Earth's Elliptical Orbit around the Sun

[peeyush_ali]

By just knowing the clues like the force of attraction between two masses and angular momentum conservation principle , linear momentum conservation principle and geometry..can we derive the trajectory of the Earth around the sun is ellipse..if so please tell me your ideas..

 

[Josyulasharma]

there are 'seasons' on Earth only bcoz Earth's orbit is ecliptic in shape.
simple proof!

 

[peeyush_ali]

prove it mathematically... <if necessary take approximations..>

I'm expecting for a solid derivation..or tell me can't it be done?..<i think it can be..because Sir Issac Newton did it..>

 

[mgb_phys]

Yes you can prove that the path of a body is an ellipse if the force is an inverse square law.
The original proof was actually the other way around, observationally it was shown by Kepler that the planets followed an elliptic orbit covering equal areas in equal times, Newton (or possibly Hooke) proved that the only way for this to happen is if gravity is 1/r^2.
Newton's original proof using geometry is a little tricky to follow, it's a bit easier using calculus and should be in any physics textbook.

 

[HallsofIvy]

there are 'seasons' on Earth only bcoz Earth's orbit is ecliptic in shape.
simple proof!

First the Earth's orbit is "elliptic" not "ecliptic". Second, there are seasons because the Earth's axis is tilted realtive to its orbit, not because it is elliptical. That is why it is summer in the southern hemisphere when it is winter in the northern hemisphere. And, in fact, the Earth is closest to the sun during winter in the northern hemisphere.

 

[mgb_phys]

there are 'seasons' on Earth only bcoz Earth's orbit is ecliptic in shape.

The seasons are due to the tilt of the Earth, the different distance only makes a small difference. This is obvious because when it is winter in the North it is summer in the South - while the Earth is at the same distance.

 

[HallsofIvy]

Of course it can be done. Just about any Calculus book will give it. There is a quick sketch here: http://www.vias.org/physics/bk2_06_12.html

 

[jtbell]

I'm expecting for a solid derivation..

Any intermediate or advanced university mechanics textbook should have this derivation. (Not the first-year introductory physics course.)

 

[Buckleymanor]

By just knowing the clues like the force of attraction between two masses and angular momentum conservation principle , linear momentum conservation principle and geometry..can we derive the trajectory of the Earth around the sun is ellipse..if so please tell me your ideas..

An experimental idea.
At noon each day go into your garden and if the sun is shineing get hold of a hosepipe and spray it useing a circular motion.
Make sure your back is towards the sun.
If the spray is fine enough and you use the correct motion a rain circle will form.
Which is a rainbow in the form of a circle.
Make sure you stand in the same spot and take a picture of the rain circle from a pre determined spot, date each picture.
After a few years assemble the pictures by date and measure the diameters of the rain circles.
If the Earths trajectory around the Sun is elliptical.
The diameters of the rain circles should vary with the trajectory of the ellipse.

 

[Cantab Morgan]

Yes, calculus can do it. But Newton did it without using calculus. In the 20th century, Feynman gave a modern non-calculus derivation as well. Try googling for "Feynman's Lost Lecture."

 

[mabs239]

An experimental idea.
At noon each day go into your garden and if the sun is shineing get hold of a hosepipe and spray it useing a circular motion.
Make sure your back is towards the sun.
If the spray is fine enough and you use the correct motion a rain circle will form.
Which is a rainbow in the form of a circle.
Make sure you stand in the same spot and take a picture of the rain circle from a pre determined spot, date each picture.
After a few years assemble the pictures by date and measure the diameters of the rain circles.
If the Earths trajectory around the Sun is elliptical.
The diameters of the rain circles should vary with the trajectory of the ellipse.

I am interested in the experimental setup but don't understand how it should work. As i think the Earth completes its orbit in one year, but you have asked to observe for years. Isn't one Earth enough?
How the rain circle would change shape with the Earth's position in its orbit?

 

[Buckleymanor]

I am interested in the experimental setup but don't understand how it should work. As i think the Earth completes its orbit in one year, but you have asked to observe for years. Isn't one Earth enough?
How the rain circle would change shape with the Earth's position in its orbit?

One year could be enough it just depends on the weather.
Some days it will be cloudy so you would be unable to take measurements on those days.
So the longer and more days measurements are taken the more accurate.
The rain circle changes shape with perspective.
At different times of the year the rain circle will appear bigger and at other times smaller depending on the Suns distance from the observer.