Help with orbital mechanics for a school project

[SlabGizor117]

Yeah, I changed that to hyperbolic, I must not have saved it. Thanks for the help!

[PB666]

A parabolic trajectory isn't suborbital, it's (barely) an escape trajectory.

Ellipse = All suborbital and closed orbital trajectories (circular is a special case of elliptical), not enough energy to escape.

Parabola = Exactly enough energy to escape.

Hyperbola = More than enough energy to escape.

You might also look into defining the six orbital elements:

Semi-major axis

Eccentricity

Inclination

Longitude of ascending node

Argument of periapsis

Mean anomaly at epoch

Those six values uniquely define an orbit.

I would add to this that Periapsis and Apoapsis are surface measured distances, not point-mass measures. As a consequence they cannot be used directly to determine the major-axis. This requires knowledge of the center of system mass and radius of the satellite. If you know what the major axis is, then e = (Apo-Pe)/Major axis, and a = major axis/2 b = f(a,e), Area = pi a * b, Sweep is a function of Area/Period, Period = f(GM,a), etc. With sweep it is possible to determine theta as a function of time. And with theta it is possible to determine radius and velocity.

The Oberth effect is the result of almost linear gain of velocity from ejecta, when combined with speed increases at periapsis and conservation of energy in an orbit allows objects burning retrograde to gain prograde motion at a discount that is realized exiting the SOI of the gravitational field.

Conversely, making inclination changes at apogee is more efficient since a change of angle of a moving object is also a function of the velocity vectors.

[SlabGizor117]

I would add to this that Periapsis and Apoapsis are surface measured distances, not point-mass measures. As a consequence they cannot be used directly to determine the major-axis. This requires knowledge of the center of system mass and radius of the satellite. If you know what the major axis is, then e = (Apo-Pe)/Major axis, and a = major axis/2 b = f(a,e), Area = pi a * b, Sweep is a function of Area/Period, Period = f(GM,a), etc. With sweep it is possible to determine theta as a function of time. And with theta it is possible to determine radius and velocity.

The Oberth effect is the result of almost linear gain of velocity from ejecta, when combined with speed increases at periapsis and conservation of energy in an orbit allows objects burning retrograde to gain prograde motion at a discount that is realized exiting the SOI of the gravitational field.

Conversely, making inclination changes at apogee is more efficient since a change of angle of a moving object is also a function of the velocity vectors.

Welp, I give up on acting like I'm smart. Bye!

[Red Iron Crown]

Welp, I give up on acting like I'm smart. Bye!

Don't be discouraged. Start with the basics and build your way up, the post you quoted will make sense to you before you know it.

[cantab]

I would add to this that Periapsis and Apoapsis are surface measured distances, not point-mass measures.

Not always. Distances from the surface are used in KSP and are often used for real satellites in Earth orbit. Distances between the centres of mass are usually used when talking about planets orbiting the Sun.

For the presentation, I would stick to using the distances from the centres of mass, with maybe a passing reference "Sometimes people measure from the surface of the planet, in that case you need to add the radius of the planet into the formulas."

[OhioBob]

Not always. Distances from the surface are used in KSP and are often used for real satellites in Earth orbit. Distances between the centres of mass are usually used when talking about planets orbiting the Sun.

For the presentation, I would stick to using the distances from the centres of mass, with maybe a passing reference "Sometimes people measure from the surface of the planet, in that case you need to add the radius of the planet into the formulas."

Making it even more confusing is that in real life there are different ways in which altitude can be expressed. Sometimes altitude is expressed as the height above an assumed spherical Earth, usually with a diameter equal to Earth's equatorial diameter. Other times it is the height above a reference ellipsoid. One has to be careful to use the correct coordinate system.

From what I can tell, there is no polar flattening KSP. All the bodies are treated as spheres, i.e. the sea level radius on Kerbin is the same across the entire globe. This isn't true on Earth.

[SlabGizor117]

Making it even more confusing

This is not what I needed.

XD

-Slab

[Raptor9]

You have to admit, there is no shortage of real-world physics knowledge on these forums. It's a great resource for sure.

[SlabGizor117]

Hey, for anyone still paying attention to this thread, I started my essay! Here's what I have so far:

Expository Essay

Orbital Mechanics

Do you ever wonder what keeps the Moon in orbit around the Earth? Or, the Earth around the Sun? Well, first, let’s figure out what an orbit is. An orbit is defined as the curved path of a celestial object or spacecraft around a star, planet, or moon. So, how does an orbit work? Let’s take the International Space Station, for example. What is it like on the ISS? You feel weightless and float around. To the body, it feels like you’re constantly falling. The truth is, it’s because you are. When you’re in orbit around Earth, gravity is always pulling you towards earth, but you keep missing. An orbit is where you’re falling towards Earth, for example, but the gravity that pulls you towards earth is canceled out by sideways motion. Any slower and gravity pulls you down. Any faster, and gravity has less effect on you. When you see a rocket launch, you’ll probably notice that the rocket tilts on its side very soon and very aggressively. This is because it takes so much sideways motion to get into orbit. In fact, the ISS orbits the earth approximately 16 times in one day.

Here’s an example: The Boeing 747 jet has been used many times to carry the Space Shuttle on its back from Edwards Air Force Base to Cape Canaveral, Florida. Its max speed is 614 miles per hour, and the Earth’s circumference is about 26,000 miles. That means it would take a 747 around 42 hours to make a trip around the Earth without refueling or landing. Well, the ISS is going about 4.76 miles per second, and around 17,150 mph. That’s almost 90 minutes per orbit. So yes, it takes a lot of sideways velocity to orbit Earth.

So what about different kinds of orbits? There are three main orbital trajectories: Circular, Elliptical, and Hyperbolic. There’s a parabolic trajectory, but it’s never really used in real life. First, though, to understand these, there are some terms to work out. The universal terms are Apoapsis and Periapsis. That is, AP-oh-ap-sis and PER-ee-ap-sis. These are two opposite points in an orbit that represent the highest and lowest point in an orbit. Apoapsis is the highest end of the ellipse and Periapsis is the lowest. With Earth, for example, the beginning of “spaceâ€Â, assuming it’s defined as the point at which there is no atmospheric drag, is at 100 kilometers. So say, in an elliptical orbit, one end is at 150km and the other is at 300km. The 150km end is the Periapsis and the 300km end is the Apoapsis, although in an Earth orbit, they’re called Apogee and Perogee, from the root word Geo, meaning Earth or ground. Likewise, the Apoapsis and Periapsis of an orbit around our moon would be Apolune and Perilune. Or for the sun, Aphelion and Perihelion.

So next is the part I worked so hard for, Circular, Elliptical, and Hyperbolic trajectories. Parabolic is getting thrown in the gutter.

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EDIT: Instead of "In fact, the ISS orbits the earth approximately 16 times in one day." I'm gonna change it to "Because of this, the ISS orbits the earth approximately 16 times in one day." Sound good?

- - - Updated - - -

EDITED EDIT: Actually, it'll be, "In fact, the ISS orbits the earth approximately 16 times in one day because of it's speed."

[OhioBob]

One thing you might consider changing is the part that says "the point at which there is no atmospheric drag, is at 100 kilometers". The 100-kilometer definition is that accepted by the Fédération Aéronautique Internationale (FAI), which is an international standard setting and record-keeping body for aeronautics and astronautics. For example, the X-15 and SpaceShipOne pilots that exceeded the 100 km limit were considered to have entered space and were deemed astronauts. However these were suborbital flights where the velocity achieved was much slower than needed to orbit. For orbital flight the velocity required is so high that even at 100 km the atmosphere is still too thick. I don't know what the bare minimum is to be able to complete a full orbit, but I know for sure that very short-term orbits can be achieved at an attitude of 90 nautical miles (103.6 statute miles, 166.7 km). For example, the last three Apollo missions to the Moon launched into parking orbits of 90 miles, but they only completed 1.5 orbits before heading out to the Moon. Geostationary satellites will also briefly park in 90-mile orbits before being transferred out to geostationary distance. The 90 nautical mile altitude is the minimum that I've seen used in actual practice. Even at that altitude the orbit cannot be maintained for long periods before atmospheric drag will cause it to decay. When an orbit must last a number of weeks, altitudes in the 200-300 km range are typical. And for very long durations, such as manned space stations, the orbits are more like 300-400 km.

[Red Iron Crown]

And for very long durations, such as manned space stations, the orbits are more like 300-400 km.

Even then, it is worthwhile to "feather" the solar panels at night to reduce drag, and the station still needs an occasional propulsive boost to maintain orbit.

[cantab]

The significance of the 100 kilometre mark is rather that for an aeroplane to fly fast enough for its wings to keep it it in the thin air, it would have to be going at orbital speed and so wouldn't need the wings anyway!

Of course it's not an exact thing, plane designs vary, but 100 km is a nice round number.

[OhioBob]

The significance of the 100 kilometre mark is rather that for an aeroplane to fly fast enough for its wings to keep it it in the thin air, it would have to be going at orbital speed and so wouldn't need the wings anyway!

Interesting, I did not know that. A good piece of trivia to log away for future reference.

[PatPL]

Write something about oberth effect. http://en.wikipedia.org/wiki/Oberth_effect

It's something like "The faster you go (the lower the periapsis but it's almost same thing) the more influence you have when you want to change your trajectory"

it's just more effective to raise your apoapsis when you're at 100km than 1000km.

[SlabGizor117]

Thanks, nice to know this thread is still alive, lol! I may do the oberth effect, I feel like I would have to dip into more than that to justify it though. Also, Thanks Bob and Cantab, what should I write instead of 100km?

Also, I'll keep posting as I write out bits and pieces for advice and correction.

Thanks for your help guys!

-Slab

[OhioBob]

what should I write instead of 100km?

First off, I'd replace the part that says "the point at which there is no atmospheric drag." Although the atmosphere gets thinner and thinner with increasing altitude, atmospheric drag is still a problem even up to hundreds of kilometers. In the U.S., the maximum lift capacity of a rocket is often stated as the amount of payload it can deliver to a 185 km orbit (100 nautical miles), and the minimum altitude for a short-term parking orbit seems to be 167 km (90 nautical miles). For any orbit that must last days or longer, I rarely see anything with a perigee below 200 km. You can choose your own words, but I'd revise it to say something like, "...the point at which the atmosphere is thin enough to allow a stable orbit, is at about 200 kilometers."

[SlabGizor117]

Cool, thanks Bob! I keep thinking you're Bob Fitch and now I have it in my subconscious that Bob Fitch is from Ohio.... XD