**Narrative**

In this, the first of a four-part interconnected space-based S.T.E.M. project, students will calculate the change in orbital velocity, called Delta V, needed to increase (or decrease) the orbital altitude of a spacecraft.

Students will also calculate the total round-trip time to transfer between orbits, and use that information to determine the duration of the space mission.

**Due Date**

End of Quarter 1

(Midterm Fall Semester)

**Mathematics Used**

Square Root Equations

Exponential Equations

**Constants**

Gravitational Parameter (km3/s2)

Earth Radius (equatorial) (km)

**Input**

Lower Orbital Altitude (km)

Higher Orbital Altitude (km)

On-Station Time (days)

**Output**

Periapsis delta V (kps)

Apoapsis delta V (kps)

Delta V Budget (kps)

Transfer Time (days)

Mission Duration (days)

**Activating Previous Learning**

Basic Mathematics

Square Roots

Scientific Calculator

__Note:__ A grateful tip of the hat goes to Metric Only, who gave a very helpful constructive criticism on the last diary: Keep the units in metric (S.I.). Thanks Metric Only!

*Continued below the fold...*

**Teacher Lesson Plan**

Use the slide-show presentation below to give a lesson about basic orbital mechanics and calculating Delta V and Orbital Transfer Time.

In this lesson, students will identify the various aspects of an orbital transfer diagram, matching them with the terms and definitions.

Students then practice the calculations using pencil, paper, and calculator.

Students then learn about the Engineering Design Process, and begin the process of laying the ground work for the calculator built with a spreadsheet. Sample Open Source computer code is provided to aid students with their spreadsheet formulas.

Some screenshots of the teacher presentation:

The slides will guide the students as they run through the lesson powered by E^8:

1. Engage

- Lesson Objectives
- Lesson Goals
- Lesson Organization

2. Explore

- The Rocket Equation
- Delta V Components and Definitions
- Additional Terms and Definitions

3. Explain

- Basic Orbital Mechanics
- Hohmann Transfer Orbit Equations
- Hohmann Transfer Time Equation
- Mission Duration Equation

4. Elaborate

- Advanced Orbital Mechanics

5. Exercise

- Space Mission Parameters
- Space Mission Design Scenario 1
- Space Mission Design Scenario 2

6. Engineer

- The Engineering Design Process
- SMDC Spaceflight Plan
- Designing a Prototype
- SMDC Software

7. Express

- Displaying the SMDC
- Progress Report

8. Evaluate

- Post Engineering Assessment

This lesson can be delivered in one or two class periods, with students working on the project after school. It is recommended that a few minutes of a few class periods be set aside for student help.

The Student Workbook below, along with the Mission Parameter Sheet (Google Slide Presentation) found in the Overview, accompanies the Teacher Lesson above.

::

**SMDC Example**

Below is an example of a prototype SMDC in the Delta V stage of development.

The calculator is initially constructed with the Input/Output sheet and the Constants sheet in place and the numbers entered.

The project info can be entered after the calculator has been built.

Screen shot of SMDC:

::

Students present the SMDC in the form of a website. A slide-show presentation educating viewers on engineering and SMDC development is embedded in the website.

Example Student Website (coming soon!)

::

**Conclusion**

The square root functions used in this project should be easy enough for the average high school pre-calculus student. The teacher may need to guide students through the setup of the equations and the calculations. As the semester progress, the concepts and the mathematics will become more challenging.

The next step is for the students to calculate the weight of their spacecraft. This will involve linear equations, and and we will use the Mission Duration output as an input for this next project.

Of course, that's a story for another day.

::

A version of this diary was cross-posted at NMSTARG.

::

**High School Classroom S.T.E.M. Projects for Pre-Calculus**

- Overview for Teachers
**Project 1: Delta V and Transfer Time: Square Roots**- Project 2: Spacecraft Weight: Linear Functions
- Project 3: Propellant Weight: Natural Logarithms
- Project 4: Mission to the Moon: Financials
- Student Presentation 1: Delta V and Transfer Time
- Student Presentation 2: Spacecraft Weight
- Student Presentation 3: Propellant Weight
- Student Presentation 4: Mission to the Moon
- Youtube Documentary: "The Making of a S.T.E.M. Project"

**High School Classroom S.T.E.M. Projects for Algebra 2**

- Overview for Teachers
- Project 1: Virgin Galactic: Quadratics
- Project 2: Reaction Engines, Ltd.: Linear Functions
- Project 3: Bigelow/Space X: Area and Volume
- Project 4: Spaceport America: Trigonometry
- Student Presentation 1: Virgin Galactic
- Student Presentation 2: Reaction Engines, Ltd
- Student Presentation 3: Bigelow/Space X
- Student Presentation 4: Spaceport America

**High School Classroom S.T.E.M. Projects for Google Technology**

- Overview for Teachers
- Project: Crowdfunding Google Chromebooks: Cloud Computing
- Student Presentation: Crowdfunding Google Chromebooks

FULL DISCLOSURE:I work for the New Mexico Space Technology Applications Research Group (NMSTARG), a commercial space flight venture, which in its current form exists as an unfinished technical paper. NMSTARG isnotaffiliated with any of the businesses that were discussed in these posting. These diaries exists as a way for the DKos community to get a first look at our research, and to ask said community for any technical and non-technical (just as important!) feedback. The paper provides information on how to make a profit in space, detailing the infrastructure that will be needed and all of the associated costs involved. As such, we hope that it eventually attracts the attention of investors, where the paper then becomes the technical portion of a space-related business plan.

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