orbit question

Suppose you have a spacecraft in a circular orbit around the Earth,
and you point the nose toward the Earth. As it goes around in its
orbit, does it keeps its nose pointed toward Earth, or does it point
to the same direction in space (assuming no thrusters are used and
nothing interferes with it).

Jan Philips wrote in
:

Suppose you have a spacecraft in a circular orbit around the Earth,
and you point the nose toward the Earth. As it goes around in its
orbit, does it keeps its nose pointed toward Earth, or does it point
to the same direction in space (assuming no thrusters are used and
nothing interferes with it).

The answer is that it depends on the initial attitude rates of the
spacecraft, and the shape of the spacecraft (i.e. the distribution of its
mass about the center of mass, also called the moments of inertia).

Assuming no external torques, Newton's laws apply, and the spacecraft will
point the same direction in space. However, the Earth imparts a gravity
gradient torque on the spacecraft that will tend to point the axis with the
minimum moment of inertia toward the Earth, and the axis with the maximum
moment of inertia perpendicular to the orbital plane.

If the "nose" of the spacecraft is along the axis of minimum moment of
inertia (and it is, for all existing manned spacecraft - Shuttle and
Soyuz), and the initial angular velocity of the spacecraft is equal to the
orbital rate, then the nose will remain pointed at the Earth. However,
depending on the values of the moments of inertia of the other two axes,
the spacecraft may roll about the nose. If the orbit is low enough for
aerodynamic torques to be significant ( 500 km), the spacecraft may
stabilize in an orientation that balances the gravity gradient and
aerodynamic torques (a so-called "torque equilibrium" attitude) or it may
oscillate forever.

If the initial angular velocity of the spacecraft is something other than
orbital rate, then the gravity gradient torque will cause the spacecraft to
oscillate about the nose-to-Earth attitude. If no other torques are
present, this oscillation will continue forever, but in the real world,
aerodynamic torques (and internal torques from propellant slosh, body flex,
etc) will eventually stabilize it.

--
JRF

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From Jorge Frank:
Jan Philips wrote in

Suppose you have a spacecraft in a circular orbit around the Earth,
and you point the nose toward the Earth. As it goes around in its
orbit, does it keeps its nose pointed toward Earth, or does it point
to the same direction in space (assuming no thrusters are used and
nothing interferes with it).

The answer is that it depends on the initial attitude rates of the
spacecraft, and the shape of the spacecraft (i.e. the distribution of its
mass about the center of mass, also called the moments of inertia).

Assuming no external torques, Newton's laws apply, and the spacecraft will
point the same direction in space. However, the Earth imparts a gravity
gradient torque on the spacecraft that will tend to point the axis with the
minimum moment of inertia toward the Earth, and the axis with the maximum
moment of inertia perpendicular to the orbital plane.

If the "nose" of the spacecraft is along the axis of minimum moment of
inertia (and it is, for all existing manned spacecraft - Shuttle and
Soyuz), and the initial angular velocity of the spacecraft is equal to the
orbital rate, then the nose will remain pointed at the Earth. However,
depending on the values of the moments of inertia of the other two axes,
the spacecraft may roll about the nose. If the orbit is low enough for
aerodynamic torques to be significant ( 500 km), the spacecraft may
stabilize in an orientation that balances the gravity gradient and
aerodynamic torques (a so-called "torque equilibrium" attitude) or it may
oscillate forever.

If the initial angular velocity of the spacecraft is something other than
orbital rate, then the gravity gradient torque will cause the spacecraft to
oscillate about the nose-to-Earth attitude. If no other torques are
present, this oscillation will continue forever, but in the real world,
aerodynamic torques (and internal torques from propellant slosh, body flex,
etc) will eventually stabilize it.

Jud,

Jorge gives a great explanation of the -how- to these attitude
stabilization effects. I will add to that here by getting toward the
-why-...

Aero-torques are straight forward enough. Molecules from the Earth's
atmosphere way up there are bouncing off the spacecraft. This creates
a tiny pressure that exerts a force on the vehicle. As with airplane
aerodynamics, the force from the air molecules will -drag- the
spacecraft's center of pressure behind the spacecraft's center of
gravity, resulting in the "pointy end" seeking the direction of orbit.

Gravity gradient torque is straight forward as well, but it can be
more difficult to grasp because the phenomenon is beyond what we
experience. It occurs as a result of gravity being an "inverse
square" law force. This means that as you get closer, the pull gets
way stronger.

One inverse square force that is easy for us to experience is
magnetism. Imagine a strong magnet pulling on a mini metallic model
of a spacecraft. If that spacecraft model had more metal on one side
than the other, we can imagine that the spacecraft will torque so that
the most massive part will align due to its stronger attraction to the
magnet.

This is exactly the same in priciple to gravity gradient torque. And
it is the most rudimentary way to achieve spacecraft stabilization.
Simply design the craft so that one side is more massive than the
other so that the Earth will keep it aligned by pulling harder on that
"heavier" side. The result is that the satellite's rotation gets
"phase locked" with its own orbit.

The most visible example of gravity gradient stabilization is our
Moon. We see only one side without seeing the far side. The Moon is
stuck in a phase locked rotational orbit.


So atmospheric pressure and gravity gradient are significant natural
phenomena that affect spacecraft stabilization. There are other, less
significant forces as well such as radiation pressure from sunshine.
Add all these effects together and you have the net of natural torques
on the spacecraft.

On top of these, engineers design attitude control systems that can
overcome the natural forces to point the spacecraft any way desired.
The most obvious way to do this is with thrusters. Blast little jets
and you torque the spacecraft with action-reaction of the RCS exhaust.

A more complex solution for attitude control is through Control Moment
Gyros (CMGs). Angular momentum (the "spin inertia") of a spacecraft
is a fixed quantity - the concept of conservation of angular momentum.
This means that if you have a massive gyro contained within the
spacecraft, increasing the spin of that gyro will result in the
reaction of decreasing the spacecraft spin in that axis. Conversely,
slowing down the gyro will result in the increase the spacecraft spin.

On ocassion you will hear the term "desaturization burn". Gyros are
limited in how fast they can spin. To prevent from reaching these
"gyro redlines", RCS burns are accomplished to "give them a break" and
slow the CMGs back down.

For spacecraft that are designed with both systems, they work
together.

Of course, one CMG is not enough for spatial stabilization. A minimum
of three are needed: one in each orthogonal axis (three dimensional
space requires stabilization in each dimension). When you double them
up for redundancy, you get...

The CMG "six-pack".


Reposting the original question...

Suppose you have a spacecraft in a circular orbit around the Earth,
and you point the nose toward the Earth. As it goes around in its
orbit, does it keeps its nose pointed toward Earth, or does it point
to the same direction in space (assuming no thrusters are used and
nothing interferes with it).

....we can see that there is *lots* interfering with the pointing of
the spacecraft: the gravity gradient, aero forces, radiation forces,
internal torques, etc.

It's easy to design a spacecraft to stay aligned to the gravity
gradient. But a spacecraft that was designed with a "nose" had lots
of other considerations designed in so we can imagine that the nose
will drift away from this pointing position.


~ CT

CORRECTION:

The CMG "six-pack".

I found a photo:

Title: Astronaut Jack Lousma hooks up cable for rate gyro six pack during EVA
http://images.jsc.nasa.gov/iams/imag...3/10076241.htm

....so it seems that Skylab's "six pack" was the RGA, not CMG.


~ CT

On ocassion you will hear the term "desaturization burn". Gyros are
limited in how fast they can spin. To prevent from reaching these
"gyro redlines", RCS burns are accomplished to "give them a break" and
slow the CMGs back down.

The pun here doesn't come through so well when spelled out...

"give them a brake"


~ CT

On 28 Sep 2003 00:57:24 GMT, "Jorge R. Frank"
wrote:

The answer is that it depends on the initial attitude rates of the ...

I asked a simple question, and ... ! Good reply, though, it is more
complicated than I thought.

On 28 Sep 2003 09:36:08 -0700, (Stuf4)
wrote:

...we can see that there is *lots* interfering with the pointing of
the spacecraft: the gravity gradient, aero forces, radiation forces,
internal torques, etc.

I meant nothing else caused by humans (thruster burns, EVA, etc) and
no collisions with something else large.

From Jan Philips:
On 28 Sep 2003 09:36:08 -0700, (Stuf4)
wrote:

...we can see that there is *lots* interfering with the pointing of
the spacecraft: the gravity gradient, aero forces, radiation forces,
internal torques, etc.

I meant nothing else caused by humans (thruster burns, EVA, etc) and
no collisions with something else large.

My reason for lumping this together was to include attitude control.


For anyone interested in that topic...

I've done a bit of reading on CMGs and found info that is different
from what I originally shared:


(From http://www.shuttlepresskit.com/STS-92/payload76.htm)
_______

Motion Control Subsystem

The motion control subsystem (MCS) hardware launched as part of the Z1
element includes the CMGs and the CMG assemblies. This hardware will
not be activated until Mission 5A, when the GN&C MDM will be activated
with the U.S. Lab.

The CMG assembly consists of four CMGs and a micrometeorite/orbital
debris shield. The four CMGs, which will control the attitude of the
ISS, have a spherical momentum storage capability of 14,000 ft-lb/sec,
the scalar sum of the individual CMG wheel moments. The momentum
stored in the CMG system at any given time equals the vector sum of
the individual CMG momentum vectors.

To maintain the ISS in the desired attitude, the CMG system must
cancel, or absorb, the momentum generated by the disturbance torques
acting on the station. If the average disturbance torque is nonzero,
the resulting CMG output torque is also nonzero, and momentum builds
up in the CMG system. When the CMG system saturates, it is unable to
generate the torque required to cancel the disturbance torque, which
results in the loss of attitude control.

The CMG system saturates when momentum vectors have become parallel
and only momentum vectors change. When this happens, control torques
perpendicular to this parallel line are possible, and controllability
about the parallel line is lost.

Russian segment thrusters are used to desaturate the CMGs.

An ISS CMG consists of a large flat wheel that rotates at a constant
speed (6,600 rpm) and develops an angular momentum of 3,500 ft-lb/sec
about its spin axis. This rotating wheel is mounted in a
two-degree-of-freedom gimbal system that can point the spin axis
(momentum vector) of the wheel in any direction.

At least two CMGs are needed to provide attitude control. The CMG
generates an output reaction torque that is applied to the ISS by
inertially changing the direction of its wheel momentum. The CMG's
output torque has two components, one proportional to the rate of
change of the CMG gimbals and a second proportional to the inertial
body rate of the ISS as sensed at the CMG base. Because the momentum
along the direction of the spin axis is fixed, the output torque is
constrained to lie in the plane of the wheel. That is why one CMG
cannot provide the three-axis torque needed to control the attitude of
the ISS.

Each CMG has a thermostatically controlled survival heater to keep it
within thermal limits before the CMGs are activated on Mission 5A. The
heaters are rated at 120 watts and have an operating temperature range
of -42 to -35°F.
_______


So according to this, only 2 CMGs are needed for 3-axis stabilization.
And I can make sense of that considering that gyros stabilize a
-plane- rather than an -axis-. And I also found it interesting to see
how gyro speed is kept constant while their pointing direction is
manipulated.

I wonder if anyone refers to this as the "four pack".


~ CT