Potential energy can be changed into kinetic energy

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Potential energy can be changed into kinetic
energy and vice versa.
h1
PE less negative here
going from h2 to h1
DPE
h2
PE negative here
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m
PE 0
Escape Velocity
infinitely far
m
R
M
M
How much speed would m have to be given (straight
up) to go to infinity and have no extra energy
(speed) left over when it got there?
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Comets and asteroids typically impact the earth
with a speed of 11.2 to 70 km/s. Thats 25,000
to 156,000 miles per hour. The oldest known
fossils of bacteria date from 3.8 billion
years ago. For almost the first billion
years impacts may have made the Earth
uninhabitable. But these same collisions may
have brought some of the chemicals necessary to
life.
Consider the impact of even a 1 km diameter rock
with density 5 gm cm-3 at 50 km s-1. The mass
would be 4/3 p r3 r, or 2.6 x 1015 gm. The energy,
equivalent to about 780,000 Megatons of high
explosive.
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Barringer Meteor Crater Arizona,
1.19 km 49,000 years
Classic simple meteorite impact crater
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Aorounga Crater, Chad Africa (Sahara Desert)
17 km in diameter 200 million years
imaged from space, evidence for multiple impacts
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Manicouagan Crater, Quebec Canada 100 km,
212 million years
one of the largest impact craters preserved on
the surface of the Earth.
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Chicxulub
Yucatan, Peninsula, Mexico 170 km across age
64.98 million years. Buried under several hundred
meters of sediment blocking it from easy view
(this picture results from local
gravitational and magnetic field variations). The
asteroid that produced this impact crater is
believed to have had a diameter of 10 to 20
km. The impact hit a region rich in sulfur
bearing rock. The sky may have been dark as night
for close to a year. Temperatures would have
been freezing. Half the species on earth
perished.
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Asteroid 2000 SG244 has a 1 in 500 chance of
hitting the Earth in 2030. It would barely nudge
the indicator from zero to 1, the only object
to do so so far. It may even be an old rocket
booster,
If it impacted it would be about 1/10 of a
Tunguska even or about 100 Hiroshima- like
bomb equivalents.
http//impact.arc.nasa.gov/news/2000/november/3.ht
ml
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Gravitational Binding Energy
What is the potential energy of a spherical shell
of mass m sitting atop a sphere of radius M and
radius R? That is how much energy would it take
to remove the outer shell and take it to infinity?
r
m
M
Take this shell off
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and what is the mass of that shell if the density
is constant (r) and the shell is very thin with
dr ltlt r.
m
r
rdr
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To remove a shell
r
dr
M
Let Mtot be the total mass of the sphere and R
its radius
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Kelvin-Helmholtz Evolution
(Lord Kelvin, Herman van Helmholtz, mid-1800s)
E.g., Divide M into 2, 4, 8, 16, ... pieces
Assuming that half of this energy goes into
radiation and using the suns current mass (2 x
1033 gm) and luminosity (3.8 x 1033 erg s-1)
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What happens to a star after it has contracted
for a Kelvin Helmholtz time?Eventually it gets
hot enough to ignite nuclear reactions because
as we will show later, in the absence of
degeneracy
As the radius shrinks the central
temperature goes up in order to support the
weight of the more compact configuration.