From: schillin@spock.usc.edu
"Wim Dekker" writes:
>"Mike Miller" wrote in message
>news:5dcb47db.0309260349.711f770@posting.google.com...
>> DP wrote in message
>news:<3f6e2897$1@nntp.unige.ch>...
>> That's a bit different than Jovian atmosphere re-entry. Like,
>> a lot slower. Cassini's RTGs were expected to (IIRC) burn off
>> 33% of their mass if Cassini hit Earth during its sling shots
>> past Earth. Cassini swung by Earth at 19km/s. Galileo hit Jupiter
>> at 48km/s. 2.5 times the entry velocity translates into 6.25
>> times the kinetic energy to be converted into heat per kilogram
>> of spacecraft.
>I don't understand why kinetic energy increases quadratically
>with speed while the energy it costs to increase speed itself
>seams to be directly proportional to the speed. After all,
>speed = acceleration * time. What's wrong with my reasoning?
The implicit assumption that acceleration is proportional to
energy or power. In fact, power = acceleration * velocity,
so when you do the integral you do get energy = 1/2 * mass *
velocity^2.
Yes, there are many propulsion systems which provide constant
thrust for a constant applied power. But they do this, at low
velocities, by applying energy to something other than the
acceleration of the vehicle (specifically, acceleration of the
exhaust), and at high velocities, by exhausting reaction mass
that has already been accelerated to high velocity at great
cost in energy.
When you do the integral over the trajectory of the vehicle,
you find that the energy applied is >= 1/2 * mass * velocity^2
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