What are the 4 orbital shapes?

Answer 1

We can come up with only three:

-- hyperbolic

-- parabolic

-- elliptical (including circular, a special case of elliptical)

Circles, ellipses, parabolas and hyperbolas are all conic sections, the intersection of a plane with a right-circular cone.

Orbitals in quantum chemistry have shapes that are spheres for s-orbitals, dumbbells for p-orbitals, and different types of d-orbital are either pairs of crossed dumbbells, or a dumbbell with a central collar. f-orbitals have yet more complex shapes, but they are not usually considered in textbooks.

In physics, p and d orbitals have rather different shapes. A s-orbital is still a sphere, but p-orbitals are either dumbbells or tyres, and d-orbitals are collared dumbbells, double (point to point) cones, or tyres.

Answer 2

Orbits are all forms of conic section, the curve formed by intersecting a plane with a symmetrical circular cone.

The shape of a conic section is defined by a parameter called eccentricity, written as e. In order of eccentricity the four orbital shapes are: circles (e=0), ellipses (0<e<1), parabolas (e=1) and hyperbolas (e>1). Planets' orbits are ellipses with e less than 0.1, so they are approximately circular. You can only get a hyperbolic orbit with a body coming in at high speed from outside the solar system, which is extremely rare.

You can make conic sections by shining a torch on a wall (a torch with a old fashioned bulb, not LEDs). It produces a cone of light, and the wall gives the intersection, so on the wall you can create those four shapes. Shining it straight at the wall gives a circle, slightly off gives an ellipse, then with one side of the cone parallel to the wall you get a parabola, and turning it further creates a hyperbola.

Answer 3

If you take Newton's formula for gravitation, MASH it together with Calculus and

Geometry, and play with them long enough, you come up with all the properties

of the orbits that we see all around us in space. Here are some of the characteristics

of gravitational orbits:

-- The entire orbit is in a plane; it's flat, and it would lie completely on a big-enough

sheet of paper.

-- The shapes of all possible paths that gravity can cause a body to take are called

the "conic sections". They're all shapes that you can get by cutting through a cone

while you hold the 'knife' at different angles.

-- If the orbiting body hasn't enough energy to escape the central body, then

it moves in an orbit the shape of an ellipse, with the central body at one focus.

-- A very special case of the ellipse, if everything is just exactly right, is a circle ...

so rare that it's virtually never seen in nature.

-- The imaginary line between the orbiting body and the central body 'sweeps out'

equal areas in equal times. That means that the orbiting body moves fastest when it's

closest to the central body, and slowest when it's farthest out in its orbit.

-- For all the bodies in orbits around the same central body ... like the planets, moons,

comets, and asteroids in the solar system ... (the square of the time it takes a body

to complete an orbit) divided by (the cube of the orbiting body's average distance from

the central body) is always the same number. That means those with larger orbits

move slower in their orbit, and take much longer to complete each revolution.

-- A small body that sails by another larger one, but has enough energy to keep going

and not get captured, has its path 'bent' by the mutual gravitational attraction

between the two of them. Technically, that's also an 'orbit' ... it's just an "open" one.

In general, every open orbit has the shape of a "hyperbola".

-- The special case that's just exactly on the borderline between the strongest closed (elliptical)

orbit and the weakest open one, is the path called a "parabola". Like the circle, it only

happens when everything is just exactly right, so it's never seen in nature.

-- Planets have elliptical orbits that are very 'un-eccentric', and look very circular.

There's not much difference between a planet's nearest and farthest distance

from the sun.

-- Comets have orbits that are very 'eccentric'; the difference between their nearest

and farthest distance from the sun can be gigantic. Since they're so small, they're

only visible for the short time when they come in close to the sun.

-- Sometimes we can observe a comet, and not be able to tell whether or not it will

ever come back again. Why is that ?

The comet may be in a closed, elliptical orbit that's so eccentric ... long and thin ...

that it returns to the inner solar system only once in a thousand years. Or, it may be

in an open orbit, just sailing past the sun in an open, hyperbolic orbit, and never

to return.

We can only see the comet for a relatively short time, while it's at its closest approach

to the sun. And at that part of the orbit, an open, low-energy hyperbola and a closed,

high-energy, highly-eccentric ellipse, have practically the same shape. Over the small

portion of the comet's orbit that we can see, the difference would be so small that we can't

measure it, and we really can't say when ... or whether ... that comet will ever return.