Eero wrote:

Consider an astronaut who orbits circularly with a spacecraft at distance L
from a planet's center. The planet's radius, mass and acceleration of
gravity at its surface are R, M and g.
Now, the astronaut wants to fire a bullet and hit the planet. What minimum
initial speed of the bullet is necessary to do this?(Supposing no air
resistence)

What have you done so far to approach this problem?

Eero wrote:

Consider an astronaut who orbits circularly with a spacecraft at distance L
from a planet's center. The planet's radius, mass and acceleration of
gravity at its surface are R, M and g.
Now, the astronaut wants to fire a bullet and hit the planet. What minimum
initial speed of the bullet is necessary to do this?(Supposing no air
resistence)

1) What is the current velocity vector?
2) What is the minimum velocity vector for orbit?
3) Do the obvious, with the angle set maximize the velocity
increment in the appropriate direction.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

Consider an astronaut who orbits circularly with a spacecraft at distance L
from a planet's center. The planet's radius, mass and acceleration of
gravity at its surface are R, M and g.
Now, the astronaut wants to fire a bullet and hit the planet. What minimum
initial speed of the bullet is necessary to do this?(Supposing no air
resistence)

"Eero" wrote in message
...
Consider an astronaut who orbits circularly with a spacecraft at distance
L
from a planet's center. The planet's radius, mass and acceleration of
gravity at its surface are R, M and g.
Now, the astronaut wants to fire a bullet and hit the planet. What minimum
initial speed of the bullet is necessary to do this?(Supposing no air
resistence)

First tell us, is this a homework problem and if so when
is it due?

In Eero wrote:
Consider an astronaut who orbits circularly with a spacecraft at
distance L from a planet's center. The planet's radius, mass and
acceleration of gravity at its surface are R, M and g. Now, the
astronaut wants to fire a bullet and hit the planet. What minimum
initial speed of the bullet is necessary to do this?(Supposing no air
resistence)


The answer is 5, using appropriate units.
--
Andrew Resnick, Ph. D.
National Center for Microgravity Research
NASA Glenn Research Center

"Uncle Al" wrote in message
...
Eero wrote:

Consider an astronaut who orbits circularly with a spacecraft at
distance L
from a planet's center. The planet's radius, mass and acceleration of
gravity at its surface are R, M and g.
Now, the astronaut wants to fire a bullet and hit the planet. What
minimum
initial speed of the bullet is necessary to do this?(Supposing no air
resistence)

1) What is the current velocity vector?
2) What is the minimum velocity vector for orbit?
3) Do the obvious, with the angle set maximize the velocity
increment in the appropriate direction.

Uncle Al, that is the worst advice you have given in a long time.

Franz

"Eero" wrote in message ...
Consider an astronaut who orbits circularly with a spacecraft at distance L
from a planet's center. The planet's radius, mass and acceleration of
gravity at its surface are R, M and g.
Now, the astronaut wants to fire a bullet and hit the planet. What minimum
initial speed of the bullet is necessary to do this?(Supposing no air
resistence)

First clue: Fire the bullet retrograde, in the direction opposite
the astronaut's orbital velocity. This will drop it out of the initial
circular orbit to a lower energy elliptical orbit. If the new orbit's
eccentricity is great enough, it'll intersect the planet. (This will
also increase the astronaut's energy, putting it into an elliptical
orbit with periapsis on the orginal orbit, and an apoapsis at a higher
altitude.)

-Mark Martin

"Greg Neill" wrote:

"Eero" wrote in message
...
Consider an astronaut who orbits circularly with a spacecraft at distance
L
from a planet's center. The planet's radius, mass and acceleration of
gravity at its surface are R, M and g.
Now, the astronaut wants to fire a bullet and hit the planet. What minimum
initial speed of the bullet is necessary to do this?(Supposing no air
resistence)

First tell us, is this a homework problem and if so when
is it due?

Google: Eero + problem

Take it as a challenge!
Me thinks Eero already knows the solution.

Franz Heymann wrote:

"Uncle Al" wrote in message
...
Eero wrote:

Consider an astronaut who orbits circularly with a spacecraft at
distance L
from a planet's center. The planet's radius, mass and acceleration of
gravity at its surface are R, M and g.
Now, the astronaut wants to fire a bullet and hit the planet. What
minimum
initial speed of the bullet is necessary to do this?(Supposing no air
resistence)

1) What is the current velocity vector?
2) What is the minimum velocity vector for orbit?
3) Do the obvious, with the angle set maximize the velocity
increment in the appropriate direction.


Well... he could angle the vector to give an otherwise OK orbit that
intersected the planet. Do you think he is up to it? Dropping the
bullet out of orbit seemed like a decent compromise.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

"Eero" wrote in message
...
Consider an astronaut who orbits circularly with a spacecraft at distance
L
from a planet's center. The planet's radius, mass and acceleration of
gravity at its surface are R, M and g.
Now, the astronaut wants to fire a bullet and hit the planet. What minimum
initial speed of the bullet is necessary to do this?(Supposing no air
resistence)

Nice quotation of a homework type question. Show us your work.