Newton’s Second Law of Motion
Learning orbital dynamics and rendevouz with orbital objects!
Students will be able to:
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What is Newton’s Second Law,
How to make Kerbal maneuver nodes,
How to perform rendezvous maneuver with an orbital object,
How to dock in KerbalEDU.
Timeline: The lesson plan is designed to span a 60-minute lesson.
Materials: KerbalEDU installed on the student computers, lesson plan. “Orbits and Docking”
mission from KerbalEDU mission library. Some keyboard maps printed for students.
KerbalEDU doesn’t support multiplayer. However, students can share computers so pairing
can be used in this lesson.
This lesson works as an introduction to the Newton’s Second Law of Motion. It provides
structured scenario with clear goals and learning targets for students. The scenario is aimed
for students who have some experience of Kerbal EDU, and it tests their creativity.
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The lesson is planned as modular with several optional topics:
Teacher is recommended to go through orientation phase, and have previous lesson
recap about orbits. After the recap class can talk about trajectories and conics if
needed. Ascending nodes and descending nodes are important terms which
students need to understand to beat the lesson challenge. Maneuver node is a
KerbalEDU tool that should be explained at least shortly before embarking on a
mission. Lesson challenge is explained to teacher in detail at walkthrough chapter
and same chapter can be referenced to explain and help students to achieve the
challenge.
Teacher role includes being a ‘flight director’. Before lesson challenge teacher should
give students a mission description and short explanation of flight plan (catching up,
interception, encounter and closing up) with screen or whiteboard and then tell
students trying it out themselves.
Please pay in mind that orbital manovering is something that was counter-intuitive
even for NASA engineers back in the days, so it is likely that some students will feel
frustration about the simulation. However the goal is to learn so end reflection of
lessons learned should be kept positive.
Learning Activities
Orientation
“Orbits are all about falling.”
The spacecraft is falling towards Kerbin, however it has enough speed so the surface
of Kerbin rounds down under it. Orbits are in fact constant falling down. The speed
which allows craft to fall indefinitely is called ‘orbital speed’ and it is dependent on
distance to planet and mass and size of the planet. Currently spacecraft has enough
orbital speed to keep its distance to planet.
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Picture: Contrary to common sense, the craft in lower orbit is actually faster.
Teacher should either draw or show picture above. There’s spacecraft on the lower
orbit and another one on the higher orbit.
Question: Which one do you think is faster?
Most likely students will tell that the craft higher is faster but in real life this is
exactly opposite: satellites and spacecraft that have higher orbit move slower
and things on lower orbit faster. Teacher should think this through with the
students for a minute: strength of the gravity is “inversely proportional to the
square of the distance between them”. Meaning craft closer to planet needs higher
momentum (speed) to win inward momentum that’s caused by the gravity.
In the astrophysics ‘trajectory’ is a flight path that a moving object follows. Orbits are
gravitationally curved trajectories that are uninterrupted. This means orbits have
enough momentum (so called “orbital speed”) to curve around a planet rather than
meet the surface.
'Escape velocity' is velocity required to establish a ‘parabolic’ orbit. For an object to
reach hyperbolic orbits, it needs to have greater velocity than escape velocity.
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Teacher should demonstrate some of the conic trajectories with screen or whiteboard:
Picture: Parabolic curves in Wikipedia.
Orbits are called ‘conic sections’. In mathematics ‘conic section‘ means a curve which is
obtained from an intersection of a plane and a cone. In astrophysics orbits around
gravity sources are elliptic by the nature of gravity.
In Kerbal Space Program ‘Patched conics’ (accessed through cheat menu by
pressing Alt-F12) offer simplification on gravity sources by turning so called ‘nbody problem’ (several gravity sources) to multiple two-body problems. Using
patched conics requires more computing power so it is not recommended for
slow computers.
Instruct: Key terms
As students play around with KerbalEDU they notice new terms and phenomena. It’s
suggested that teacher takes time to go through key terms that are used in the
simulation. As for orbital simulation students probably wonder what ‘Ap’ and ‘Pe’ stand
for?
‘Orbit’ is an uninterrupted trajectory. According to Kepler’s laws all closed orbits are in
the shape of ellipse. Circular orbits are cases where both higher point and lower point
of orbit are close. Periapsis (Perigee, Pe) is the point of closest orbit, and Apoapsis
(Apogee, Ap) the farthest.
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Example: International space station has perigee of 400.2 km and apogee 409.5
km, making it practically a ‘circle orbit’.
Orbital eccentricity is a parameter which determines the amount of orbit deviation
from a perfect circle (0 being circular, values between 0 and 1 being an elliptical orbit, 1
being a parabolic escape orbit, and 1+ being hyperbolic orbit). Comets have high
eccentricity.
Source: http://wiki.kerbalspaceprogram.com/wiki/Terminology
Note: This lesson plan is not about lecturing all of the terms to students, however
teacher should be somewhat familiar to most of them because they can be learned as
the side effect of lesson challenges.
‘Ascending Node’ and ‘Descending Node’ are parts of orbit where orbit
crosses reference plane (equator).
‘Inclination’ is number in degrees that tells how much the orbit differs from
equatorial orbit (90 degrees being polar orbit).
Optional: Kepler’s Laws
Johannes Kepler’s research improved on heliocentric theory by Copernicus. Isaac
Newton based his law on universal gravitation on Kepler’s laws. Curriculums like Next
Generation Science Standards tell that understanding Newtons Laws are fundamental
for learning, however older theories that Newton based on his work are for teacher to
decide if they fit to curriculum. If phenomenon based learning is in the use, this would
tie physics to the history subjects:
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“In astronomy, Kepler's laws of planetary motion are three scientific laws describing the
motion of planets around the Sun.
1. The orbit of a planet is an ellipse with the Sun at one of the two foci.
2. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals
of time.
3. The square of the orbital period of a planet is proportional to the cube of the semi-major
axis of its orbit.“ (Source: Wikipedia)
Instruct: Maneuver Nodes
This chapter is written on the assumption most of the students are not first-timers
with KerbalEDU but they are definetly not experienced ‘Kerbonauts’. Maneuver nodes
are important tool in the game and teacher should provide enough information to get
students figure rest out by themselves. Teacher should go through basic functions of
maneuver node and navball with whiteboard or screen before advancing to lesson
challenge.
Maneuver nodes are tools for planning orbital maneuvers and predicting
trajectories. The nodes are set in Map mode (‘M’ key) by right clicking the future
orbit to create a maneuver node. The node can be removed by clicking the ‘x’
which appears when mouse is on the node. The nodes use the same set of
markers that you have seen in the Navball.
Picture: Green icons across the trajectory: Retrograde and Prograde.
Markers can be dragged to create solution for new orbit. Dragging green prograde icon
forward sets up a burn that increases craft’s momentum and creates more ellipsoid
orbit. Ready maneuver nodes are shown in yellow six pointed icons in map mode.
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Picture: Two maneuver nodes, later in edit mode.
Picture: Navball
Blue maneuver node appears to navball and right side indicates what kind of the next
maneuver is going to be (from top to bottom):
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Amount of (m/s) thrust required for the node.
Estimated burn time (with full thrust)
Encounter with node.
Navball markers tell that player needs to wait until the time is right and point the craft
to the direction of the blue maneuver node and thrust the engines (‘Z’ is full thrust and
‘X’ engine cut-off) enough to meet the momentum requirement.
Optional question: You are waiting for the right time to engage the rocket engine. The
burn time is 30 seconds. When would you would start acceleration? Before the
calculated time, just right time or after?
Answer: As the game calculates the optimal time for thrust the long burns should be
divided evenly before and after the target time. Start the engines 15 seconds before
the node and continue until 15 seconds after!
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Note: Managing burn time is highly important when any of students start to plan
low powered ion engine probes or longer space flight with higher mass craft.
Pilots can cause well planned maneuver nodes to fail if they do burns in a
lackluster way (0.1-0.3 m/s difference can change the direction). Luckily, the blue
maneuver marker changes its place accordingly correct alignment for course
that’s plotted so students can compensate even if they missed the original node.
Note: Saving the game
If the mission allows saving ‘F5’ quicksaves the game and ‘F9’ quickloads. This
saves the trouble of starting all over again, and reduces frustration. When a
student is trying again they should think what went wrong and how would they
avoid problems? Note: Please take care not to save when the craft is in danger
(landing, crashing etc.)
Lesson challenge
Setting up: Start up first lesson from Kerbal EDU Mission library by pressing blue
“Launch in KerbalEdu”-button. The game should start from the starting point of the
scenario.
Scenario: “Jebehdah has forgotten his snacks on Kerbin. Luckly his friend is ready to share
snacks but he’s on the different orbit. Jebehdiah needs to perform a rendevouz in a orbit or
spend rest of the space flight without snacks. Since this is not possible we need to guide Jebs
ship to encounter with Snackship”
Execution: Goal of this challenge is to use orbital nodes to change orbits, observe
orbital speeds and manage them to get an encounter with Snackship.
Managing encounter would mean good understanding on Newtonian physics and
management of maneuver node. Managing dock would mean excellent control and
understanding on the mechanics!
The mission itself requires some skills on gameplay. Using different keys to RCS thrust
and tracking movement on the instruments is not an easy task. However in later
lessons students could form up teams with dedicated pilot and navigator.
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Reflection: Before class is dismissed teacher should reflect learnings with the
students. The questions asked here are “what happened”, “theory why it happened”
and how observations are connected to things learned?
For example teacher can ask what kind of observations students made. Did the
Snackship orbit change? Why do students think this happened?
During the challenge, please point out to students that:
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Frustration will lead to bad calls and mistakes.
Even real life SpaceX cargo ships have multiple “hold points” when making final
approach towards International Space Station
Starting over is always possible and recommended because most flights end horribly
wrong in Kerbal.
Docking is hard and even NASA had own program just to train for it!
Everything is matter of training, next time the operation would go better.
The goal of this exercise is to understand orbital dynamics enough to make a
rendevouz, with the hard dock being A-grade performance.
Picture: After hard work Jeb can reward himself with some snacks.
Walkthrough: Orbital Maneuvering.
This chapter is dedicated as ‘walkthrough’ of the lesson challenge and in depth
explanation for teacher. The basics of orbital maneuvering should be discussed with
students before giving challenge because some of the orbital dynamics are counterintuitive.
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At the beginning of the mission Jebediah is on the lower orbit, while his friend is on the
higher orbit. In the beginning of the mission we have zero inclination between
spacecrafts, so students need to control only the ‘altitude’ of Jebs craft.
In KerbalEDU orbital rendezvous is a difficult task, much like in real life. The
rendezvous includes four steps: 1) coasting closer, 2) plotting the interception, 3)
encounter, and 4) approaching and docking. More information can be found from
Kerbal wiki: Orbital Rendezvous.
Jebs craft is in the lower orbit than ‘Snackship’. This is actually good thing because his
orbital speed is actually higher than those above him, meaning Jeb is gaining on the
Snackship with every orbit. Switch to map ‘M’ screen and select Snackship. Students
should create ready maneuver node about just before Jebs ship is about to pass under
the Snackship. Making maneuver nodes for rendezvous requires lot of trial and error.
However as maneuver nodes are getting familiar teacher can plan more complex tasks
for students (Like Apollo-style flight needing skills for docking).
Picture: First interesection of Snackship orbit is far (orange) but second is right on target.
Teacher can tell students to orbit few times and make maneuver nodes trying to
search the solution. Not every solution works or is practical (unneccesearly hard
burns would mean that craft doesn’t have enough fuel for encounter). Adjust prograde
and retrograde markers carefully to see encounter indicators change (Indicators tell
separation with target - optionally this should be below 5km). Kerbal takes account
second orbit as well so you can see if you’re closing on target. If you pass the target,
just rise Jebs ship orbit higher and let Snackship to close in turn.
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Picture: When danger of passing snacks, rise orbit.
When ships have distance < 5km student needs to perform ‘encounter manouver’ –
practically this means matching the speed with the target and doing the final
approach. For maneuver to be successful the Snackship should be selected as target
from the map screen. At this point the navball will switch to target mode and display
relative velocity with target. Press F5 to save the game. Toggling soft controls with
Caps Lock is also advisable. For successful final approach:
a. Aim the retrograde symbol of navball and burn until your relative speed is
zero.
b. Aim for target prograde (purple curvy symbol) and burn for 1-2 m/s (more if
you’re far away). Aiming towards the target would be possible but needs you
to adjust your trajectory more.
c. As you get to suitable distance turn the face to retrograde symbol again and
burn enough to stop.
d. Repeat steps b-c until you’re within 100m and use RCS Thrusters from there
on.
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Picture: Performing encounter burn.
RCS Thrusting
Although Jeb could take his jetpack and fly to get some snacks it’s more sporty to
actually dock the spacecraft. Enable RCS from ‘R’ key. In the normal game mode RCS
has different keys from other controls. ‘H’ - Foward ‘N’ - Backwards ‘I’ - Down ‘J’ - Left ‘K’ Up ‘L’-right. As this can be tricky the WASD-keys can be changed to direct RCS like you
would use in EVA-mode:
If you have ‘docking mode’ engaged (round symbol in left corner of the screen,
below green rocket) you can use WASD controls like in EVA mode. ‘Shift’ - up
‘Control’ - Down ‘A’ - Left ‘D’- Right ‘W’- up ‘S’ - Down.
Picture: Right click and select docking port to change navball relative to port.
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Remember that student can enable SAS (toggle ‘T) to keep craft stabile and switch it off
when magnetic docking collars start to connect.
While docking is interesting exercise it shouldn’t be mandatory for all students in the
class because need of actual gameplay skills and clear understanding of what’s
happening. Usually it takes few hours to actually get first docking right so don’t be
alarmed if students don’t get it right. For the lesson purposes the actual rendevouz
maneuver and both time and effort it actually takes is an important discovery!
Picture: ‘Docking mode’ is round symbol on right. Source: KSP Wiki
Throughout the lesson the students are producing hypotheses and measurements. Evaluate
their work as individuals but also as members of a group. What kind of role did they assume
in their group? Did they share the workload evenly? Did they find solution in organized
manner or by randomly trying everything? Did they come up with plausible theory of why the
solution worked?
Diffrent orbits in nature
 Horseshoe and Tadpole
 Molniya orbit
Open (or escape) trajectories
 Parabolic trajectories
 Hyperbolic trajectories
Maneuver nodes and orbital physics
 Normals and Anti-Normals
 Radial and Anti-Radial
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Next Generation Science Standards
MS-PS2-1
Apply Newton’s Third Law to design a solution to a problem involving the motion of
two colliding objects.
MS-PS2-2.
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.
MS-PS3-2
Develop a model to describe that when the arrangement of objects interacting at a
distance changes, different amounts of potential energy are stored in the system.
MS-ETS1-2
Evaluate competing design solutions using a systematic process to determine how well
they meet the criteria and constraints of the problem.
MS-ETS1-3
Analyze data from tests to determine similarities and differences among several design
solutions to identify the best characteristics of each that can be combined into a new
solution to better meet the criteria for success.
HS-PS2-1
Analyze data to support the claim that Newton’s second law of motion describes the
mathematical relationship among the net force on a macroscopic object, its mass, and
its acceleration.
HS-PS2-2.
Use mathematical representations to support the claim that the total momentum
of a system of objects is conserved when there is no net force on the system.
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