Possibly Dim Witted Question Regarding Comets (Orbits)

One of those things you suddenly think of for the first time in the middle
of the night..

Considering long period comets that have dropped in all the way from the
Oort cloud; how come they don't just plough straight into the sun? Surely
the comets in the cloud are moving very slowly (escape velocity at 1 light
year must be very small) and any such transverse (correct term?) velocity
will be negligible by the time the comet has plunged that far; with all the
time the sun's gravitational pull tugging the comet towards the sun.

So how come they miss?

Sorry if this question strikes anybody as idiotic.

Ian

"J" == Jaxtraw writes:

J Considering long period comets that have dropped in all the way
J from the Oort cloud; how come they don't just plough straight into
J the sun? Surely the comets in the cloud are moving very slowly
J (...) and any such transverse (...) velocity will be negligible by
J the time the comet has plunged that far; with all the time the
J sun's gravitational pull tugging the comet towards the sun.

Think back to why the comets orbit at all. Suppose you have a body at
some distance from the Sun with no transverse velocity. (In this
case, transverse means perpendicular to the line joining the Sun and
the body.) What will happen to it? It will simply fall toward the
Sun and plunge into it.

What if the body has even a little bit of transverse velocity? Then
it has some angular momentum, which is given roughly by L = mvr, where
r is its distance from the Sun, v is its velocity, and m is its mass.
Angular momentum is a conserved quantity, meaning that unless there
are *dissipative* forces (like frictional forces) it doesn't change.

As the comet falls toward the inner solar system, m changes only very
slightly, but r decreases dramatically. In order for L to remain
unchanged, v must increase by the same fraction. Thus, the comet has
a high transverse velocity and misses the Sun.

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Joseph Lazio wrote:
"J" == Jaxtraw writes:

Considering long period comets that have dropped in all the way
from the Oort cloud; how come they don't just plough straight into
the sun? Surely the comets in the cloud are moving very slowly
(...) and any such transverse (...) velocity will be negligible by
the time the comet has plunged that far; with all the time the
sun's gravitational pull tugging the comet towards the sun.

Think back to why the comets orbit at all. Suppose you have a body at
some distance from the Sun with no transverse velocity. (In this
case, transverse means perpendicular to the line joining the Sun and
the body.) What will happen to it? It will simply fall toward the
Sun and plunge into it.

What if the body has even a little bit of transverse velocity? Then
it has some angular momentum, which is given roughly by L = mvr, where
r is its distance from the Sun, v is its velocity, and m is its mass.
Angular momentum is a conserved quantity, meaning that unless there
are *dissipative* forces (like frictional forces) it doesn't change.

As the comet falls toward the inner solar system, m changes only very
slightly, but r decreases dramatically. In order for L to remain
unchanged, v must increase by the same fraction. Thus, the comet has
a high transverse velocity and misses the Sun.

Many thanks for your reply! It's one of those things that seems (to me
anyway) counter-intuitive; which just shows how useless intuition can be

Ian

"Joseph Lazio" wrote in message
...
"J" == Jaxtraw writes:

J Considering long period comets that have dropped in all the way
J from the Oort cloud; how come they don't just plough straight into
J the sun? Surely the comets in the cloud are moving very slowly
J (...) and any such transverse (...) velocity will be negligible by
J the time the comet has plunged that far; with all the time the
J sun's gravitational pull tugging the comet towards the sun.

Think back to why the comets orbit at all. Suppose you have a body at
some distance from the Sun with no transverse velocity. (In this
case, transverse means perpendicular to the line joining the Sun and
the body.) What will happen to it? It will simply fall toward the
Sun and plunge into it.

What if the body has even a little bit of transverse velocity? Then
it has some angular momentum, which is given roughly by L = mvr, where
r is its distance from the Sun, v is its velocity, and m is its mass.
Angular momentum is a conserved quantity, meaning that unless there
are *dissipative* forces (like frictional forces) it doesn't change.

As the comet falls toward the inner solar system, m changes only very
slightly, but r decreases dramatically. In order for L to remain
unchanged, v must increase by the same fraction. Thus, the comet has
a high transverse velocity and misses the Sun.

As an exercise for the alert reader, calculate the maximum
transverse velocity for a body at aphelion at the distance
of the Oort Cloud to be able to intersect the surface of
the Sun at perihelion.

Any velocity in excess of this value guarantees a miss.