## Get Me Off This Planet!

This hands-on activity about the factors involved in getting astronauts off Mars is part of a *TeachEngineering.org* Mission to Mars curricular unit.

**Summary**

In this lesson to teach middle school students how a spacecraft gets from the surface of the Earth to Mars, students first investigate rockets and how they are able to get us into space, then discuss the nature of an orbit as well as how orbits enable us to get from planet to planet.

**Engineering Connection**

**Educational Standards**

**Common Core State Standards for Mathematics**

- 2. Fluently divide multi-digit numbers using the standard algorithm. [Grade 6]
- 3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. [Grade 6]
- 4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [Grade 7]
- 3. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 10
^{8}and the population of the world as 7 × 10^{9}, and determine that the world population is more than 20 times larger. [Grade 8]

- G. Transportation vehicles are made up of subsystems, such as structural propulsion, suspension, guidance, control, and support, that must function together for a system to work effectively. [Grades 6 – 8]

**Next Generation Science Standards**

- Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object. [Grades 6 – 8]

**Learning Objectives**

- Describe how a rocket must overcome the forces of gravity and drag in order to get out of the atmosphere.
- Explain that thrust is the force created by a rocket.
- Describe how an orbit is the balance of gravity and an object’s tendency to follow a straight path.
- Explain some challenges that engineers face in getting a rocket to Mars.

**Introduction/Motivation**

*Expect students to indicate that it takes a very large rocket to get there.)*Why do you need such a large rocket? (

*Expect answers such as: We need to overcome gravity, Mars is a far away, when we go to Mars, we have to take a lot of supplies and equipment, and maybe even, we have to overcome gravity and the drag of our atmosphere.*)

*weightlessness*, and it does not mean that gravity is not there. It is as if both the astronaut and spacecraft are perpetually falling, but never actually get any closer to the surface of the Earth.

*orbit*around the Earth. What is an orbit?

*(Listen to student suggestions.*) An orbit is a regular, repeating path that one object in space takes around another one. What is the shape of most orbits? (

*Listen to their answers; most will suggest the shape of a circle.)*It is elliptical. An ellipse is essentially an oval. While a circle is a special kind of ellipse, engineers and scientists use the term ellipse to describe orbits around Earth and other bodies such as the Sun. So, if a spacecraft is in orbit around Earth, how does it get to Mars?

*(Listen to student answers.)*Well, it uses another rocket. If the rocket moves the craft fast enough, it can overcome the Earth’s gravity and start heading for Mars. Elliptical orbits also help to move a rocket between planets. However, many other factors must be taken into consideration when traveling between planets. Today we are going to talk about the basics of traveling from Earth to Mars.

**Lesson Background and Concepts for Teachers**

Getting off Earth – Launch

*launch*. Launch is the act of getting a spacecraft off the surface of the Earth and into an orbit around it. It takes a lot of energy to reach an orbit above Earth. Consider that just to jump a couple feet off the ground takes all the energy we can muster. To get a thousand kilogram spacecraft off the ground takes an incredible amount of energy. Not only do we have to overcome Earth’s gravity, but also the drag of the atmosphere.

Let’s consider the forces acting on a rocket. Look at Figure 1 showing a rocket just before liftoff. The two forces acting upon the rocket in this scenario are the rocket’s weight (W) and a normal force (N). A normal force is a force that acts on an object by a contact surface (in this case, the ground). A normal force also acts perpendicularly to the surface – because the ground is horizontal, the normal force acts vertically. If we add the forces together, we will find the net force (F_{net}) acting on the rocket: F_{net} = N – W. The weight is preceded by a minus sign because the weight of the rocket acts downward (the normal force acts upward and is thus positive, but does not require a plus sign by common mathematical sign convention). It is easy to understand from this situation that because the rocket is not moving, the weight is balanced by the normal force: N = W. Thus, the net force is zero.

_{T}; more on this later). Because the rocket is travelling in Earth’s atmosphere, there is a drag force (F

_{D}; we can feel drag when we put our hands out a moving car’s window). Let’s find the net force acting on this rocket: F

_{net }= F

_{T}– F

_{D}– W. The motion of the rocket depends on the magnitudes of these forces at an instant in time.

_{T}< F

_{D}+ W –> the rocket falls back towards Earth

_{T }= F

_{D}+ W –> the rocket continues at the same velocity

_{net }= ma, where m is the mass of the rocket and a is its acceleration. Thus, it is easy to see that the acceleration of a rocket is dependent upon the net force and the mass of the rocket.

_{T}> F

_{D}+ W –> the rocket accelerates

_{net}= ma

_{net}/m

_{net}/ 1 = F

_{net}

_{net}/ 2 = ½ F

_{net}

_{net}/ ½ = 2 F

_{net}

*V*means velocity.

_{Launch}is the total change in velocity needed to launch a spacecraft into an orbit around Earth. ∆V is the final velocity minus the initial velocity. Since the velocity of the spacecraft is initially zero while it is on the ground, ∆V is simply the final velocity. ∆V

_{burnout}is the leftover velocity that we need to maintain and orbit around Earth. We will talk about this velocity a little later. ∆V

_{gravity}is the change in velocity needed to overcome the gravity of Earth. ∆V

_{drag}is the change in velocity required to overcome drag.

*launch vehicle*, dwarfs the actual spacecraft, which is referred to as the

*payload*. For a typical mission into Low Earth Orbit (LEO) the mass of the launch vehicle and the fuel is roughly 40 times the mass of the actual payload.

*action*. The

*reaction*is that the rocket moves in the opposite direction, forwards.

*thrust*— the force that pushes the rocket into orbit. We calculate the amount of thrust a rocket produces by using the following equation:

_{e}). The mass flow rate is how fast mass is coming out of the rocket. The mass is the exhaust gas that comes from the burning fuel. Mass flow rate is measured in kilograms per second (kg/s). The exhaust velocity is a measure of how fast the hot gas leaves the rocket nozzle.

*specific impulse*(I

_{sp}) — a measure of the energy content of a propellant and how efficiently it is converted into thrust. Basically, the specific impulse tells us how much “bang for the buck” we get out a certain type of rocket. To calculate the specific impulse, we divide the thrust by the weight flow rate:

^{2}). The specific impulse has units of seconds. The I

_{sp}measures how much thrust we are getting for how much fuel weight we are using. A higher I

_{sp}means that we are getting more thrust for less fuel, and it is a more efficient system.

*Chemical rockets*are the most common typein use today, and include liquid fuel rockets, solid fuel rockets and a hybrid of the two. Chemical rockets rely on chemical combustion that creates a super-heated, high-pressure gas. This high-pressure gas can only escape through the nozzle. According to Newton’s third law of motion, this gas leaving the rocket at a very high velocity is the action, while the rocket moving in the opposite direction is the opposite reaction.

_{sp}), but they are very simple and cheap. They are often used on spacecraft to make very small velocity changes where large rockets are overkill. The rocket packs that astronauts use when they are outside the space shuttle or international space station use cold gas rockets.

Orbits

*orbit*. An orbit is a circular or elliptical path around a celestial body (sun, star, planet, asteroid, etc.) on which an object such as a spacecraft follows. One common misconception is that no gravity exists on the space shuttle and international space station. In fact, gravity

*is*acting on a person in orbit around the Earth, but s/he does not feel it like we feel it on Earth, because no ground exists to push back on a person in space. So, why doesn’t a spacecraft just fall back to Earth once the rockets shut off? This is because the velocity of the spacecraft wants to move it past the Earth, while gravity pulls it back. These two actions cancel out to form an orbit. An orbit can be explained by Newton’s first law of motion, which tells us that an object in motion stays in motion unless a force acts against it. This means that an object will move in a straight line unless a force pushes it in a different direction. For any object to change the direction in which it is moving, a force must act upon it. For example, when you are on a bike and want to turn (change directions), your tire must apply a force to the ground. This force is called friction; without friction, it would be like biking on perfectly smooth ice. If you tried to turn, there would be no frictional force; you would keep moving in a straight line as Newton’s first law describes. Just like your bike, a spacecraft will not turn unless a force acts on it. The force that acts on objects — ultimately causing them to orbit a planet or a star — is gravity. An orbit is just a balance between the velocity of an object and gravity.

*escape velocity*, and it is the minimum velocity needed to escape the Earth’s gravity.

Getting to Mars

*periapsis*, which is the point on the elliptical orbit that is closest to the planet or sun; and the

*apoapis*, the point furthest from the planet or sun. You may have also heard these points called

*perigee*and

*apogee*. These are the periapsis and apoapsis for an elliptical orbit around Earth, respectively. In an elliptical orbit, the Earth (or other massive body) is located at one of the two foci. Elliptical orbits enable movement between planets. Using the Sun as one of the foci, and the Earth as the periapsis, the spacecraft will actually be closer to the Sun when it is at the periapsis. When the spacecraft is at the apoapsis, it will be further away from the sun. This is useful for traveling to planets further from the Sun such as Mars. Figure 5 shows how half an elliptical orbit can be used to get from Earth to Mars.

### Vocabulary/Definitions

apoapsis: |
The point in an orbit farthest from the center of attraction (that is, the planet or sun). |

chemical rocket: |
A rocket that relies on a chemical combustion to create a super-heated, high-pressure gas that is used for thrust. |

cold gas rocket: |
A rocket that uses escaping pressurized gas as a source of thrust. |

electrical rocket: |
A rocket that creates thrust by using electricity to accelerate charged particles, which are directed out the back of the vehicle. |

ellipse: |
A closed curve resembling a flattened circle. Most orbits are in the shape of an ellipse. |

escape velocity: |
The minimum velocity needed to escape from the gravitational pull of a celestial body (Earth, Sun, etc). |

foci: |
Two points on an ellipse in which the sum of the distances to the foci from any point on the ellipse is a constant. |

Newton’s 1st Law of Motion: |
For an object being acted on by balanced forces: if the object is at rest, it will remain at rest; if an object is in motion, it will remain in motion (“law of inertia”). |

Newton’s 2nd Law of Motion: |
For an object being acted on by unbalanced forces: the acceleration of an object is dependent on its mass and the net force. Described by the equation Fnet = ma. |

Newton’s 3rd Law of Motion: |
For every action, there is an equal and opposite reaction. |

normal force: |
A force provided by a contact surface (e.g., the ground) that acts perpendicularly to the surface. |

orbit: |
The path of a planet, moon, spacecraft, or any other object in space as it revolves around another object, such as the sun. |

periapsis: |
That point in an orbit closest to the center of attraction (that is, the planet or sun). |

specific impulse: |
A measure of rocket efficiency that is equal to the thrust of the rocket per weight of the fuel. |

thrust: |
The forward reaction to the rearward movement of exhaust from a rocket engine. |

universal gravitational constant: |
The constant that relates the gravity of two objects depending on their masses and the distance between them. |

### Associated Activities

- The Great Gravity Escape – Students use water balloons and a length of string to understand how gravity and the speed of an orbiting body balance to form an orbit. They also see that when the velocity exceeds the escape velocity, the object will escape the gravity of the sun or planet that it is orbiting around.

### Lesson Closure

### Assessment

Pre-Lesson Assessment

*Discussion Questions:*Solicit, integrate and summarize student responses.

- What does it take for us to get to Mars? What does it take to get a spacecraft off the ground?
- What do you know about rockets? How do they work? Can you name any rockets? (Answer: US space shuttles: Saturn, Atlas, Titan, Delta, Ariane, Pegasus, etc.)
- Once a spacecraft is out of the Earth’s atmosphere, it goes into an orbit. What is an orbit? (Answer: An orbit is a curved path on which a planet, star, spacecraft, etc. moves around another object or celestial body.)

*Voting:*Ask a true/false question and have students vote by holding thumbs up for true and thumbs down for false. Count the votes and write the totals on the board. Give the right answer.

- Is gravity acting on the space shuttle and its crew? (Answer: Gravity is acting on them and creates the centripetal force that keeps the space shuttle from flying in a straight line off into space. They do not feel it because the inertia of their orbit is perfectly balanced with the centripetal force from gravity.)

Post-Introduction Assessment

*Discussion Question:*Ask the students and discuss as a class:

- Why does it take so much energy to get to Mars? (Possible answers: We have to overcome the gravity of Earth; we have to overcome the drag of Earth’s atmosphere; we have to get enough speed to get to Mars in a reasonable time; and/or we have to slow down once we get to Mars so we do not just fly past the planet.)
- If a rocket is moving at constant velocity and the thrust force is equal to the sum of its drag force and its weight, what will happen to the rocket? What law describes this situation? (Answers: The rocket will continue to move at the same velocity. Newton’s 1st Law of Motion.)
- If a rocket constant is moving at constant velocity and the thrust force is less than the sum of its drag force and its weight, what will happen to the rocket? What law describes this situation? (Answers: The rocket will begin to fall back to Earth. Newton’s 2nd Law of Motion.)

Lesson Summary Assessment

*Numbered Heads:*Divide the class into teams of three to five students each. Have students on each team pick numbers so each has a different number. Ask the students a question and give them a short time frame for solving it (~1 minute). The members of each team should work together on the question until everyone on the team knows the answer. Call a number at random. Students with that number should raise their hands to answer the question. If not all the students with that number raise their hands, give the teams more time to work on the question. Example questions:

- Which of Newton’s laws of motion states that for every action there is an equal and opposite reaction? (Answer: Newton’s third law of motion.)
- What must a rocket overcome in order to reach orbit? (Answer: Gravity and drag.)
- What is the force created by a rocket called? (Answer: Thrust.)
- What do we call the measurement of a rocket’s efficiency? (Answer: Specific impulse.)
- What happens if a spacecraft in orbit slows down too much? (Answer: If the spacecraft slows down a little it moves into a lower orbit — closer to Earth; if the craft slows down too much it will not be able to maintain an orbit and will crash — if they did not mean to slow down — or land — if they did mean to slow down.)
- What happens if a spacecraft in orbit reaches the escape velocity? (Answer: The spacecraft will overcome the Earth’s gravity.)
- What do we call the point on an elliptical orbit that is furthest from the planet/Sun? (Answer: Apoapsis.)
- What do we call the point on an elliptical orbit that is closest to the planet/Sun? (Answer: Periapsis.)
- Two rockets have the same thrust force. Rocket A is half the mass of Rocket B. If the thrust force is greater than the sum of each rocket’s mass and drag force, which rocket will accelerate faster? How much faster will this rocket accelerate? (Answer: Rocket A will accelerate twice as fast as Rocket B according to F
_{net}= ma).

*Using the Equations:*Ask students to solve the following problem using the equations from the Lesson Background. A rocket’s engine expels mass at a rate of 10 kg/s with an exhaust velocity of 3,000 m/s. Calculate the thrust produced from the rocket. Express your answer in scientific notation. What is the specific impulse? (Answer:Thrust: F

_{T}= m * V

_{e}= 10 kg/s * 3,000 m/s = 30,000 kg*m/s

^{2}= 3.0 x 10

^{4 }kg*m/s

^{2}. Specific impulse: I

_{sp}= F

_{T}/ (m * g)= 3.0 x 10

^{4}kg*m/s

^{2}/ (10 kg/s * 9.81 m/s

^{2}) = 305.81 s)

### Lesson Extension Activities

### References

National Aeronautics and Space Administration, Mars Exploration Program

National Aeronautics and Space Administration, Space Place How Orbits Work

Wertz, James R. and Larson, Wiley J. * Space Mission Analysis and Design, 3rd Edition,* Space Technology Library, Volume 8, New York, NY: Springer Publishing Company, 1999.

**Contributors**

Geoffrey Hill, Daria Kotys-Schwartz, Chris Yakacki, Janet Yowell, Malinda Schaefer Zarske © 2004 by Regents of the University of Colorado.

**Supporting Program**

Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder

**Acknowledgements**

Last modified: September 11, 2015

Filed under: Class Activities, Grades 6-8, Grades 6-8, Lesson Plans

Tags: Aerospace, astronauts, calculations, Class Activities, forces, Grades 6-8, Grades 9-12, Humans in Space, Lesson Plans, Mars, motions, NASA, Physics, trajectory