New Mars Forums

tahanson43206

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Registered: 2018-04-27

Posts: 17,181

Re: Orbital Mechanics

This post is a place holder for planned text to be written using GW Johnson's Lesson 1 of 3 as a source

Draft in progress:
Figure 1 Lesson 1

Begin Text representation of Figure 1:
Title: Figure 1 – Basic Elliptic Orbit Geometry, Part 1: Two Endpoints Case
Text at top: eccentricity”e” determines how ovalized the path is
Drawing: ellipse centered in rectangle of frame
Drawing: central body shown at center of focus on left
Drawing: semi-major axis centered in ellipse in x axis
Text above semi    -major axis inside ellipse: central body occupies one focus
Text at far left inside ellipse: Rmin above arrow from central body to ellipse
Text at far right above semi    -major axis: other focus unoccupied
Text inside ellipse above and left of center: center
Text below semi-major axis on right inside ellipse: Rmax
Text below semi-major axis on left inside ellipse: major axis

Text to left of ellipse: near endpoint “periapsis”
Text to right of ellipse: far endpoing “apoapsis”

End Text representation of Figure 1.

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tahanson43206

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Registered: 2018-04-27

Posts: 17,181

Re: Orbital Mechanics

As a follow up to Post #176, I asked ChatGPT for advice on how to use text to represent one of Dr. Johnson's images.

Today's session went on for several phases. The transcript below is the final session.

Hello again! I'd like to continue working on improving my ability to deliver the contents of an image of mathematical shapes and associated arrows and text and formulas in the form of text so you can work with students who can see the images. What we are attempting is to see if you can help students to "internalize" course material. In our last discussion, you suggested identifying arrows by stating where the head of the arrow might be, and where the base of the arrow might be. It occurred to me to wonder what kind of reference system you might need internally, to organize this material. The goal is for you to be able to ask questions of the student about the image which they can see but you cannot see, or to point out something in the image that the student can see but you cannot. Please advise on what kind of reference framework might work for you. To help, I will offer the information that the images of interest are constructed by the author inside rectangular forms using a graphics tool of some kind.  The result of the author's work is then published inside a pdf document, along with text that comprises the course material.  We have four such images in the first lesson of the course we are attempting to prepare to give to you, so you can coach students.

To provide accurate and clear descriptions of the mathematical shapes, arrows, text, and formulas within the images, a useful reference framework would be to use a systematic approach to describe the location and properties of each element within the rectangular form.

Here are some possible steps to follow:

Start by identifying the rectangular form that contains the mathematical shapes, arrows, text, and formulas. You can describe the dimensions and location of the form, such as "a rectangular form with a width of 10 centimeters and a height of 8 centimeters located in the upper left corner of the page."

Next, divide the rectangular form into smaller sections or grids to provide a more precise reference system. For example, you could divide the form into a grid of 10 columns and 8 rows, each with a size of 1 centimeter. This would allow you to describe the location of elements more precisely, such as "the circle is located in column 3, row 4 of the rectangular form."

Once you have established a reference grid, you can begin to describe the mathematical shapes, arrows, text, and formulas within the rectangular form. For each element, you can describe its location within the grid and any relevant properties, such as its size, color, and shape. For example, you could describe a circle located in column 3, row 4 as "a red circle with a diameter of 2 centimeters."

When describing arrows, you can use the base and head of the arrow to establish its direction and location within the grid. For example, you could describe an arrow from column 2, row 5 to column 5, row 5 as "an arrow that starts at the base in column 2, row 5 and points to the head in column 5, row 5."

Finally, when describing text and formulas, you can use the same reference system to describe their location and any relevant formatting, such as font size and style. For example, you could describe a formula located in column 6, row 3 as "a formula in Times New Roman font with a font size of 12 points."

By following these steps and establishing a consistent reference framework, you should be able to accurately and effectively describe the contents of the images to students who can see the images but you cannot.

Your reply is most helpful.  I am encouraged, despite the daunting nature of what we are undertaking. Let me now ask if you would find it helpful if the angle of a line is included in the description. for example, if an arrow ascends upward at an angle of 280 degrees from the origin, would you be able to "understand" the orientation of the arrow, if the angular structure is defined for you at the beginning of the section?

Yes, including the angle of a line or arrow can be helpful in providing a more complete description of the image. If you define the angular structure at the beginning of the section, it can help me understand the orientation of the arrows and lines within the image.
However, it's important to note that angles are relative to a reference point, so it would be useful to establish a consistent reference point for each image. For example, you could use the top-left corner of the rectangular form as the reference point and describe angles relative to the positive x-axis (going from left to right) or the positive y-axis (going from top to bottom). This would allow you to provide a more precise description of the orientation of lines and arrows within the image.

Once again I am encouraged by your reply, and hopeful we may be able to 'solve' this challenging problem.  You have suggested a grid, and a reference point at the top left corner of the image. By happy coincidence, this is precisely what a software writing to a computer monitor is doing. I can imagine writing a software program to analyse an image, so that the grid corresponds to the actual pixel layout of the image, and key points can be identified by X-Y coordinates in the image. Does this approach sound feasible to you?

Yes, it is certainly feasible to write a software program that can analyze an image and identify key points using X-Y coordinates corresponding to the pixel layout of the image. This type of program is commonly used in image processing and computer vision applications.

To implement this approach, you would need to use an image processing library or software development kit (SDK) that provides functions for analyzing and manipulating images. These libraries typically have functions for loading images from files or memory, converting between different color spaces, and performing various operations on images, such as filtering, segmentation, and feature detection.

Once you have loaded the image into memory, you can use the library functions to identify key points within the image, such as the top-left corner of the rectangular form, the location of mathematical shapes, arrows, text, and formulas, and any other relevant features.

To establish the grid, you can use the pixel layout of the image to define the dimensions and spacing of the grid, and then use the library functions to assign X-Y coordinates to each cell in the grid. This would allow you to describe the location of each element within the image using X-Y coordinates that correspond to the pixel layout of the image.

Overall, this approach can be an effective way to analyze and describe images containing mathematical shapes, arrows, text, and formulas, and would enable you to work with students who can see the images but you cannot.

Your boundless patience and eternal optimism are essential as we proceed to the next question: How would you like to have the course presented to you so you can work with it in text form while the student works with the printed document that includes images?  We have four images in lesson one, and we have four pages of text.  We have to start a session from scratch, because at present your management team has chosen NOT to save anything between sessions. In order to help you to help the student, I must deliver to you all the text (for the lesson itself and separately for the images) and ** then ** advise you that the student is online and ready to begin. I'd like to prepare the material ahead of time so it flows easily into your computing structure.

Thank you for considering the best way to present the course material to me. To make it easier for me to work with the text form of the course material, it would be helpful if you could provide the following:

A clear and organized outline of the course material, including a description of the topics covered in each lesson.

A separate document that includes the text from each page of the printed document, along with a description of the corresponding image (if any) and its X-Y coordinates on the grid.

For each image, a description of the mathematical shapes, arrows, text, and formulas it contains, along with their X-Y coordinates on the grid and any relevant angles or dimensions.

A consistent and well-defined reference system for describing the X-Y coordinates and angles within each image.

Providing this information in a clear and organized manner would make it easier for me to understand and work with the course material. Additionally, having the material prepared ahead of time would allow for a smoother and more efficient session with the student.

OK .... please create a framework/outline that you would like to see. Include in your answer the items you want to see as described in the answer immediately above this point. To help you prepare your outline, I will once again describe this specific course: Title: Orbital Mechanics using Spreadsheet Lesson 1: Basic Ellipses Text: four pages of text Figure 1: text for figure Figure 2: text for figure Figure 3: text for figure Figure 4: text for figure.

Sure, I'd be happy to provide a framework/outline that would help to organize the material for me. Here's what I suggest:

I. Course Outline
A. Introduction
Overview of the course and its goals
Description of the software used (spreadsheet)
B. Lesson 1: Basic Ellipses
Overview of the lesson and its goals
Description of the four pages of text
C. Lesson 2: Orbits around a Point Mass
Overview of the lesson and its goals
Description of the text and figures
D. Lesson 3: Orbits around a Central Body
Overview of the lesson and its goals
Description of the text and figures
E. Lesson 4: Kepler's Laws
Overview of the lesson and its goals
Description of the text and figures
II. Text for Lesson 1
Page 1
Page 2
Page 3
Page 4
III. Figures for Lesson 1
A. Figure 1
Description of mathematical shapes, arrows, text, and formulas contained in the figure
X-Y coordinates of key points on the grid
Any relevant angles or dimensions
B. Figure 2
Description of mathematical shapes, arrows, text, and formulas contained in the figure
X-Y coordinates of key points on the grid
Any relevant angles or dimensions
C. Figure 3
Description of mathematical shapes, arrows, text, and formulas contained in the figure
X-Y coordinates of key points on the grid
Any relevant angles or dimensions
D. Figure 4
Description of mathematical shapes, arrows, text, and formulas contained in the figure
X-Y coordinates of key points on the grid
Any relevant angles or dimensions
By providing the material in this framework, it would make it easier for me to access and understand the course material. Additionally, having the figures and their associated descriptions separated from the text would allow me to easily reference them during a session with a student.

Awesome! Unlike you, I am now tuckered out, and the work hasn't even begun. It will be a while before you have to deal with this challenge, but on the ** other ** hand, I think it might be possible to have a first draft ready for your review within a week. Catch you next time!

Sounds good! Take your time and feel free to reach out if you have any further questions or concerns. I'm always here to help. Have a good rest!

The direction indicated is to use the coordinate system used by the computer software that created the image rendered in the pdf document that the student sees.

(th)

tahanson43206

Moderator

Registered: 2018-04-27

Posts: 17,181

Re: Orbital Mechanics

This is a follow up to post #176

The grid system for location of points within an image is separate from but overlaid on the coordinate system needed for description of arrows that are included in diagrams.  I observe that in the images prepared by Dr. Johnson, there may be a Zero x-y point inside each ellipse, and arrows may originate from or point to that location. Other arrows are for information only, and these start and end without reference to the ellipse.

For the purpose of preparing text for ChatGPT, it might be sufficient to provide the start point and the end point for lines, and to ignore the angles, unless the angle is essential for a mathematical definition of the line.

(th)

tahanson43206

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Registered: 2018-04-27

Posts: 17,181

Re: Orbital Mechanics

While looking for something else, I found this online resource:

http://www.nssc.ac.cn/wxzygx/weixin/201 … 698873.pdf

Orbital Mechanics for
Engineering Students
Howard D. Curtis
Embry-Riddle Aeronautical University
Daytona Beach, Florida

The publication date is 2005

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SpaceNut

Administrator

From: New Hampshire

Registered: 2004-07-22

Posts: 28,884

Re: Orbital Mechanics

Here is another reason to know where we are in time...
NASA can’t talk to its Mars robots for two weeks because the sun is in the way

The pause started on Saturday and will go on until November 25. A Mars solar conjunction occurs every two years, and while the rovers will be able to send basic health updates home throughout most of the period, they’ll go completely silent for the two days when the sun blocks Mars entirely.

tahanson43206

Moderator

Registered: 2018-04-27

Posts: 17,181

Re: Orbital Mechanics

For SpaceNut re Post #180

Thanks for this advance notice ... I can watch for the Sun crossing the star map where I check on Mars every morning.

(th)

SpaceNut

Administrator

From: New Hampshire

Registered: 2004-07-22

Posts: 28,884

Re: Orbital Mechanics

Calculate how long it would take to reach planets, stars, or galaxies, as well as fuel mass, velocity and more!

Calliban

Member

From: Northern England, UK

Registered: 2019-08-18

Posts: 3,433

Re: Orbital Mechanics

A lagrange point finder.
http://orbitsimulator.com/formulas/Lagr … inder.html

For those who don't want the bother of building their own spreadsheet.

---

"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."

tahanson43206

Moderator

Registered: 2018-04-27

Posts: 17,181

Re: Orbital Mechanics

For Calliban re #183

Thanks for this nice addition to the topic!

For those who might wish to test the calculator, you'll need some values to enter to run a test.

Google provides them quickly, but to save you a few seconds, here are initial values you can use:

Moon's semi-major axis in orbit around Earth: 384000 km
Earth mass: 5.972 × 10²⁴ kilograms
Moon mass: 7.34767309 × 1022 kilograms

SearchTerm:Calculator LaGrange points
SearchTerm:LaGrange points calculator

(th)

GW Johnson

Member

From: McGregor, Texas USA

Registered: 2011-12-04

Posts: 5,459

Website

Re: Orbital Mechanics

Just a test.  Having trouble posting at all.

GW

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GW Johnson
McGregor,  Texas

"There is nothing as expensive as a dead crew,  especially one dead from a bad management decision"

tahanson43206

Moderator

Registered: 2018-04-27

Posts: 17,181

Re: Orbital Mechanics

This post is intended to hold data about the orbital velocity of satellites in orbit around Mars...

SearchTerm:Velocity of a satellite in orbit around Mars

Circular orbit speed or velocity m/s   
3500.10  m/s

Below are details of the computation.

Mathematics of Satellite Motion

The Physics Classroom
https://www.physicsclassroom.com › circles › Lesson-4
The orbital speed can be found using v = SQRT(G*M/R). The R value (radius of orbit) is the earth's radius plus the height above the earth - in this case, 6.59 x ...

Here is the mass of Mars:

Mars/Mass
6.39 × 10^23 kg

Again from Physics Classroom:

Taking the square root of each side, leaves the following equation for the velocity of a satellite moving about a central body in circular motion

where G is 6.673 x 10-11 N•m2/kg2, Mcentral is the mass of the central body about which the satellite orbits, and R is the radius of orbit for the satellite.

and

upload.wikimedia.org/wikipedia/commons/0/0c/Mars_-...
Mars' mass is 6.42 x 1023 kilograms, about 10 times less than Earth. This affects the force of gravity. Gravity on Mars is 38 percent of Earth's gravity, so a 100-pound person on Earth would weigh 38 pounds on Mars. Mars is home to both the highest mountain and the deepest, longest valley in the solar system.Aug 2, 2012

How Big is Mars? | Size of Planet Mars - Space.com

We also need the radius of Mars...

2,106.1 mi
With a radius of 2,106 miles (3,390 kilometers), Mars is about half the size of Earth. If Earth were the size of a nickel, Mars would be about as big as a raspberry. From an average distance of 142 million miles (228 million kilometers), Mars is 1.5 astronomical units away from the Sun.

Mars: Facts - NASA Science

Returning to the equation: v = SQRT(G*M/R)

From above:
G = 6.673 x 10-11 N•m2/kg2
M = 6.42 x 10^23 kilograms
R = 3390 km + 100 for satellite or 3490 km >> 3.49 x 10^6 meters

Result: To save time, I went to Google and found: https://www.satsig.net/orbit-research/o … -speed.htm

This web site offers a calculator with drop down menus including Mars:

Circular orbit height and speed calculator
Main body name
Mars
Height above surface of main body
100
km       ft
  If "Other", edit: Main body mass:
5.972E24
kg   
If "Other", edit: Main body diameter=
12756
km     

Orbit height km   
100
km
Orbit height ft   
328084
ft

Circular orbit speed or velocity m/s   
3500.10  m/s

Circular orbit speed or velocity ft/sec   
11483.12
ft/sec
Period of circular orbit minutes   
104.60
minutes
Period of circular orbit hours   
1.743
hours
Period of circular orbit days   
0.0726
days
Period of circular orbit years   
0.0002
years
    
Gravitational constant G    6.6743 x 10-11 Nm2s-2
Mass of the main body M   
6.417e+23
kg
Standard gravitational parameter for main body μ  = GM  km3s-2   
42828
km3s-2
Diameter of main body   
6792
km
Radius of orbit (= height + diameter of main body / 2 )   
3496.0
km

This page is about orbital height, speed and period.  It works for circular orbits.

(th)

GW Johnson

Member

From: McGregor, Texas USA

Registered: 2011-12-04

Posts: 5,459

Website

Re: Orbital Mechanics

I built that and much more into the first 3 lessons of the orbit mechanics course and the spreadsheet it uses.

The speed of a circular orbit comes from a simple derivation,  but it is also the degenerate case of the speed anywhere around an elliptical orbit.  V = square root of [G M ( 2/R - 1/a)]

GW

---

GW Johnson
McGregor,  Texas

"There is nothing as expensive as a dead crew,  especially one dead from a bad management decision"

tahanson43206

Moderator

Registered: 2018-04-27

Posts: 17,181

Re: Orbital Mechanics

For GW Johnson!

Thanks for the reminder that so much valuable knowledge is locked up in the courses you have prepared.

So far, we (friends of yours, mostly) have been unable to find anyone able and willing to study the material you have carefully prepared.

The people who are going to be landing on or just flying to Mars are alive on Earth today. Many of those folks would benefit if they could study the material you have prepared, but I have no idea how to find them.  The course material is offered for free, and it is available to anyone with Internet access, but the budget for marketing anything on this site is zero.

In the mean time, Gemini.Google.Com came up with 700 meters per second as the velocity of interest for a space craft on a Hohmann orbit;

Discussion with Gemini.Google.com on 2024/02/21 regarding velocity at Mars.

The estimated velocity difference is given as 700 meters per second.

This is an estimate, because many variables are in play when a space craft approaches the orbit of Mars while on a Hohmann orbit.

A Hohmann Orbit is a kind of spacecraft flight path that has advantages and disadvantages over other choices. I would like to have an estimate of the velocity of a spacecraft on a Hohmann orbit from Earth as it approaches the orbit of Mars with  Mars coming up behind. It is necessary for the spacecraft to accelerate to match the velocity of Mars. However, I suspect the actual value depends upon a great number of values. Is there a generally accepted approximate value that is commonly used for flight planning?

You're correct that a Hohmann orbit has advantages and disadvantages, and the velocity of a spacecraft approaching Mars on this path depends on several factors. However, there is a commonly used approximate value for flight planning purposes.

Here's the breakdown:

Factors affecting velocity:

    Relative positions of Earth and Mars at launch: This affects the transfer time and, consequently, the necessary velocity change.
    Launch efficiency: Achieving the ideal Hohmann transfer requires precise timing and thrust, which may not be possible in reality.
    Mid-course corrections: Minor adjustments are usually needed during the journey, influencing the final velocity.

Approximate value for flight planning:

Despite these variables, a commonly used approximation for the velocity difference between a spacecraft on a Hohmann transfer and Mars at the encounter point is:

ΔV ≈ 0.7 km/s

This value represents the additional velocity boost the spacecraft needs to match Mars's orbital velocity. It's important to understand that this is just an approximation and the actual value could vary slightly based on the specific mission parameters.

Why this approximation is useful:

    It provides a starting point for trajectory planning and fuel calculations.
    It simplifies complex calculations for initial planning stages.
    It offers a good balance between accuracy and ease of use.

Remember:

    This approximation is for educational purposes and should not be taken as absolute in real mission planning.
    Precise calculations require detailed mission parameters and advanced software.

Further details:

    For more accurate calculations, consider tools like NASA's Trajectory Browser or GMAT software.
    Understanding orbital mechanics concepts like vis-viva equation and Hohmann transfer specifics will provide deeper insights.

I hope this explanation clarifies the situation and helps you understand the role of this approximation in planning missions to Mars.
profile picture
Thank you ** very ** much for the value of 700 meters per second for early planning purposes. I have a related question, and I'm hoping your ability to access resources on the Internet may be helpful. A small group is considering a flight to deliver a payload to Mars. The space craft that is one the Hohmann trajectory would NOT accelerate as Mars approaches from behind. The concept for payload delivery is to accelerate ONLY the payload and the hardware needed for landing. It is estimated that the effective atmosphere is below 135 kilometers above the surface. The question I am hoping you can answer is: How low into the atmosphere of Mars can we fly the space craft without risking damage due to over heating. Your answer would surely depend upon the material used for the space craft, so we will specify stainless steel as used in the SpaceX Starship.

(th)

tahanson43206

Moderator

Registered: 2018-04-27

Posts: 17,181

Re: Orbital Mechanics

For GW Johnson...

Here is a question better suited for the Orbital Mechanics topic ...

We are considering a space craft flight plan that drops off a payload at Mars after making a Hohmann orbit flight from Earth.  The space craft will be given momentum by Mars due to the gravity of Mars as the space craft approaches and departs.

The question at hand is whether a careful planning of the flight will allow the space craft to return to Earth rapidly (or more rapidly) than would have been the case with a simple Hohmann orbit.

For GW Johnson re #9

Thanks for mentioning the acceleration that will be imparted to a space  craft that just flies by on a Hohmann trajectory!  I was planning to ask about that, so I appreciate your including it in your post.

It seems to me that a mission planner with the appropriate software could find a path for the  space craft that does something useful with the acceleration provided by Mars as it roars by the pokey space craft.   Mission planners (are reported to) use such planetary encounters to give their space craft impulses of momentum that add up to useful inputs to a mission.  In this case, we would like Mars to fling the space craft onto a path that brings it back to Earth sooner rather than later.

This topic is the Cycloid Payload Delivery topic, so I'll move this question over to Orbital Mechanics.

(th)

GW Johnson

Member

From: McGregor, Texas USA

Registered: 2011-12-04

Posts: 5,459

Website

Re: Orbital Mechanics

Those questions can only be answered using a 3-body computer code.  Hand calculations cannot do that.  My "3-body work-around" using 2 sets of 2-body numbers determines only speed magnitudes,  not directions.  It is directions that are critical to the answers you seek.

GW

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GW Johnson
McGregor,  Texas

"There is nothing as expensive as a dead crew,  especially one dead from a bad management decision"

tahanson43206

Moderator

Registered: 2018-04-27

Posts: 17,181

Re: Orbital Mechanics

For GW Johnson!

Thanks for considering the question!

Three is a free advanced orbit planning software called GMAT.  I understand this software is 'sponsored' by NASA but it is (reportedly) maintained by volunteers.

It is possible for you to run this software on a personal computer.  The wrinkle that has stopped me from pursuing this is that it uses MATLAB, which is a licensed software that is routinely made available to college students, but which is otherwise licenses at the rate of about $100 per year.

You've often reported feeling elderly, but the fact is you are still a young whipper snapper compared to your elders.

You have spent many decades accumulating the wisdom you already have, so it is understandable if you were to decide to stop learning.

However, if the opportunity to learn GMAT were to present itself, there is a (very slim) chance you would be tempted.

The wrinkle is that $100 annual license fee.

If you can afford that, then I can show you how to install the software on your laptop, and you will be able to take the next step beyond your (already powerful) spreadsheet.

(th)

GW Johnson

Member

From: McGregor, Texas USA

Registered: 2011-12-04

Posts: 5,459

Website

Re: Orbital Mechanics

I don't know anything about MATLAB either,  although I know that such a thing exists.  And that is all that I know.

The last computer languages that I knew were Fortran IV (not Fortran 77,  earlier!),  and QuickBASIC 4.5.  They would run on mainframes,  and DOS-operated desktops,  respectively.  I know absolutely nothing of anything since.  And that would be the early 1980's. 

I had QuickBASIC 4.5 operational on laptops up through Windows 98 in the DOS shell option,  but that capability zeroed in later versions of Windows.  It took a gamer's shell program to run QuickBASIC in versions of Windows up to 7.1,  but nothing since.  I have been unable to use it since then,  some 5 years ago.

I utterly despise Windows 10 (on this laptop) because they hid so effectively everything I really need.  I refuse to upgrade to Windows 11 for that same reason.  If I could dispense with Microsoft Windows entirely,  I would do so.  It hasn't been worth a shit since before Bill Gates retired from running Microsoft.  It was a good outfit long ago,  but no more.

GW

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GW Johnson
McGregor,  Texas

"There is nothing as expensive as a dead crew,  especially one dead from a bad management decision"