Orbital Mechanics 101

arcadiastreet.com

This thread is designed to help members and viewers alike learn a basic understanding of orbital mechanics. I feel that it is especially necessary, not only for common knowledge of 21st century science, but for all who seek to believe and prove the existence of UFOs and aliens to have a basic understanding of the basic principles governing space flight. I have always firmly believed that mankind's fate is in the stars, and think we will see that realized to a much greater extent in the years to come. First a few links to threads I have created that you might find helpful in learning about space and physics science.

* Astronomy 101
* On Parallel Universes
* On Superluminal Propulsion

Now I realize that many members and viewers here probably already know this, this is for the ones that don’t, or for anyone who wants a refresher. Well I hope everyone enjoys reading this and learns something.

Chapter Summary
1.Introduction and Basic Terms
2. Types of Orbit and Newton
3. Celestial Motions and The Launch of A Space Vehicle
4. Orbital Perturbations, Maneuvers, and Escape Velocity

1. Introduction and Basic Terms


projectrho.com

Orbital Mechanics, also known as flight mechanics, is the study of the motions of artificial space vehicles (satellites and spacecraft) under the influence of the forces such as gravity, atmospheric drag, thrust , and so on. Orbital mechanics is a derivative of celestial mechanics which has its roots in the 17th century with the great Sir Isaac Newton. Orbital mechanics is obviously the modern continuation of celestial mechanics (with our ability to fly into space). Some engineering applications are as follows:
* Ascent Trajectories
* Reentry and Landing
* Rendezvous Computations
* Lunar and Interplanetary Trajectories

Now lets take a look at some vocabulary terms….

* Ellipse- A curve in which the sum of its distance from two fixed points (foci) is constant.
Picture of an ellipse courtesy of gap-system.org

* Primary- Body that a craft is orbiting.
* Major Axis- Longest line that can be drawn through the center of an ellipse.
* Minor Axis- Shortest line that can be drawn through the center of an ellipse.
* Semi-Major Axis- One half of the major axis and represents a crafts mean distance from its primary.
*Eccentricity- Distance between the foci divided by the length of the major axis and is a number between zero and one. A number of zero indicates a circle.
* Inclination- Angular distance between a crafts orbital plane and the equator of its primary.
* Prograde Orbit- When a craft orbits in the same direction as its primary.
* Retrograde Orbit- When a craft orbits opposite the direction of its primary.
* Orbital Plane- Geometrical plane in which a crafts orbit is embedded in around its primary.
* Equator- Intersection of the Earths surface with the plane perpendicular to the axis of rotation, also contains the center of Earths mass.
* Axis of Rotation- The circular movement of the Earth around an imaginary line called the axis.
Representation of rotational axis courtesy of Wikipedia.org


* Periapsis (Perigee)- The point in an orbit closest to the primary.
* Apoapsis (Apogee)- The point in an orbit furthest from the primary.
* Argument of Periapsis- Angular distance between the ascending node and the point of periapsis.
* Time of Periapsis Passage- Time in which a craft moves through its point of periapsis.
* Node- Points in orbit where a craft crosses a plane, such as crossing the equator.
* Ascending Node- Crossing of a plane from south to north.
* Descending Node- Crossing of a plane from north to south.
* Longitude of the Ascending Node- Nodes celestial longitude.
* Celestial Longitude- Celestial coordinate system analogous to the latitude and longitude system on Earth.
* Period- Length of time required for a craft to complete one orbit.
* True Anomaly- Angular distance of a point of orbit past the point of periapsis, measured in degrees.
* Orbital Velocity- Orbital speed of a craft needed to maintain orbit.
* Escape Velocity- Speed needed to escape a bodies gravitational pull.
* Launch Window- Time frame a craft must be launched in order to complete its mission.
* Decay- Deterioration of a crafts orbit.

Inclination is the angular distance between a satellite's orbital plane and the equator of its primary (or the ecliptic plane in the case of heliocentric, or sun centered, orbits). An inclination of zero degrees indicates an orbit about the primary's equator in the same direction as the primary's rotation, a direction called prograde (or direct). An inclination of 90 degrees indicates a polar orbit. An inclination of 180 degrees indicates a retrograde equatorial orbit. A retrograde orbit is one in which a satellite moves in a direction opposite to the rotation of its primary.

braeunig.u

Following images courtesy of braeunig.us




Those were all considered orbital elements.

2. Types of Orbit and Newton

For a spacecraft to achieve Earth orbit, it must be launched to an elevation above the Earth's atmosphere and accelerated to orbital velocity. The most energy efficient orbit, that is one that requires the least amount of propellant, is a direct low inclination orbit. To achieve such an orbit, a spacecraft is launched in an eastward direction from a site near the Earth's equator. The advantage being that the rotational speed of the Earth contributes to the spacecraft's final orbital speed. At the United States' launch site in Cape Canaveral (28.5 degrees north latitude) a due east launch results in a "free ride" of 1,471 km/h (914 mph). Launching a spacecraft in a direction other than east, or from a site far from the equator, results in an orbit of higher inclination. High inclination orbits are less able to take advantage of the initial speed provided by the Earth's rotation, thus the launch vehicle must provide a greater part, or all, of the energy required to attain orbital velocity. Although high inclination orbits are less energy efficient, they do have advantages over equatorial orbits for certain applications.

braeunig.us

* Geosynchronous Orbit (GEO) – Circular orbits around Earth having a period of 24 hours. If the orbit has an inclination of zero it is called a geostationary orbit. A craft in GEO will appear to remain stationary over a position on the equator. A craft in an inclined GEO will appear to make regular figure eight motions across the sky every orbit.
* Polar Orbit- Orbit with an inclination of 90 degrees.
* Walking Orbit- A orbit that accounts for celestial effects by inducing precession of said craft.
* Sun Synchronous Orbit (SSO) – A type of walking orbit that processes with the primaries orbital period.
*Molniya Orbit- Highly eccentric Earth orbits that have a orbital period of 12 hours (2 revolutions per day). This orientation can provide good ground coverage at high northern latitudes.
* Hohmann Transfer Orbit- Interplanetary trajectory that uses the least amount of propellant. This is also known as “Gravity Assist”, basically the craft is sent into a Sun orbit with an aphelion equal to the orbit of the outer planet, the craft must then slow down to enter orbit of target planet.

To send a spacecraft to an inner planet, such as Venus, the spacecraft is launched and accelerated in the direction opposite of Earth's revolution around the sun (i.e. decelerated) until it achieves a sun orbit with a perihelion equal to the orbit of the inner planet. It should be noted that the spacecraft continues to move in the same direction as Earth, only more slowly.
To reach a planet requires that the spacecraft be inserted into an interplanetary trajectory at the correct time so that the spacecraft arrives at the planet's orbit when the planet will be at the point where the spacecraft will intercept it. This task is comparable to a quarterback "leading" his receiver so that the football and receiver arrive at the same point at the same time. The interval of time in which a spacecraft must be launched in order to complete its mission is called a launch window.

braeunig.us


Continued Below



[edit on 5/5/2009 by jkrog08]

[edit on 5-5-2009 by spacedoubt]

Orbital Maneuvers

At some point during the lifetime of most space vehicles or satellites, we must change one or more of the orbital elements. For example, we may need to transfer from an initial parking orbit to the final mission orbit, rendezvous with or intercept another spacecraft, or correct the orbital elements to adjust for the perturbations discussed in the previous section. Most frequently, we must change the orbit altitude, plane, or both. To change the orbit of a space vehicle, we have to change its velocity vector in magnitude or direction. Most propulsion systems operate for only a short time compared to the orbital period, thus we can treat the maneuver as an impulsive change in velocity while the position remains fixed. For this reason, any mane

Newtons Law of Motion and Universal Gravitation

Newtons Laws of Motion describe a particle and forces acting on it.
Here are the laws…

* 1st Law- With no forces acting a object rest will remain at rest and a object in motion will remain in motion in a straight line.
* 2nd Law- If a force is applied there will be a change in velocity proportional to the magnitude and in the direction of the force applied. This can be represented as the following equation: F=ma, where F is force, m is mass, and a is the acceleration.
* 3rd Law- Commonly stated; For every action there is an equal and opposite reaction.

Law of Universal Gravitation…

* Two particles having masses represented here as m1 and m2 and separated by distance of r are attracted to each other by forces equal and opposite directed along the line joining the particles. This is directly analogous to the Sun and Earth in orbit.
The following expresses the action in terms of equation:

Courtesy of braeunig.us

G is the universal constant of gravitation and has the value of 6.67259x10-11 N-m2/kg2 (3.4389x10-8 lb-ft2/slug2).

Let's now look at the force that the Earth exerts on an object. If the object has a mass m, and the Earth has mass M, and the object's distance from the center of the Earth is r, then the force that the Earth exerts on the object is GmM /r2 . If we drop the object, the Earth's gravity will cause it to accelerate toward the center of the Earth. By Newton's second law (F = ma), this acceleration g must equal (GmM /r2)/m.
At the surface of the Earth this acceleration has the valve 9.80665 m/s2 (32.174 ft/s2).
Many of the upcoming computations will be somewhat simplified if we express the product GM as a constant, which for Earth has the value 3.986005x1014 m3/s2 (1.408x1016 ft3/s2). The product GM is often represented by the Greek letter .

braeunig.us

3. Celestial Motions and The Launch of A Space Vehicle

Celestial Motions

Keplers Laws of Planetary Motion

* All planets move around the Sun in elliptical orbits with the Sun at one focus.
* A line joining any planet to the Sun sweeps out in equal areas at equal times.
* The square of a period of any planet about the Sun is proportional to the cube of the planets mean distance from the Sun.

These laws can be deduced from Newton's laws of motion and law of universal gravitation. Indeed, Newton used Kepler's work as basic information in the formulation of his gravitational theory.
As Kepler pointed out, all planets move in elliptical orbits, however, we can learn much about planetary motion by considering the special case of circular orbits. We shall neglect the forces between planets, considering only a planet's interaction with the sun. These considerations apply equally well to the motion of a satellite about a planet.
Let's examine the case of two bodies of masses M and m moving in circular orbits under the influence of each other's gravitational attraction. The center of mass of this system of two bodies lies along the line joining them at a point C such that mr = MR. The large body of mass M moves in an orbit of constant radius R and the small body of mass m in an orbit of constant radius r, both having the same angular velocity . For this to happen, the gravitational force acting on each body must provide the necessary centripetal acceleration. Since these gravitational forces are a simple action-reaction pair, the centripetal forces must be equal but opposite in direction. That is, m 2r must equal M 2R. The specific requirement, then, is that the gravitational force acting on either body must equal the centripetal force needed to keep it moving in its circular orbit.

braeunig.us

If one body has much greater mass than the other (Sun to Earth) its distance to the center of mass is shorter than that of the other body. Think of ‘condensation’ of mass.

Launch of A Space Vehicle

In order to launch a spacecraft into orbit you must have a period of powered flight to accelerate the craft out of the atmosphere and achieve orbital velocity. Powered flight concludes at a burnout (with current chemical based rocket technology) at which time the craft begins free flight and is subject only to gravitational forces of the primary. If the craft moves further out it will eventually be subject to the gravitational forces of the Moon, Sun, or other body.

A space vehicle's orbit may be determined from the position and the velocity of the vehicle at the beginning of its free flight.

Courtesy of braeunig.us
4. Orbital Perturbations, Maneuvers, and Escape Velocity

Orbital Perturbations

Perturbations, or forces acting on a craft that corrupt a crafts orbit are a issue that must be dealt with by any craft going into orbit.
*Third-body perturbations are from the gravitational forces of the Sun and Moon.
*Perturbations due to non-spherical Earth are caused by the fact that the Earth, or any body in space is not a perfect sphere.
*Perturbations from Atmospheric Drag are caused by the drag forces when moving through a planets atmosphere. In Low Earth Orbit a craft is still subjected to the drag of the thin Earth atmosphere at that high altitude, this can cause a crafts orbit to decay and spiral back towards the primary (of course only if an atmosphere exists). If a craft comes within 160-120 km of the Earths surface it will come crashing down within a few days. Final disintegration will happen at about 80 kilometers above Earths surface. Above 600 km the drag is so weak that orbits for satellites usually last for more than ten years, usually long past their lifetime.

The region above 90 km is the Earth's thermosphere where the absorption of extreme ultraviolet radiation from the Sun results in a very rapid increase in temperature with altitude. At approximately 200-250 km this temperature approaches a limiting value, the average value of which ranges between about 600 and 1,200 K over a typical solar cycle. Solar activity also has a significant affect on atmospheric density, with high solar activity resulting in high density. Below about 150 km the density is not strongly affected by solar activity; however, at satellite altitudes in the range of 500 to 800 km, the density variations between solar maximum and solar minimum are approximately two orders of magnitude. The large variations imply that satellites will decay more rapidly during periods of solar maxima and much more slowly during solar minima.

braeunig.us

*Perturbations from solar radiation are caused by periodic solar events.



Continued Below...



[edit on 5/5/2009 by jkrog08]

Orbital Maneuvers

At some point during the lifetime of most space vehicles or satellites, we must change one or more of the orbital elements. For example, we may need to transfer from an initial parking orbit to the final mission orbit, rendezvous with or intercept another spacecraft, or correct the orbital elements to adjust for the perturbations discussed in the previous section. Most frequently, we must change the orbit altitude, plane, or both. To change the orbit of a space vehicle, we have to change its velocity vector in magnitude or direction. Most propulsion systems operate for only a short time compared to the orbital period, thus we can treat the maneuver as an impulsive change in velocity while the position remains fixed. For this reason, any maneuverchanging the orbit of a space vehicle must occur at a point where the old orbit intersects the new orbit. If the orbits do not intersect, we must use an intermediate orbit that intersects both. In this case, the total maneuver will require at least two propulsive burns.

braeunig.us

*Orbital Altitude Changes- This means exactly how it sounds, a craft changes altitude of orbit. When changing from a smaller to larger orbit the change of velocity is applied in the direction of the motion. When transferring from a larger to smaller orbit the opposite function is performed.

Ordinarily we want to transfer a space vehicle using the smallest amount of energy, which usually leads to using a Hohmann transfer orbit. However, sometimes we may need to transfer a satellite between orbits in less time than that required to complete the Hohmann transfer. The figure to the right shows a faster transfer called the One-Tangent Burn. In this instance the transfer orbit is tangential to the initial orbit. It intersects the final orbit at an angle equal to the flight path angle of the transfer orbit at the point of intersection. An infinite number of transfer orbits are tangential to the initial orbit and intersect the final orbit at some angle. Thus, we may choose the transfer orbit by specifying the size of the transfer orbit, the angular change of the transfer, or the time required to complete the transfer. We can then define the transfer orbit and calculate the required velocities.

Source and image courtesy of braeunig.us


* Orbital Plane Changes- The changing of a crafts orbital plane.


Courtesy of braeunig.us

* Orbital Rendezvous- This is a docking maneuver, both objects MUST arrive at the same point in space at the same time, this requires a phasing orbit, which is when a craft reaches the desired geometry relative to the target so it can initiate a Hohmann transfer.
* Launch Window and Orbit Maintenance- The launch window is the time frame when a mission (craft) must be launched to be able to utilize the principles of orbital mechanics. Orbital maintenance is the maintaining of the craft after reaching orbit, in the case of satellites no additional thrust is needed once they reach orbit but after the mission is done two main options arise; Either to let the satellite decay and use a velocity change to speed up the process. The other option is to place the satellite into a higher altitude so the chances of colliding with another craft is unlikely. This is all determined by the budget and cost of particular mission and orbit.

Escape Velocity


Courtesy of allposters.com

We know that you must reach a certain speed to escape the pull of any body in space, here on Earth the required velocity is around 25,000 mph, which is why the space shuttle needs all the fuel you see on the three rocket boosters. But we will see below there is a way around having to achieve that speed. The space shuttle only needs to achieve a speed of about 17,500 mph to go into LEO (Low Earth Orbit) , where from there it can easily break free of the Earths gravity.

Defined a little more formally, "escape velocity" is the initial speed required to go from an initial point in a gravitational potential field to infinity with a residual velocity of zero, with all speeds and velocities measured with respect to the field. Additionally, the escape velocity at a point in space is equal to the speed that an object would have if it started at rest from an infinite distance and was pulled by gravity to that point. In common usage, the initial point is on the surface of a planet or moon. On the surface of the Earth, the escape velocity is about 11.2 kilometers per second (~6.96 mi/s), which is approximately 34 times the speed of sound (mach 34) and at least 10 times the speed of a rifle bullet. However, at 9,000 km altitude in "space", it is slightly less than 7.1 km/s.
The escape velocity relative to the surface of a rotating body depends on direction in which the escaping body travels. For example, as the Earth's rotational velocity is 465 m/s at the equator, a rocket launched tangentially from the Earth's equator to the east requires an initial velocity of about 10.735 km/s relative to Earth to escape whereas a rocket launched tangentially from the Earth's equator to the west requires an initial velocity of about 11.665 km/s relative to Earth. The surface velocity decreases with the cosine of the geographic latitude, so space launch facilities are often located as close to the equator as feasible, e.g. the American Cape Canaveral (latitude 28°28' N) and the French Guiana Space Centre (latitude 5°14' N).

Wikipedia.org

Although it should be stated that the primary surge of power from the space shuttle is used to get into Low Earth Orbit, from there the shuttle then uses the remaining surge to achieve a much easier escape velocity.

Well this concludes my thread on Orbital Mechanics 101, I sincerely help everyone likes it and learns from it, as I did try to lay it out in a well organized manner. Let us all remember that these forces may not be as big of an issue to any visitors from space, but these rules I stated still apply. Plus as far as we know we humans are the only beings flying around in space and we will be for the many years to come. So I feel it is nessicary to understand the mechanics of our future, which is the true final frontier-space.


Courtesy of flckr.com

Sources
nasa.gov
Wikipedia.org
braeunig.us






[edit on 5/5/2009 by jkrog08]

[edit on 5/5/2009 by jkrog08]

There is probably no other aspect of physics which is directly observable yet less intuitive than orbital mechanics.

In order to obtain a higher orbit you expend energy to slow down. To reach a lower orbit you expend energy to speed up. Goofy.

If you are in an orbit only slightly lower that the spacecraft you want to rendezvous with and you point your nose at it (or even ahead of it) and apply thrust, you end up getting farther away from it.

If you really want to get frustrated, load up this free simulator and try docking with the space station manually. You'll quickly find out just how tricky it is.
orbit.medphys.ucl.ac.uk...

Originally posted by Phage
There is probably no other aspect of physics which is directly observable yet less intuitive than orbital mechanics.

In order to obtain a higher orbit you expend energy to slow down. To reach a lower orbit you expend energy to speed up. Goofy.

If you are in an orbit only slightly lower that the spacecraft you want to rendezvous with and you point your nose at it (or even ahead of it) and apply thrust, you end up getting farther away from it.

If you really want to get frustrated, load up this free simulator and try docking with the space station manually. You'll quickly find out just how tricky it is.
orbit.medphys.ucl.ac.uk...

I have heard of it, but right now I get frustrated enough with other problems! I will try it soon though.

Very Interesting Topic.

I have tried Orbiter (that Sim) and yes, it really IS as difficult as it sounds... I tend to zoot right past the ISS and into interplanetary space,

It is Definately worth a crack though... Perhaps we can get members to try it out and report back as to how many actually do manage to get into orbit and dock...

Originally posted by Havoc40k
It is Definately worth a crack though... Perhaps we can get members to try it out and report back as to how many actually do manage to get into orbit and dock...

Oooh, I'd like to volunteer for that. Orbiter is my favorite computer "game." I just finished construction of a custom space station and I've been preparing for a simulated journey to Mars (for uber-geek points I'm going to carry out the trip in realtime by simulating it one week at a time - it will take me 7-8 months just to reach Mars). My earth departure stage is already in orbit waiting for my manned vehicle to launch and dock with it. I'll use fraps or something similar to record it and make into a tutorial video.

Great thread, thanks for making it. There's a lot to be learned here, and even I picked up a few things about the formal definitons of the terminology.

[edit on 5-5-2009 by ngchunter]

So does this space simulator all use real time frame....ie; does a 7 month trip to Mars take 7 months in the game?

Theoretically, you could leave it up for 7 months straight and simulate an entire mars trip in complete realtime, and yes, it would take 7 months of realworld time as well as in the game. You can also use time acceleration to speed it up to just a few hours, basically like microsoft flight simulator, though 7 months will still pass in the game. I will basically be doing a hybrid where once a week I time accelerate through that week and perform any manuevers, course corrections, check fuel/oxygen status and anything else that needs doing during that part of the trip to mars. You can even use add-ons to recreate historical or current missions in full detail:
Mars exploration rovers:
www.orbithangar.com...
LRO and LCROSS:
www.orbithangar.com...
Apollo:
nassp.sourceforge.net...
Some people even go so far as to recreate the actual shuttle missions as they happen so that they are simulating in sync with the real mission:
www.orbithangar.com...

[edit on 5-5-2009 by ngchunter]

Wow, that sound pretty cool, I will have to try it sometime.

reply to post by jkrog08
Excellent thread It'll take me a good while to digest and go on the usual fact-finding missions that these subjects demand. For each new fact this type of thread provides, I'll learn many more reading around it to gain better understanding. Hard science, backed up and sourced. Love it.

reply to post by ngchunter

I just finished construction of a custom space station and I've been preparing for a simulated journey to Mars (for uber-geek points I'm going to carry out the trip in realtime by simulating it one week at a time - it will take me 7-8 months just to reach Mars). My earth departure stage is already in orbit waiting for my manned vehicle to launch and dock with it.

Now that put a smile on my face. With an ETA of somewhere around the New Year, you'll be pretty excited as the 'Red Planet' looms closer ahead. Your posts on various NASA and Moon-based threads are always authoritative and now I get a better idea why...enthusiasm and dedication. I don't know it works, but Subject Matter Expert should be a matter of time for you and Phage



EDIT (3rd time lucky) for screwing up the STS 114 video.

[edit on 5-5-2009 by Kandinsky]

[edit on 5-5-2009 by Kandinsky]

[edit on 5-5-2009 by Kandinsky]

Thanks for dropping by, I am glad you found the information insightful. There is a lot of information out there free of charge to learn about, all you gotta do is ask.

reply to post by Kandinsky


That is a great video by the way.

Great thread having taken University Physics II a couple of semesters ago I knew most of info but I learned a lot and you laid the information out in such a way that it is easily accessible. This would have made a nice study guide for that portion of my midterm :p

Reply to Num1Skeptic

Thanks, so what is your major? I intend on majoring in theoretical physics or cosmology. Although I might decide on astrophysics.

[edit on 5/5/2009 by jkrog08]

reply to post by jkrog08


oh, I am a computer engineer I had to take physics for the electromagnetics and basic knowledge. I am a fourth year and recently finished school.

Good luck on that one of my good friends was a physics major with a focus in quantum mechanics we always had great talks about physics although they were one-sided. haha

LOL, I know what you mean about the one sided talks. BTW, is that you in your avatar?

Originally posted by jkrog08
We know that you must reach a certain speed to escape the pull of any body in space, here on Earth the required velocity is around 25,000 mph, which is why the space shuttle needs all the fuel you see on the three rocket boosters. But we will see below there is a way around having to achieve that speed. The space shuttle only needs to achieve a speed of about 17,500 mph to go into LEO (Low Earth Orbit) , where from there it can easily break free of the Earths gravity.

Sorry to nitpick, but the way this is written bugs me. The shuttle doesn't really break free of earth's gravity, it can only go to LEO. Maybe it's just semantics, but I think of breaking free as being interchangeable with escape velocity. Even with every ounce of maneuvering fuel it can't come close to escape velocity.

Although it should be stated that the primary surge of power from the space shuttle is used to get into Low Earth Orbit, from there the shuttle then uses the remaining surge to achieve a much easier escape velocity.

Actually the remaining fuel is used to circularize the orbit once it's on the oppsite side of the earth so that periapsis (or perigee if you prefer) is above the atmosphere, and then used again later to set the periapsis within the atmosphere to return to earth. All that said, in the past the orbiter has been used as a platform for satellites like Galileo to launch themselves beyond escape velocity to explore other planets, but the shuttle always remains in earth orbit. Perhaps that's what you were describing, but I just thought it could use clarification.

[edit on 5-5-2009 by ngchunter]

Perhaps that's what you were describing, but I just thought it could use clarification.

I appreciate it, I didn't want to get into to technical of an explanation, so I just kind of 'summed it up' if you will. But thanks for the clarification, I am sure the other members will see it!

Wow nice thread jkrog08! Nice information. They didnt do much orbital mechanics in my astrophysics/physics papers at Auckland university.

I have always thought a very good way to get into low orbit would be a space elevator positioned in an easterly direction high up on a mountain range, where the dense lower atmosphere has very little effect.... But thats another threads discussion anyways...

Thanks and looking forward to future threads by you