What is the celesteal sphere ?
406955
It is the imaginary sphere on which all celestial objects are plotted. It is basically a map of the sky as seen from the Earth. Something like a globe, but seen from the inside. Knowing the coordinates of a star or planet on the celestial sphere tells you which way to look to see it but does not tell you how far away it is.
494502
This question is answered very well in solid geometry.\n\nOn a plane, it's a straight line.\n\nOn the surface of a sphere, it's a curved-line called a great circle.\n\nIn space, considering the curvature caused by the masses of any nearby bodies between you and the destination point, it may be a complex three-dimensional curve.
202397
Presumably the mooon is approximately spherical for the same reason that the earth or other round celestial bodies are approximately spherical. Some comments: \n\n1. For solid bodies like the moon and the earth:\n\nThey probably formed as molten, self gravitating bodies, and the sphere is the minimum energy shape. If they rotate, hydrodynamic forces flatten them slightly, making the semimajor axis aligned with the axis of rotation shorter than the other two axes in general. \n\n2. For stars:\n\nAgain, the minimum energy configuration for many standard isolated stars is roughly spherical. If they are rotating, they might be oblate spheroids, but still close to spherical, as long as there are no other very massive bodies close to distort their shape. \n\n3. For nonspherical bodies like asteroids and comets:\n\nThese irregular chunks might have formed after some large body cooled, or not had sufficient mass for gravitational forces to constrain the shape to be spherical. \n\n4. For nonspherical stars:\n\nThere are many stars that are binaries, and the two stars are so close that their shapes are distorted (i.e., their Roche lobes are filled so they look like egg shapes, or they have accreation disks, etc). There might be other processes active that distort them away from spherical shapes. Even large close planets might distort their shapes in some cases.
988952
because gravity points to the center of the sphere, so no matter where you are on teh sphere, the down direction is towards the center of teh planet, wich allows penguins in teh south pole to walk on teh surface of the planet.\nIf you look at constelation however, they do appear upside down when viewed from below the equator, proving that we are walking on a sphere
1132291
do you mean the hemispheres?\n\ntry http://en.wikipedia.org
508642
Well you can't really have a center of the diameter line of a sphere.  But I guess the common dividing point would be where the prime merdian (zero degrees longitude) passes through the equator.  The intersection point is in the eastern Atlantic ocean, south of Ghana in Africa.
788662
It's a parabola. I believe the astronomer Roger Angell proposed a parabolic reflector using mercury in a spinning container. The paraboloid is the natural equilibrium shape of minimum potential energy. The liquid assumes a level consistent with the local acceleration, which is the sum of gravity and radial acceleration given by w^2*r, where w is the rotational rate in rad/sec and r is the radius. The resulting paraboloid surface is perpendicular to the acceleration at all points.
1108757
I suppose you do know this\nIn mathematics, a hypersphere is a sphere which has dimension 3 or higher\nThe set of all points on this sphere has dimension n − 1, so it is called the (n − 1)-sphere and is denoted . It may be written as (x1,x2,...,xn) where\n\nThe hyperdimensional volume of the space which a (n − 1)-sphere encloses (the n-ball) is\n\n    _\nV=II^n/2. R^n/Γn/2=1  II-pie\n   \n\nIf the dimension,  , is not limited to integral values, the hypersphere volume is a continuous function of  with a global maximum for the unit sphere in "dimension" n = 5.2569464... where the "volume" is 5.277768...\n\nThe hypercube circumscribed around the unit n-sphere has an edge length of 2 and hence a volume of 2n; the ratio of the volume of the hypersphere to its circumscribed hypercube decreases monotonically as the dimension increases.\n\n\nHEY I KNOW ONLY THE VOLUME
198263
So far, the answers have addressed a variety of ways of looking at "above and below" the solar system.  A few have only looked at things from the earth's perspective, which does not seem to be what you're looking for.  Someone mentioned the galactic plane, which is a better answer.  However, you specifically mention the planets revolving around the Sun, which leads me to believe you are specifically interested in what lies above and below the plane of the those orbits.\n\nThe plane in which most of the planets (Pluto being the exception) orbit is called the ecliptic plane.  Earth's axis is tilted relative to this plane by 23.5 degrees, so "above and below" doesn't quite coincide with above and below the Earth's poles.  If you look at the points north and south of the ecliptic plane, they lie in the constellations Draco and Dorado, respectively.  Neither of these constellations lie in the galactic plane.  In Draco, there are a few bright stars, and a number of galaxies are visible in a good size telescope.  In Dorado, which is only visible from the southern hemisphere, one finds the Large Magellanic Cloud.  This a galaxy separate from our own Milky Way; it is a companion to our galaxy, 180,000 light years distant.\n\nThe galactic plane intersects the ecliptic plane in Gemini and Sagittarius.  Aside from these areas of the sky, the bulk of the galaxy is above and below the solar system.  The center of the galaxy, though, lies in Sagittarius.  Thus, the thickest part is, by coincidence, in the same plane as the solar system, though much more distant.\n\nLocally, there are comets that have orbits that are steeply inclined to the ecliptic plane, so there are nearby objects that spend most of their time above and below the solar system.  There are some asteroids that fit this description as well.  Even the newly discovered object 2003UB313, which is bigger than Pluto, has an orbit that is inclined 44 degrees to the ecliptic plane.  It is part of this solar system, for certain, but it spends most of its time outside of the plane of the other planets' orbits.
291242
It is in the northern hemisphere. In the northern half of the planet.
1044842
simply round... or shall i say spherical objects contains the most volume in the least surface area possible, in other words, the surface area of a cube is larger than of a sphere if they have the same volume and so on and so on, for an example in the case of an air bubble and a water drop, the surface tension effect tends to decrease the surface area thus creating a sphere, same thing with planets but here, gravity also has a roll to contain as much volume as close as possible and as you know planets were created from molten rock so the surface tension also played the same roll of decreasing the surface area here too...
296045
Try looking it up on Galileo or EBSCOHost database.
580033
You've probably seen the pictures of a grid with a giant funnel extending infinitely downward.  That's not the shape of the hole itself, but a map of the curvature of space near the singularity.  The singularity, or "hole" itself is a point of infinitely large density and infinitely small size.
1076251
It is never-ending, continuous.  It is a symbol of rebirth, of the turning of the seasons, of life.  There are many special things about the circle.  As a sphere, it is not as subject to the elements as other 3-D shapes.  Wind and water go right over or around it.
411812
The ecliptic is the path in space that we see traced out as the earth rotates around the sun.  The angle between this plane and the equatorial plane is what gives us the seasons.
1001159
it is 4/3*pi*r^3\n\ngo to this website for an explanation\n\nhttp://www.qc.edu.hk/math/Junior%20Secondary/Sphere.htm
1059594
http://www.pantheon.org/articles/m/mermaid.html\nGood luck!