in ellipses with the Sun at one focus.

 

This question had been bugging me.

There are two foci in an ellipse. If this theory is true, what would be at the other focus point?

 

Kepler's Laws

[Ophiolite]

Nothing. There doesn't need to be anything.

[Jordan14]

There is no second foci this focus is just imaginary:

 

http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

[Paul Trow]

On the contrary, the ellipse does have a second focus - there's just nothing there, as Ophiolite pointed out.

[Jordan14]

Sorry Paul that was me being badly word again what you said was what I meant see the link

[brave_new_world]

There has to be some sort of mass at the second foci in order to cause the planets to orbit in ellipses.

 

I must be missing something, can someone please explain how there can be elliptical orbits without a second mass?

 

Also, does the moon or in an elliptical or circular motion?

[Jacques]

I just thaught that the planet of the solar system have small eccentricity: maybe the second focis is in the sun. I found the orbital element of the planet and of the sun.

JPL's solar system dynamics WWW

Mean Orbital Elements

The sun have a diameter of 1,390,000 km.

Quick calculation:

e:=eccentricity

c:=half distance focis

a:=semi-major axis

e=c/a

=> 2c=2ea

 

The less eccentric orbit is Venus and it gave a distance betwen the 2 focis of 1,450,000 km.

Earth 5 millions km (eccentricity=0.016)

So no the other focis is not in the sun. It's somewhere betwen the sun and the planet.

Is it a special point ? Mathematically YES

Physicaly ? I don't think

 

A good thing about this forum is that it force me to use some little math something I didn't do since a long time. I always been interested in astronomy from a general point of view. I know many different concept without much math around it.

Elementary math for many people, here in this forum.

I am new here and happy to exchange with you!

So much thing to learn and unlearn...

[swansont]

There has to be some sort of mass at the second foci in order to cause the planets to orbit in ellipses.

 

I must be missing something' date=' can someone please explain how there can be elliptical orbits without a second mass?

 

Also, does the moon or in an elliptical or circular motion?[/quote']

 

No, there doesn't. It's because of the 1/r² force.

 

Circular orbits are elliptical orbits, but the foci are co-located. However, the moon's eccentricity is 0.0549, so it's not circular, but it's close.

 

(e=(aphelion - perihelion distance)/(2 x semi-major axis), so e=0 is circular)

[brave_new_world]

What is the 1/r squared force?

[swansont]

The gravitational force varies as the inverse-square of r.

[brave_new_world]

So are you saying that the orbits of the planets are slightly elliptical because the radius of the sun is not the same throughout? Also since the earth is not a perfect sphere it casues the moon to orbit slightly elliptical.

[DarthDooku]

wouldnt the second foci be Earth itself. Do the Earth and the Sun pull on each other like the Earth and moon.