nt the graph and attach.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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### Assignment: Graphing Circular Orbits

**Objective:** 
This lesson will guide you through graphing a circular orbit of a rocket around the planet Kerbin using Desmos.com. You will represent Kerbin and the rocket's orbit utilizing different mathematical equations and graphing methods.

**Instructions:**

1. **Graphing Kerbin:**
   - Use Desmos.com to create a circle with radius \( R = 600 \). This circle represents Kerbin in the 2D orbital plane.

2. **Graph the Rocket's Orbit:**
   - Plot the circular orbit of the rocket at a 100 km altitude from the surface of Kerbin. Use different representations for the equations of the circle including parametric, polar, and rectangular equations.

3. **Combination of Equations:**
   - Combine all forms of the equations of the rocket's orbit within the same graph. This will help confirm that they coincide as the same path around the planet.

**Tasks to Complete:**

- **Graph Creation:** Use the tools available on Desmos.com to accurately plot the circle representing Kerbin and the orbit of the rocket. Ensure that the radius of Kerbin is 600 units on the graph.
  
- **Equation Representation:**
  - **Parametric Equation:** Formulate and plot the parametric equations for the orbit.
  - **Polar Equation:** Formulate and plot the orbit using the polar coordinate system.
  - **Rectangular Equation:** Formulate and plot the orbit using the rectangular form.

- **Graph Integration:** Display all forms of equations on one graph. They should all depict the same circular path around the planet Kerbin, showcasing the accuracy and consistency of different mathematical representations.

- **Graph Submission:** Print the complete graph showing all representations and attach it to your submission.

Remember, the goal of this assignment is to understand how different mathematical equations can represent the same shape and to visually confirm their equivalence using a graphing tool.
Transcribed Image Text:### Assignment: Graphing Circular Orbits **Objective:** This lesson will guide you through graphing a circular orbit of a rocket around the planet Kerbin using Desmos.com. You will represent Kerbin and the rocket's orbit utilizing different mathematical equations and graphing methods. **Instructions:** 1. **Graphing Kerbin:** - Use Desmos.com to create a circle with radius \( R = 600 \). This circle represents Kerbin in the 2D orbital plane. 2. **Graph the Rocket's Orbit:** - Plot the circular orbit of the rocket at a 100 km altitude from the surface of Kerbin. Use different representations for the equations of the circle including parametric, polar, and rectangular equations. 3. **Combination of Equations:** - Combine all forms of the equations of the rocket's orbit within the same graph. This will help confirm that they coincide as the same path around the planet. **Tasks to Complete:** - **Graph Creation:** Use the tools available on Desmos.com to accurately plot the circle representing Kerbin and the orbit of the rocket. Ensure that the radius of Kerbin is 600 units on the graph. - **Equation Representation:** - **Parametric Equation:** Formulate and plot the parametric equations for the orbit. - **Polar Equation:** Formulate and plot the orbit using the polar coordinate system. - **Rectangular Equation:** Formulate and plot the orbit using the rectangular form. - **Graph Integration:** Display all forms of equations on one graph. They should all depict the same circular path around the planet Kerbin, showcasing the accuracy and consistency of different mathematical representations. - **Graph Submission:** Print the complete graph showing all representations and attach it to your submission. Remember, the goal of this assignment is to understand how different mathematical equations can represent the same shape and to visually confirm their equivalence using a graphing tool.
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