[LINK] Finally up to date on the Shuttle
Stephen Wilson
swilson@securenet.com.au
Mon, 17 Feb 2003 05:43:29 +1100
Actually, the "bottom line" is not nearly so convoluted. Orbital dynamics was worked out by Kepler, one of the empirical heroes in the discovery of gravity [Newton's contribution was to see that gravity acted between every body in the universe, not just between the planets and our sun]. Tony and Bernard did a neat job of relating the situation in terms of potential and kinetic energies.
For a satellite in elliptical orbit around a planet of mass M, the orbital period T is given by Kepler's Third Law:
T = sqrt(4pi^2a^3 / GM)
where G = Newton's Gravitational Constant
a = length of the semi-major axis of the ellipse
( = r in the case of a circular orbit)
Thus, the orbital period decreases as the satellite descends. And of course the period is independent of the mass of the satellite, just as the acceleration due to gravity (g) is independent of the mass of the falling body.
Cheers,
Steve.
Stephen Wilson
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> -----Original Message-----
> From: Frank O'Connor [mailto:foconno1@bigpond.net.au]
> Sent: Sunday, February 16, 2003 5:23 PM
> To: Chirgwin, Richard
> Cc: 'Link '
> Subject: RE: [LINK] Finally up to date on the Shuttle
>
>
> I suppose an easy way of looking at it might be to make gravity
> central to the equation ... which it is.
>
> a. Now with gravity you have the Inverse Square Rule ... which means
> the closer you are to a body the more gravitational effect it will
> have on you.
>
> b. That means to stay in a stable lower level orbit requires more
> energy that to stay in a higher level stable orbit.
>
> c. The energy used to maintain this stability is the centrifugal
> force ... and is an accelerative/velocity function of the momentum of
> a body around a central point. (It can be anchored by gravity, string
> or whatever.)
>
> d. Reduce this energy when gravity is the anchor, and gravitic
> attraction becomes greater than the centrifugal force which was
> balancing the orbit ... reducing the distance between yourself and
> the attracting body - and increasing the gravitic effect as you drop
> lower.
>
> e. The simple act of this reduction in velocity and acceleration and
> close relations with the attracting body however converts potential
> energy that had been stored into the orbiting body getting it into
> the orbit (in which kinetic energy was converted to potential energy)
> back into kinetic energy ... but on a different vector to the
> centrifugal energy (which had been vectored/angled away from the
> attracting body) and toward the attracting body.
>
> Hence the increase in speed (due to gravitc attraction) as a result
> of backing off on your centrifugal energy.
>
> The bottom line is that there are a number of different vectors and
> forces that come into play, and a number of conversions of potential
> (stored) energy that relate to getting the orbiting body to where it
> was at in the first place.
>
> As I said in another post ... I wish someone would invent viable
> ant-gravity. :)
>
> Regards,
>
> At 4:46 PM +1000 16/2/2003, Chirgwin, Richard wrote:
> >Thanks to all who helped with this.
> >
> >So, to my clumsy understanding - you preserve momentum. In
> descending orbit,
> >you decelerate; but acquire angular velocity because of the descent.
> >
> >Ie, to begin decending, you slow down; but the ACT of
> decending speeds you
> >up. Or to ascend, you speed up, but the result is lower
> velocity. Yes?
> >
> >Richard
> >
> >-----Original Message-----
> >From: James Pearce
> >To: Link
> >Sent: 14/02/03 16:53
> >Subject: Re: [LINK] Finally up to date on the Shuttle
> >
> >That's phenomenal, Bernard!
> >
> >As a body in orbit decelerates towards the earth (or at
> least, reduces
> >it's
> >acceleration) it's speed increases! That would happen, too.
> Physics is
> >weird...
> >
> >
> >----- Original Message -----
> >From: "Bernard Robertson-Dunn" <brd@austarmetro.com.au>
> >To: "Link" <link@anu.edu.au>
> >Sent: Friday, February 14, 2003 4:07 PM
> >Subject: Re: [LINK] Finally up to date on the Shuttle
> >
> >
> >> Re all this orbital mechanics stuff.
> >>
> >> The dynamics of an orbiting body is a combination of kinetic and
> >potential
> >> energy.
> >>
> >> An orbitting body at (say) 500km altitude has a
> particular velocity.
> >To
> >get
> >> to an alltitude of 1000km, it has to fire its rockets.
> Once it gets
> >into
> >> its higher orbit it is actually going slower than at
> 500km. The energy
> >from
> >> the rocket firing has initially been converted kenetic
> energy but with
> >an
> >> increase of altitude this changes into potential energy.
> >>
> >> Every orbital altitude equates to a particular velocity
> (both angular
> >and
> >> rotational).
> >>
> >> The reason why a body has to decelerate to go into a
> lower orbit, but
> >> higher velocity, is because it has excess potential energy. Total
> >energy
> >> level (KE+PE) needs to be reduced in order to get to a
> lower orbit.
> >This
> >is
> >> done initially by reducing the KE. As it moves to a lower
> orbit the PE
> >> reduces but the KE increases to a level that was greater
> than at the
> >higher
> >> orbit.
> >>
> >> --
> >> I know that this defies the law of gravity, but, you see, I never
> >studied
> >> law.
> >> --Bugs Bunny
> >>
> >> Regards
> >> brd
> >>
> >> Bernard Robertson-Dunn
> >> Canberra Australia
> >> brd@austarmetro.com.au
> >> _______________________________________________
> > > Link mailing list
> >> Link@mailman.anu.edu.au
> >> http://mailman.anu.edu.au/mailman/listinfo/link
> >
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