Do satellites affect planetary rotational inertia?

I know that a rigid body's rotational inertia increases as its density
decreases (for example, if I stretch my arms out while whirling on a
swivel chair, I spin slower). Does this effect occur when an artificial
satellite launches into orbit and thereby spreads out the rotating
terrestrial mass?

A satellite does not have much mass compared to the planet's mass, but we
are mathematicians, so we know that we will eventually have to cope with
the problem of "limit of rotational inertia as satellite mass approaches
planetary mass."

[Mod. note: top-posting fixed. Please don't top-post -- mjh]

Josh Sorkin wrote:
I know that a rigid body's rotational inertia increases as its
density decreases (for example, if I stretch my arms out while
whirling on a swivel chair, I spin slower). Does this effect occur
when an artificial satellite launches into orbit and thereby
spreads out the rotating terrestrial mass?

Josh,

A body's (or a system's) _angular momentum_ is conserved, so if the
mass distribution, in toto, moves further from the center of rotation,
the speed of rotation will slow, and vice versa. (That's often
illustrated by the ice skater spinning and pulling in their arms with
their spin speeding up.)

So taking the matter gravitationally bound to the Earth as the whole
Earth system, yes, moving things outward slows the system's rotation.
But keep in mind that the orbital angular velocity change (from the
one revolution per day that characterizes anything fixed to the Earth's
surface) that applies to all artificial satellites other than the
geosynchronous ones must be taken into account, too. Since we have few
(any?) orbiting satellites beyond the geosynchronous range, this means
that launching satellites slows the Earth's rotation even more than
would be the case in the ice skater illustration (assuming the
satellite has a non-zero orbital component in the same direction as
the Earth's rotation--the satellite would slow the Earth if it orbits
in the opposite direction). Any polar component of the satellite's
orbit will end up causing some rotation in the Earth system in the
opposite direction as the orbit.

Note, too, that pretty much all of the momentum transfer that gets
satellites into orbit is balanced by momentum transferred to rocket
exhaust, which becomes part of the atmosphere and not (immediately)
the planet per se. So keep in mind that you have to take into account
the motion of the atmosphere, too--it all contributes to the net
angular momentum of the Earth system.

Lastly, mass that was not formerly gravitationally bound to the Earth
is falling into the Earth system all the time, so the amount of
gravitationally bound mass in the Earth system is steadily increasing.
Depending on the trajectory on which it falls in, it could either
increase or decrease the magnitude Earth system's net angular momentum
and will typically change its direction somewhat. (But that of the
Solar system would remain constant, apart from any mass that enters
our system and becomes gravitationally bound to it.)

I seem to recall reading a few years ago that very precise
measurements of the Earths rotational rate have disclosed the effects
of large dams holding more mass (the water they contain) at a greater
distance from the Earth's center than was the case before those dams
were built. Assuming that was an accurate report, it's the same
phenomenon.


Randall Schulz

[Mod. note: top-posting fixed. Please don't top-post -- mjh]

Josh Sorkin wrote:
I know that a rigid body's rotational inertia increases as its
density decreases (for example, if I stretch my arms out while
whirling on a swivel chair, I spin slower). Does this effect occur
when an artificial satellite launches into orbit and thereby
spreads out the rotating terrestrial mass?

Josh,

A body's (or a system's) _angular momentum_ is conserved, so if the
mass distribution, in toto, moves further from the center of rotation,
the speed of rotation will slow, and vice versa. (That's often
illustrated by the ice skater spinning and pulling in their arms with
their spin speeding up.)

So taking the matter gravitationally bound to the Earth as the whole
Earth system, yes, moving things outward slows the system's rotation.
But keep in mind that the orbital angular velocity change (from the
one revolution per day that characterizes anything fixed to the Earth's
surface) that applies to all artificial satellites other than the
geosynchronous ones must be taken into account, too. Since we have few
(any?) orbiting satellites beyond the geosynchronous range, this means
that launching satellites slows the Earth's rotation even more than
would be the case in the ice skater illustration (assuming the
satellite has a non-zero orbital component in the same direction as
the Earth's rotation--the satellite would slow the Earth if it orbits
in the opposite direction). Any polar component of the satellite's
orbit will end up causing some rotation in the Earth system in the
opposite direction as the orbit.

Note, too, that pretty much all of the momentum transfer that gets
satellites into orbit is balanced by momentum transferred to rocket
exhaust, which becomes part of the atmosphere and not (immediately)
the planet per se. So keep in mind that you have to take into account
the motion of the atmosphere, too--it all contributes to the net
angular momentum of the Earth system.

Lastly, mass that was not formerly gravitationally bound to the Earth
is falling into the Earth system all the time, so the amount of
gravitationally bound mass in the Earth system is steadily increasing.
Depending on the trajectory on which it falls in, it could either
increase or decrease the magnitude Earth system's net angular momentum
and will typically change its direction somewhat. (But that of the
Solar system would remain constant, apart from any mass that enters
our system and becomes gravitationally bound to it.)

I seem to recall reading a few years ago that very precise
measurements of the Earths rotational rate have disclosed the effects
of large dams holding more mass (the water they contain) at a greater
distance from the Earth's center than was the case before those dams
were built. Assuming that was an accurate report, it's the same
phenomenon.


Randall Schulz

Randall R Schulz wrote:

Any polar component of the satellite's
orbit will end up causing some rotation in the Earth system in the
opposite direction as the orbit.

What does "polar" mean in this context? Does it refer to polar
coordinates or a component in the direction of the planet's poles?


Note, too, that pretty much all of the momentum transfer that gets
satellites into orbit is balanced by momentum transferred to rocket
exhaust, which becomes part of the atmosphere and not (immediately)
the planet per se.

How does the problem change in the case of a body without atmosphere,
such as the Moon?

Lastly, mass that was not formerly gravitationally bound to the Earth
is falling into the Earth system all the time, so the amount of
gravitationally bound mass in the Earth system is steadily increasing.

Does the rate of satellite mass increase exceed the
rate of extraterrestrial mass arrival?

Since I first posted, I've thought about decaying orbits that bring the
matter back to the planet; I wonder if enough re-entry occurs to
counteract the
effect of orbitally stretching the planet.

But if the effect nevertheless occurs (however damped), can we exploit it
to gain control of the rotation period?

Randall R Schulz wrote:

Any polar component of the satellite's
orbit will end up causing some rotation in the Earth system in the
opposite direction as the orbit.

What does "polar" mean in this context? Does it refer to polar
coordinates or a component in the direction of the planet's poles?


Note, too, that pretty much all of the momentum transfer that gets
satellites into orbit is balanced by momentum transferred to rocket
exhaust, which becomes part of the atmosphere and not (immediately)
the planet per se.

How does the problem change in the case of a body without atmosphere,
such as the Moon?

Lastly, mass that was not formerly gravitationally bound to the Earth
is falling into the Earth system all the time, so the amount of
gravitationally bound mass in the Earth system is steadily increasing.

Does the rate of satellite mass increase exceed the
rate of extraterrestrial mass arrival?

Since I first posted, I've thought about decaying orbits that bring the
matter back to the planet; I wonder if enough re-entry occurs to
counteract the
effect of orbitally stretching the planet.

But if the effect nevertheless occurs (however damped), can we exploit it
to gain control of the rotation period?

Josh,

Josh Sorkin wrote:

Randall R Schulz wrote:


Any polar component of the satellite's orbit will end up causing
some rotation in the Earth system in the opposite direction as
the orbit.


What does "polar" mean in this context? Does it refer to polar
coordinates or a component in the direction of the planet's poles?

It means an orbit inclined to the equator. If it was inclined 90
degrees, it would be a purely polar orbit. If it was inclined 0
degrees, it would be a purely equatorial orbit.


Note, too, that pretty much all of the momentum transfer that
gets satellites into orbit is balanced by momentum transferred to
rocket exhaust, which becomes part of the atmosphere and not
(immediately) the planet per se.


How does the problem change in the case of a body without
atmosphere, such as the Moon?

Possibly not at all. If the rocket exhaust has enough velocity to
escape, then the body from which the satellite is being launched is
not affected since the particles and molecules of the exhaust gas are
no longer part of that body and any matter gravitationally bound to
it. If the exhaust gases do not have escape velocity, then they'll
repeatedly strike the surface and rebound and each such even will
cause momentum transfer and so the analysis is the same as the
atmospheric case (in effect, those gases are or are part of the
planet's atmosphere, even if it's extremely tenuous). It's similar if
the exhaust gases become bound to the surface, just that the momentum
transfer is slightly different.


Lastly, mass that was not formerly gravitationally bound to the
Earth is falling into the Earth system all the time, so the
amount of gravitationally bound mass in the Earth system is
steadily increasing.


Does the rate of satellite mass increase exceed the rate of
extraterrestrial mass arrival?

Not even close. The first estimate I could find in a cursory Google
search stated that the Earth gains 40,000 metric tons every year.


Since I first posted, I've thought about decaying orbits that bring
the matter back to the planet; I wonder if enough re-entry occurs
to counteract the effect of orbitally stretching the planet.

Well, a satellite that comes back down leaves the whole system the way
it was when it left (ignoring the mass gain from extraterrestrial
infall, anyway).

If you want to get very persnickety about it, you'd have to consider
what happens to the expelled exhaust gases used for orbital and
attitude control and other station-keeping operations required by
satellites that are to remain in long-term orbits. If any of those
gases escape the Earth (probably unlikely, but that's just my offhand
intuition), then once the satellite was de-orbited, there'd be a
little "unrecovered" momentum.


What do you mean by "orbitally stretching the planet?" You're planning
ahead for the sun's increase in output as it ages towards its future
as a red giant? It's hard to see how that's a priority problem, right
now.


But if the effect nevertheless occurs (however damped), can we
exploit it to gain control of the rotation period?


Eh? Control the Earth's rotational period? The Earth may be an
insignificant speck of the overall solar system, it's pretty damn
heavy. The business about rotational period changes from water in dams
and changes in the wind patterns (both vastly more significant than
anything we have or could hope to do in terms of moving mass into
orbit) is still measured in mere milliseconds.

Besides, what's the point in changing the Earth's rotational rate? You
want to create permanent jet-lag among all diurnal species?

Randall Schulz

Josh,

Josh Sorkin wrote:

Randall R Schulz wrote:


Any polar component of the satellite's orbit will end up causing
some rotation in the Earth system in the opposite direction as
the orbit.


What does "polar" mean in this context? Does it refer to polar
coordinates or a component in the direction of the planet's poles?

It means an orbit inclined to the equator. If it was inclined 90
degrees, it would be a purely polar orbit. If it was inclined 0
degrees, it would be a purely equatorial orbit.


Note, too, that pretty much all of the momentum transfer that
gets satellites into orbit is balanced by momentum transferred to
rocket exhaust, which becomes part of the atmosphere and not
(immediately) the planet per se.


How does the problem change in the case of a body without
atmosphere, such as the Moon?

Possibly not at all. If the rocket exhaust has enough velocity to
escape, then the body from which the satellite is being launched is
not affected since the particles and molecules of the exhaust gas are
no longer part of that body and any matter gravitationally bound to
it. If the exhaust gases do not have escape velocity, then they'll
repeatedly strike the surface and rebound and each such even will
cause momentum transfer and so the analysis is the same as the
atmospheric case (in effect, those gases are or are part of the
planet's atmosphere, even if it's extremely tenuous). It's similar if
the exhaust gases become bound to the surface, just that the momentum
transfer is slightly different.


Lastly, mass that was not formerly gravitationally bound to the
Earth is falling into the Earth system all the time, so the
amount of gravitationally bound mass in the Earth system is
steadily increasing.


Does the rate of satellite mass increase exceed the rate of
extraterrestrial mass arrival?

Not even close. The first estimate I could find in a cursory Google
search stated that the Earth gains 40,000 metric tons every year.


Since I first posted, I've thought about decaying orbits that bring
the matter back to the planet; I wonder if enough re-entry occurs
to counteract the effect of orbitally stretching the planet.

Well, a satellite that comes back down leaves the whole system the way
it was when it left (ignoring the mass gain from extraterrestrial
infall, anyway).

If you want to get very persnickety about it, you'd have to consider
what happens to the expelled exhaust gases used for orbital and
attitude control and other station-keeping operations required by
satellites that are to remain in long-term orbits. If any of those
gases escape the Earth (probably unlikely, but that's just my offhand
intuition), then once the satellite was de-orbited, there'd be a
little "unrecovered" momentum.


What do you mean by "orbitally stretching the planet?" You're planning
ahead for the sun's increase in output as it ages towards its future
as a red giant? It's hard to see how that's a priority problem, right
now.


But if the effect nevertheless occurs (however damped), can we
exploit it to gain control of the rotation period?


Eh? Control the Earth's rotational period? The Earth may be an
insignificant speck of the overall solar system, it's pretty damn
heavy. The business about rotational period changes from water in dams
and changes in the wind patterns (both vastly more significant than
anything we have or could hope to do in terms of moving mass into
orbit) is still measured in mere milliseconds.

Besides, what's the point in changing the Earth's rotational rate? You
want to create permanent jet-lag among all diurnal species?

Randall Schulz

Randall R Schulz wrote:
What do you mean by "orbitally stretching the planet?" You're planning
ahead for the sun's increase in output as it ages towards its future
as a red giant? It's hard to see how that's a priority problem, right
now.

I used the term "orbital stretch" incorrectly, I think; I've since seen it
refer to the time interval of a planet's revolution about a star. I
wanted to describe the launch-caused decrease in density. If the planet
has a greater volume (because more pieces of it are farther from the
center, it also has a greater surface area. This permits lower population
density (assuming we can make habitable satellites), which addresses the
relatively urgent problem of overcrowding.



But if the effect nevertheless occurs (however damped), can we
exploit it to gain control of the rotation period?

[snip]

what's the point in changing the Earth's rotational rate? You
want to create permanent jet-lag among all diurnal species?

In general, science seems to progress as we gain the ability to modify
values of a system. We will make better astrophysics if we can compare a
rotating world to a non-rotating one.

Moreover, the planet's angular motion suggests the analogy of a gear. Can
we make it do work in the same way we harness smaller gears?

Lastly, changing spin rates generally produces interesting
consequences, as shown by playing a "33 rpm" record at 45 revolutions per
minute.

Randall R Schulz wrote:
What do you mean by "orbitally stretching the planet?" You're planning
ahead for the sun's increase in output as it ages towards its future
as a red giant? It's hard to see how that's a priority problem, right
now.

I used the term "orbital stretch" incorrectly, I think; I've since seen it
refer to the time interval of a planet's revolution about a star. I
wanted to describe the launch-caused decrease in density. If the planet
has a greater volume (because more pieces of it are farther from the
center, it also has a greater surface area. This permits lower population
density (assuming we can make habitable satellites), which addresses the
relatively urgent problem of overcrowding.



But if the effect nevertheless occurs (however damped), can we
exploit it to gain control of the rotation period?

[snip]

what's the point in changing the Earth's rotational rate? You
want to create permanent jet-lag among all diurnal species?

In general, science seems to progress as we gain the ability to modify
values of a system. We will make better astrophysics if we can compare a
rotating world to a non-rotating one.

Moreover, the planet's angular motion suggests the analogy of a gear. Can
we make it do work in the same way we harness smaller gears?

Lastly, changing spin rates generally produces interesting
consequences, as shown by playing a "33 rpm" record at 45 revolutions per
minute.