Re: a surprising escape speed problem

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

Carl E. Mungan wrote:

> Okay, I see there have been some interesting messages so far. Let me
> indicate two ways of getting the answer I got. Then you can see if
> there's a flaw in it.
>
> METHOD #1. Use the result for escape from the solar system and simply
> "turn off" the sun's contribution.
>
> For escape from the solar system, the escape speed is given by
> Problem 5.17 in Barger and Olsson "Classical Mechanics" (2nd ed.) to
> be:
>
> v = (v_earth,esc)^2 + (v_sun,esc - v_earth,orbit)^2 = 16.7 km/s
>
> relative to earth. Here v_sun,esc = 42.1 km/s. Now set v_sun,esc = 0
> to get my previously quoted answer.

Barger and Olsson's equation is easily obtained by thinking about
energy conservation.  The first term gets the probe out of the
potential well created by the Earth (and leaves it moving at the
orbital speed of the Earth about the Sun at no additional cost!)  The
second term gets it out of the potential well created by the Sun.

If there is no potential well due to the Sun, you don't need the
second term,  Hence,

  v = v_earth,esc

I'm still trying to follow METHOD #2.

--
John Mallinckrodt        mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.