PS: 1. Why is orion's belt visible in the night sky all year round?
The star systems in the belt are far away from each other so not gravitationally bound and are even farther from us so don't appear to move from our location. Kepler's laws are of no relevance other than defining their nearly circular orbit around the galaxy (which takes about 220 million years). This will give you some basic facts about the three main star systems, one is single, one double and one a triple star system:
PS: 2. Why do we only see Halley's comet once every 70 year's?
It was in an elliptical orbit around the Sun with that period. Kepler's laws apply. It may have now broken up. You can get all the orbital parameters in the sidebar here:
It is physically impossible for a free macro body to revolve around another moving body in any type of geometrically closed path. This can be observed by watching a person trying to move around another person running along a defined path. Planets are free macro bodies, central body (the sun) is a moving body and circular/elliptical path is a geometrically closed path. See: http://vixra.org/pdf/1311.0018v1.pdf
'Kepler's laws on planetary motion' deal with relative positions of central and planetary bodies in a planetary system. They predict the relative positions of planets with respect to the moving sun. Suggested paths are not real paths of planets in space. The same principles apply to the appearances of all other macro bodies in space. As nobody (except stable galaxies) can stay without translation in space, no physical body can revolve around another body.
1. Why is orion's belt visible in the night sky all year round?
It isn't! The Orion's celestial coordinates are RA~5h and dec~5deg (i.e. it is only 5 deg above the celestial equator). Hence in the northern spring it is only ~10 deg from the Sun, so it is not visible during the night. We can only nicely see it during northern winter.
However, this has nothing to do with the Kepler's law.
2. Why do we only see Halley's comet once every 70 year's?
Because its orbit is elongated and it takes 70 years to come back to the same position. Most of the time it is too far away and not active enough to be seen.
The only stars which are visible all year round are the circumpolar stars, which go round the celestial poles, neither rising nor setting as the Earth rotates. The altitude of the celestial pole above the north or south horizon (depending which hemisphere you're in) is equal to the latitude of the observer. So for an observer on 50 degrees north latitude, say, any star which is closer to the pole than (90 minus 50 degrees, i.e. within 40 degrees of the pole, will be circumpolar. Where I am, in the central belt of Scotland at 55 degrees north, the circumpolar stars include Ursa Major (including the Plough, also known as the Big Dipper), Cassiopeia, Vega in the constellation Lyra and Capella in the constellation Auriga. When Capella is high overhead in winter, Vega is skirting the northern horizon, and vice versa in summer. The celestial equator passes through Orion's Belt, so the constellation Orion cannot be circumpolar anywhere on Earth.
However the situation changes over a period of 26,000 years due to the wobble of the Earth's axis, called the Precession of the Equinoxes. Around 3000 BC, at the time of building Stonehenge 1 and the Pyramids, the north pole star was Thuban in Draco. Orion was still not circumpolar in the UK, indeed it then rose considerably further south, but neither was Capella, though getting near it. On the far side of the precessional cycle, 13,000 years ago during the last Ice Age, Vega was the pole star and Orion was still further south, so there has never been a time when it was visible all year round from here.
I hope this helps! For diagrams, please see Chapter 2 of my book "The Stones and the Stars" (Springer, 2012). I believe you can order the individual chapter online if that's all that you need, though you might enjoy the book as a whole.
Concerning Halley's Comet, it was last close to the Sun in 1985-86, on its elliptical orbit, and is now near its furthest point from it, well beyond the orbit of Neptune. It will be back, but not for another 33 years or so!
Thanks for taking part in my debate, no one agrees with my observations that Orion's belt is visible in the night sky all year round, and the connection to Kepler's law on planetary motion was also challenged. The only way forward is to launch my investigation on the first clear night after the spring equinox. Full details of how my observations evolve from a fixed point in space and time, will be given with my first monthly report to this debate. at the end of 1 year of data, the relation to Kepler's law, and Halley's comet will be discussed. Once again thanks for your comments
Paul Somerville I didn't mean that Orion is not visible after the spring equinox. Even now the Sun is too close to Orion to see it during a night. You can maybe see it briefly during dusk or dawn just before sunrise or just after sunset if you have clear horizon and excellent visibility.
The fact that the Kepler's laws have nothing to do with Orion is because these laws applies to bodies which interact gravitationally. The stars and the nebula in the Orion constellation are too far for any gravitational force to be measurable (and all these objects are even at different distances from us). Their motion with respect to the observer on Earth and the relation with the position of the Sun is just the consequence of the Earth rotation and orbital motion, so is purely a geometrical effect.
PS: no one agrees with my observations that Orion's belt is visible in the night sky all year round
If you measure carefully where it is seen at midnight, the position will change by slightly less than 1 degree per day, 360 degrees in a year. In winter it is visible to the south at night while in summer it seen to the south in the day, but usually hard to see due to sunlight. There is no sudden cutoff, just a slow progressive shift.