Hi people,
it is stated in the recent report: http://www.straightdope.com/mailbag/mlunarrotate.html
that:
“An orbit can be considered as a balance between gravity and centrifugal force” <snip> “But these forces aren’t uniform: Centrifugal force gets stronger as you get further from the center, while gravity gets weaker as you get further from the center.”
This sounds like an unstable balance. If the earth gets an inch closer to the sun, this difference could trigger a fatal plunge into the fiery flames of our beloved god Ra!
Why doesn’t this happen? How come planet orbits are so stable?
It’s complicated without some fairly advanced math, but the natural tendency when something pushes an orbiting body inward is for the orbit to speed up, which increases the centrifugal force, which balances the added gravity.
Orbital mechanics are very counterintuitive – the classic example is: if you are chasing someone in orbit, the way to catch up with him is to slow down, which will make you go faster.
It’s really hard to move something from its given orbit. You knw those curved funnel-shaped tracks that you see in science museums, the ones you roll marbles on and they keep going around and around, slowly spiralling in as friction slows them, until finally they drop into the hole in th middle? (Some malls have started puttig n “wishing wells” in his shape – you roll your quarters on the sides. A neat way to collct money for charities.) The cross-section is in the sha[pe of the ravitational potential, an it does a pretty good job of duplicating orbits. Ijn the absence of friction, the ball woul keep orbiting at th same level. Slow it down a bit and it drops a little lower. Speed it up a bit and it goes a little faryher from he “sun” at the center. Give it a little push and the orbi turns just a shade elliptical. To cause your marble to drop to a fietry doom in the center requires a big enough push to make the orbit seriously elliptical (or else a long and gradual push, like the friction, making it spiral in). Objects in orbit tend to be pretty stable.
Shouldn’t that read “centripetal force”? Back when I was failing out of physics for engineers, my professor was very adamant about pointing out the supposed misuse of the term “centrifugal.”
If your universe is rotating at a steady rate, centrifugal force becomes a useful concept (e.g. in designing space-stations). But in orbital mechanics the rotation (revolution) rate is among the least stable of the numbers you’re working with.
In particular, you don’t get to apply the same system to different planets. If Venus and Earth were attached to the same turntable, it would be true that ``Centrifugal force gets stronger as you get further from the center’’ - but they’re not; Venus orbits more quickly.
Furthermore, a given planet does not always move at the same speed. (This was a big problem for astronomers; Kepler’s solution to that problem led to Newton’s grand formulation of universal gravity.) A planet with an eccentric orbit, like Mars, moves most quickly when nearest the sun; if you try to analyze its motions in terms of a constantly rotating reference frame, you get a mess.
Better to think of orbits in terms of conservation of energy, though that’s something of an abstraction. An orbiting body maintains a constant sum of gravitational potential energy (which depends on its distance from other masses) and kinetic energy (which depends on speed). A body in perfectly circular orbit has kinetic energy (positive) equal to exactly half of its gravitational potential energy (negative). A body with `too much’ speed for its distance moves outward.
When Mars is nearest the Sun, its potential energy is lowest and its kinetic energy is highest, so it moves outward. And, of course, vice versa.
Thanks for the replies.
I totally get CalMeachams “funnel-track” analogy,
and as JWKennedy explained simply, if the earth gets closer to the sun, it will orbit faster, and therefore compensate.
Now I can sleep tight.