Posted on 09/28/2005 1:16:19 PM PDT by saganite
(Actually, to get real technical, gravity isn't truly a force either, according to Einsteinian physics, but a illusion caused by multi-dimensional curvatures of the time-space continuum being mapped across our 3-dimensional experience of a multi-dimensional world. However, since Newtonian physics are still useful to describing and constructing mechanics, Gravity is still referred to as a force.
The thinking goes like this: The application of a force is the transfer of kinetic energy from one object to another. There is no medium between two objects in empty space, so there is no force.
The problem with such thinking is that there does exist a weak force, which seems to act to subtle direct extremely large masses (i.e., superclusters of galaxies) to draw them away from each other.
I would expect that the stages would become exponentially longer as the relative change in gravity per mile decreased.
whats up with the 5 pings :)
make that 6 pings....
Wow! Six pings! First time I have seen that happen!
Geosynchronous Orbit
A geosynchronous orbit is an orbit that has the same period (single revolution) that is equal to the time it takes the Earth to complete one revolution about its axis (one sidereal day). A sidereal day is measured with respect to the stars as apposed to the sun (one solar day). This is approximately 23 hours and 56 minutes. The semi-major axis for a circular orbit that has this period is approximately 42,164 kilometers and a mean altitude of approximately 35,790 kilometers above mean sea level. One of the unique features of this orbit is that as the inclination approaches zero (stays on the equator) and the orbit is circular, the object orbiting will stay over the same location on the Earth due to the fact it is moving at the save speed as the Earth is turning under it. This special type of geosynchronous orbit is called a Geostationary Orbit (stationary with respect to the surface of the Earth). As the inclination increases for a geosynchronous orbit, the ground trace of the orbit on the Earth plots a figure eight (8) pattern.
A more in depth discussion of geostationary orbits
First, from the above paragraph, you may have deduced that a geosynchronous orbit is not necessarily a geostationary orbit. However a geostationary orbit must be a geosynchronous orbit. These terms are often used interchangeably since most geosynchronous orbits are also geostationary. However, that is not always the case. It is the zero (0) degree inclination that makes it that special orbit called the geostationary orbit.
I used the term sidereal day for describing geosynchronous orbits. How do we measure a day? Usually we measure it in reference to the sun being in the same position from one day to the next (i.e. noon to noon). However, that is not the same time it takes the Earth to rotate once on its axis. Remember the Earth is also in orbit around the sun requiring it to travel just a tiny bit further in its rotation for the same spot on the Earth to be pointing towards the sun each day. This is the difference between the Mean Solar Day (our normal 24 hour day) and the Sidereal Day. The difference is approximately 4 minutes per day.
For a geosynchronous orbit, this orbit must be synched to the actual rotation period of the Earth (sidereal day). Even though a satellite is place in a near geostationary orbit upon launch there are forces that act upon the satellite that increase the orbital inclination. Remember an inclination of zero (0) for a geosynchronous orbit is also a geostationary orbit. The primary cause of this is that the equatorial plane is coincident with the ecliptic. So both the sun and the moon slowly over time increase the satellite’s orbital inclination. Also since the Earth is not a true sphere, the geosynchronous satellites drift (in-track) towards two stable equilibrium points over the Earth’s equator. This is why “station keeping” is required for geostationary satellites. Satellites are typically maintained within a band that is approximately 0.10 degrees. When station keeping is no longer possible (all the fuel is used) or there is a satellite malfunction, most geostationary satellites are boosted into a higher orbit (end of life orbit boost) so they will not drift into an area where another geostationary satellite is operating.
Here is another non-intuitive repositioning delta-v. For a geostationary satellite, you fire the thrusters in the same direction you want the vehicle to move. What is happening is you are changing the velocity of your vehicle that directly correlates to Kepler's third law. So if you fire the thrusters away from (behind) the direction of flight, causing the satellite to increase its altitude just a tiny bit, its velocity in respect to the velocity of the surface if the Earth will actually be slower. This allows the Earth to turn underneath it faster and the satellite’s subpoint (the point directly below the satellite) will move westward (or backwards in the same the direction you fired the thrusters).
If you fire the thrusters in the direction of flight (eastward), the satellite will drop to a lower orbit causing it to speed up relative to its subpoint and it will move relative to the surface of the Earth in the direction you fired the thrusters once again.
With only two firings (this is a Hohmann transfer orbit BTW) you can reposition a geostationary satellite.
Now that we are this far along, how about a little chat on satellites and spacecraft since they have been in the news recently:
Since the Earth is not a perfect sphere (it is an Oblate Spheroid), satellites drift from their predicted position due to the Earth’s non-spherical shape. Also at low Earth orbits, the atmosphere creates a drag on the satellite also causing a drift (perturbation) in its orbit. At higher altitudes, such as a geosynchronous orbit, the solar wind and effects from the moon are more pronounced. This requires us to update the ephemeris periodically.
Satellites (and spacecraft) are incredibly precise machines with exquisite craftsmanship. The life of a satellite is often computed by the onboard fuel requirements. For geostationary satellites, periodic maneuvers (delta-Vs) must be accomplished to keep them on station. This is also required for many lower orbiting satellites as well. For an orbit plane change (move it into a different orbit), mass must be ejected to move the satellite.
Note: Super geek alert #1:
The Hohmann transfer orbit is the most energy efficient (minimum energy solution) way of getting from one circular orbit to a higher or lower circular orbit. This type of transfer orbit is used by interplanetary spacecraft to travel to the other planets in our solar system.
Now that we have a better understanding of its orbital position, we need to concentrate on its pointing (Attitude Control).
Why do we need to worry about pointing? If the satellite has solar panels (arrays), they need to point towards the sun to provide power. Sensors need to point at their respective targets, such as a star sensor, sun sensor etc. Thermal and possible contamination consideration must be taken into effect when pointing also.
Remember for every action there is an equal and opposite reaction. So if I spew mass (jet of gas out of a thruster nozzle), the satellite will move in the opposite direction. Also if I spin a wheel onboard the satellite, the result will be the satellite spins in the opposite direction.
Since fuel is precious and usually cannot be replenished (called consumables), other methods of pointing were devised that did not require mass ejecta from the satellite. Spinning reaction wheels were one. If you have orthogonal reaction wheels, just by spinning them you can provide precise pointing. Unfortunately, external forced (perturbations) adds unwanted momentum to the wheels. To compensate (unload momentum from the wheels) for this, I have seen both low-level monopropellant jets or torque rods used for this purpose.
Note: Super geek alert #2:
A monopropellant is one that does not require an oxidizer to function. Usually monopropellants are composed of a liquid compound called Hydrazine (N2H4). When this liquid comes in contact with a platinum catalyst, it is decomposed into gaseous ammonia (Nh3), nitrogen and hydrogen. This gas is then ejected (fired thru a nozzle) out a jet to providing motion for the satellite or spacecraft.
An ingenious method of unloading momentum without the use of fuel was devised using simple electromagnets. Remember the Earth is surrounded by a magnetic field (why your compass works). If you attach orthogonal electromagnets on your satellite and turn them on, the resultant field interacts with the Earth’s field causing a torque on the satellite. These are what are known as Torque Rods.
Since the reaction wheels, gyros, and torque rods all work using electricity and the solar arrays provide that electricity, theoretically the life of the satellite is indefinite. Unfortunately, there are degradations of the thermal coatings, blankets, sensors, and failures of both the gyros and reaction wheels that ultimately limit the life of any satellite.
Over a period of time, these degrade to the point that the satellites can no longer function within design spec. At some point, you either have to replace the satellite, repair it, or say farewell.
Final note: Even though the geostationary satellite (your TV satellite is one) appears to just “hover” over the equator, it is actually in orbit (falling around the Earth) at the same rate the Earth is turning beneath it.
An orbit is a nothing more than an object falling around another object. Both Kepler and Newton came up with a set of laws that describe this phenomenon.
Kepler’s 3 laws of planetary motion:
1) The orbit of a planet is an ellipse with the sun at one of the foci.
2) The line drawn between a planet and the sun sweep out equal areas in equal times.
3) The square of the periods of the planets is proportional to the cubes of their mean distance from the sun.
So what is that telling us? In a nutshell, all orbits are ellipses, the close to the body you are orbiting the faster you go (e.g. if you have a highly elliptical orbit the satellites velocity will increase as it approaches the object being orbited and decrease as it get further away), and the further away an orbit is, the slower the object moves.
These laws not only apply to planets, but to any orbiting body.
Note: Super geek alert #1:
For an orbiting body this is not entirely correct. It turns out that both bodies end up orbiting a common center of mass of the two-body system. However, for satellites, the mass of the Earth is so much greater than the mass of the satellite, the effective center of mass is the center of the Earth.
Newton’s three laws (and law of gravitation)
1) The first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. (Commonly known as inertia)
2) The second law states that force is equal to the change in momentum (MV) per change in time. (For a constant mass, force equals mass times acceleration F=ma)
3) The third law states that for every action there is an equal and opposite reaction. In other words, if an object exerts a force on another object, a resulting equal force is exerted back on the original object.
Newton’s law of gravitation states that any two bodies attract one another with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
Note: Super geek alert #2:
Actual observed positions did not quite match the predictions under classical Newtonian physics. Albert Einstein later solved this discrepancy with his “General Theory of Relativity”. In November of 1919, using a solar eclipse, experimental verification of his theory was performed by measuring the apparent change in a stars position due to the bending of the light buy the sun’s gravity.
So what is all this trying to tell us? Planets, satellites, etc orbit their parents in predictable trajectories allowing us to “know” where they will be at any given time. A set of coordinates showing the location of these objects over a period of time is called its ephemeris.
Since the Earth is not a perfect sphere (its an Oblate Spheroid), satellites drift from their predicted position due to the Earth’s non-spherical shape. Also at low Earth orbits, the atmosphere creates a drag on the satellite also causing a drift (perturbation) in its orbit. At higher altitudes, such as a geosynchronous orbit, the solar wind and effects from the moon are more pronounced.
This requires us to update the ephemeris periodically.
Wow! A five alarmer!
a serious case of computer hiccups...
I am still wondering about gravitational red shift, which has been observed, and the Hubble red shift, which has not been satisfactorily explained. Hubble's red shift gives the age of the universe as a billion years, but other information indicates 14 billion years.
Sorry to burst your bubble - the geostationary point is 22,300 miles about our planet. That is where the TV satellites are. That is what you can have a fixed DISH for digital TV.
Everything closer in than that is either in orbit or powered.
It took me a few passes to figure out why you figure you are contradicting me... then I realized that I wrote "hundreds of miles." OK... 223 is a lot of hundreds. :^) Amazingly, no one picked up two major gaffes I made about centifugal force and weak force: Weak force is at the opposite end of the scale spectrum than I placed it, and I inverted the action of the larger object in my brief description of the minority definition of centrifugal force.
It took me a few passes to figure out why you figure you are contradicting me... then I realized that I wrote "hundreds of miles." OK... 223 is a lot of hundreds. :^) Amazingly, no one picked up two major gaffes I made about centifugal force and weak force: Weak force is at the opposite end of the scale spectrum than I placed it, and I inverted the action of the larger object in my brief description of the minority definition of centrifugal force.
I believe the Space Shuttle flies in the hundereds. Like 300 miles.
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.