Re: What would be Earth's new Orbit if an Asteroid slowed it's speed down by half?

On Jun 26, 1:06 am, The Ghost In The Machine
<e...@xxxxxxxxxxxxxxxxxxxxxxx> wrote:
In sci.physics.relativity, g...@xxxxxxxxxxx
<g...@xxxxxxxxxxx>
wrote
on Mon, 25 Jun 2007 20:14:03 -0700
<1182827643.282464.65...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>:

On Jun 25, 6:25 pm, Eric Gisse <jowr...@xxxxxxxxx> wrote:
On Jun 25, 1:54 pm, "g...@xxxxxxxxxxx" <g...@xxxxxxxxxxx> wrote:
[...]

http://www.amazon.com/Mechanics-3rd-Keith-R-Symon/dp/0201073927

Another boring problem thought up by an equally boring mind. You would
know how to do this *** if you just STUDIED a little.

Liar, do it.

I need the practice. :-)

Assuming the Earth's orbit is currently perfectly circular (which it's
not, but this is a back-of-the-envelope calc), we currently have an
orbital velocity of 30 km/s. The asteroid (which would have to be
pretty big!) would reduce that velocity to 15 km/s, at what will
essentially become the new aphelion.

It turns out that the old orbit energy is dependent solely on the
semimajor axis (the old radius). Since the old orbit was 1 AU,
we can express the energy as

E_old = -G*M_sun * M_earth / (2*1 AU) = -K/2


One thing I don't understand exactly, Since E= F * r for both kinetic
and potential:

Where Fk = Fc= mv^2/r (Fc = Centrifugal Force) and Fg= GMm/r^2

thus using E= F*r therefore Ek= (mv^2/r) * r thus Ek =mv^2 and not
1/2mv^2??



where K is some constant. The kinetic energy of this orbit turns
out to be +K/2; therefore

E = -K + K/8 = -7K/8 = -G*M_sun * M_earth / (2 * (4/7 AU))

With aphelion of 1 AU and semimajor axis of 4/7 AU, we get
4/7 * (1 + e) = 1 or e = 3/4; therefore perihelion is
4/7 * 1/4 = 1/7 AU.

Since T = 2*pi * a^(3/2) / sqrt(G*M_sun), and T_old = 1 year,
T_new = (4/7)^(3/2) = 157.8 old days (the new day, of course,
will depend on precisely where the asteroid hits).


Therefore the Earth would now be closer to the Sun and it's new
average distance (since it's an Ellipse) from the Sun is 4/7 AU (4/7
of the Earth original distance from the Sun, before the Asteroid
collision slowed it down).


Global warming will be the least of our problems. :-)

http://scienceworld.wolfram.com/physics/Orbit.html

http://en.wikipedia.org/wiki/Ellipse

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