## Introduction: Physics in Videos: Soyuz Launches Gaia

“(...) the way in which science subjects are taught has a great influence on students' attitudes towards science and on their motivation to study and, consequently, their achievement.”

Encouraging STEM studies for the Labour Market (European Parliament)

When students solve a "traditional" physics problem, they are usually given a clearly defined situation with all the information they need. Consequently most of the time the way of solving these problems is very mechanical: they just have to look for a mathematical expression that matches the description of the problem, then they substitute the given data, and finally they solve the equation to obtain the numerical solution.

In this Instructable we are going to present an alternative way of posing a problem. Instead of giving a verbal, well-defined description of the problem, the students watch a video from which they must extract information to obtain the answer. The problems thus posed are usually poorly defined, such as those presented in real life. Besides, the video can provide more data than necessary, and other data may be missing. Therefore with this approach the students must have a more critical and active attitude. They analyze the problem from different angles to find possible ways to solve it, they decide which of these methods is the most suitable to obtain the solution, they look for the missing information, and finally, they solve it and evaluate the results.

In this activity we will show an example of the use of video to solve a specific problem about dynamics, but you can adapt it to a wide variety of other mechanics topics: kinematics in one and two dimensions, circular motion, rotational dynamics, Newton’s laws, conservation of mechanical energy, simple harmonic motion…

### Grades

Secondary education (15-18 years)

### Physics concepts

- Resultant force
- Newton’s second law
- Uniformly accelerated rectilinear motion
- Distance-time and speed-time graphs

### Material

Computer with a video analysis tool. The following options are free to download and use:

- Tracker Video Analysis and Modeling Tool (Windows, Mac OSX and Linux): https://physlets.org/tracker/
- Kinovea (Windows): https://www.kinovea.org/

## Step 1: Motivation

This text and video can serve as a motivating introduction for the students:

*The European satellite Gaia is entrusted with an unprecedented mission: to analyze a billion stars in the Milky Way to build the most comprehensive and precise three-dimensional map of our galaxy. With its two powerful telescopes, Gaia will not only monitor the motion, luminosity, temperature and composition of its target stars with an accuracy never before reached—it is capable of measuring the diameter of a human hair from a distance of 1,000 kilometers—but is as well expected to discover hundreds of thousands of new celestial objects. All the data collected by Gaia will help us understand the origin, structure, and evolution of the Milky Way.*

*Gaia has been launched on a Soyuz-STB/Fregat-MT rocket from the European Spaceport in Kourou, French Guiana, on December 19, 2013.*

Video: "Gaia: launch to orbit" https://www.youtube.com/watch?v=9XcJ1wFRCk8

After they have read the text and watched the video, the teacher asks the students how much they know about telescopes, rockets or space research, and starts a group discussion about these topics.

More information about Gaia:

- Inside Gaia’s billion-pixel camera (video with Spanish and English subtitles): https://www.youtube.com/watch?v=2r4owXLoXc0
- Gaia overview: http://www.esa.int/Our_Activities/Space_Science/Gaia/Gaia_overview

More information about launch vehicles:

## Step 2: The Problem

The teacher shows the students the video of the first seconds of the Soyuz rocket launching the Gaia satellite into space:

Video: ESA's billion-star surveyor Gaia launching into space at 09:12UT/10:12CET on 19 December 2013. Footage courtesy of ESA - European Space Agency / CNES / Arianespace (https://youtu.be/YZ9DymZ1te0)

Then he poses the question that the students must answer by analyzing the motion of the rocket in the video:

**What is the thrust of Soyuz boosters during the first three seconds of flight?**

## Step 3: Strategies to Solve the Problem

To calculate the thrust of the rocket a few assumptions have to be made (very reasonable assumptions, anyway). You can discuss them with the students beforehand to stress the fact that real problems are not “ideal”. These assumptions are:

- Air drag is negligible. Air resistance is proportional to the square of the speed of the moving object. In the first seconds after the liftoff, the speed of the rocket is very small, so air drag is not significant compared to the other forces acting on the rocket. This statement can be easily checked in this online calculator: “Force of drag: https://www.vcalc.com/wiki/vCalc/Force+of+Drag”
- The mass of the rocket is constant. Although the loss of mass due to the burnt fuel is very significant in the complete flight, it is safe to assume that in the first seconds the mass that is lost is very small compared to the total mass of the rocket.
- The rocket lifts off vertically. Well… Obvious from the video, isn’t it?
- The boosters exert a constant thrust on the rocket. The design of the propulsion system of the rocket determines the thrust of the engine at a given atmospheric pressure. Then, for the low altitudes attained in the first seconds, we can assume it to be constant.

After talking about these necessary assumptions the students, guided by the teacher, answer the following questions:

- What forces are acting on the rocket?
- Are the forces balanced or unbalanced?
- How does the speed of the rocket change?
- How is the trajectory of the rocket?
- What type of movement does the rocket have?

The discussion of the above questions should lead the students to this conclusion: as a consequence of the unbalanced forces acting on the rocket (thrust and weight), it will lift off with rectilinear motion with a constant acceleration.

Then they discuss the possible approaches to solve the problem. There are two main strategies:

- calculating the acceleration of the rocket, and using Newton’s second law to obtain the thrust, or
- calculating the final speed of the rocket, and using the equivalence between impulse and change in momentum to obtain the thrust.

## Step 4: Data

Regardless of the chosen strategy to solve the problem, the students will need some more information to calculate the thrust of the rocket.

The necessary **kinematic magnitudes** (speed and acceleration) must be measured from the video, and this is where the video analysis software comes into play. We will explain how to obtain them in the following steps.

They will also need some more data that is not available in the video. These references contain all the **additional information** they might need:

- Soyuz - The medium launcher: http://www.arianespace.com/vehicle/soyuz/
- Soyuz Flight VS06 with Gaia - Launch kit: http://www.arianespace.com/wp-content/uploads/2015/10/VS06-launchkit-GB2.pdf
- Soyuz brochure: http://www.arianespace.com/wp-content/uploads/2019/04/ARIANESPACE-ENG-FLYER-SOYUZ-APRIL2019-WEB.pdf

## Step 5: The Video

To measure physical magnitudes from a video we are going to use Tracker (https://physlets.org/tracker/), a video analysis tool from the Open Source Physics project (https://www.compadre.org/osp/). It can analyze digital videos in different formats (.mov, .avi, .mp4, .flv, .wmv, .ogg, etc.), animated GIFs and even image sequences (.jpg or .png).

The video that we will work with is available to download from the European Space Agency’s website in this link: https://www.esa.int/spaceinvideos/Videos/2013/12/Gaia_launch_-_Lift-off. You can download here a shortened version (footage courtesy of ESA - European Space Agency / CNES / Arianespace).

Now that you have Tracker installed on your computer, and you have downloaded the video to your local drive, you are ready to start working with it!

## Step 6: Tracker’s User Interface

Open Tracker and you will see the default window with the three different views of the phenomenon we are studying:

- Main view: video and trajectory (1)
- Plot view: data plot (2)
- Table view: data table (3)

Above the main view, you can find the menu bar (4) that provides access to the program commands and settings, and the toolbar (5) with shortcuts to the most common instructions. Just below the main view, the video player (6) lets you control the video playback and the clip settings.

## Step 7: Analysing the Video

In short, these are the steps you must follow to analyze a video:

**#1: Prepare the video **

- Open the video
- Choose the initial and final frames

**#2: Set the time scale **

- Establish the time interval between frames

**#3: Set the frame of reference **

- Identify a known distance
- Place the coordinate axes

**#4: Track the movement **

- Create a point mass
- Mark the position

**#5: Analyze the data **

- Plot the variables
- Fit the data to a function
- Obtain the fitting coefficients

We will briefly explain each of these steps. For a more comprehensive explanation, please refer to Tracker’s online help (https://physlets.org/tracker/help/frameset.html).

## Step 8: Open the Video

Open the video by clicking on the Open button in the toolbar, or by selecting Open File in the File item of the menu bar. You can as well drop the video file in the main view.

Now the video is ready to be used. But before going any further you must decide the point that you will use to track the rocket’s motion. Play the video and look for an appropriate point. For example, you could use the white spot that can be seen in the third stage of the rocket.

## Step 9: Choose the Initial and Final Frames

Using the video player, play the video and decide when the rocket starts moving and when you will stop analyzing its motion. These are the values you have to determine:

- Start frame: frame number of the first step
- End frame: frame number of the last step
- Step size: frame increment between successive steps (you just have to change the default value of 1 if the motion is too slow)

You can select the start and end frames by dragging the black markers below the slider in the video player.

## Step 10: Establish the Time Interval Between Frames

The time interval between frames is necessary to properly calculate the kinematic magnitudes of the rocket motion.

Click on the Clip Settings button on the toolbar to open the clip inspector. There you can see (and change) the current video clip settings: start frame, step size, and end frame. The other settings are:

- Start time: time assigned to step 0. It will normally be 0 seconds.
- Frame rate: frame rate at which the video was recorded, in frames per second (fps). This value is very important for high-speed or time-lapse videos. Usually, the program automatically detects it, so most of the time you can leave the default value.
- Frame dt: time interval between frames. This value is the inverse of the frame rate and is calculated by the program, so you don’t need to change it.

## Step 11: Identify a Known Distance

You have just determined the time elapsed between two frames. Now you need to establish a spatial scale to calculate position and speed.

First of all, you must find a known length in the video. From the Soyuz brochure (http://www.arianespace.com/wp-content/uploads/2019/04/ARIANESPACE-ENG-FLYER-SOYUZ-APRIL2019-WEB.pdf) we know that “The Soyuz fairing has a diameter of 4.11 m and an overall length of 11.4 meters – enabling it to accommodate the full range of payloads in the launch vehicle’s performance category”. So you can use this diameter as a reference.

The calibration stick is a tool that defines the ratio of a real distance (in meters) to the image distance between two points (in pixels). Click on the Calibration Tools button in the toolbar and select New > Calibration Stick to create a calibration stick.

Shift-click on the video to mark both ends of the scale (zoom in the video so it is more precise). You can drag the ends to adjust them. Then introduce the known distance.

Now that the scale is set, you can hide the calibration stick (and show it again) just by clicking on the Calibration Tools button.

## Step 12: Place the Coordinate Axes

To establish a frame of reference, click on the Coordinate Axes button in the toolbar. You can now see the coordinate axes on the video. Usually, the origin of coordinates is placed in the initial position of the moving object, so drag the origin of the axes to that point.

## Step 13: Create a Point Mass

The temporal and spatial scales have already been established. Before you start tracking the trajectory of the rocket you must create a point mass. This point mass is an abstraction of the rocket as a point-like object, which simplifies the study of its movement. Create a point mass by clicking on the Create button in the toolbar.

You are now ready to track the position of the rocket as it lifts off!

## Step 14: Mark the Position

To track the movement of the rocket, consider the white spot on the third stage, or any other point you decide. You are going to mark the position of that point on each frame in the video clip. To do so, hold down the shift key (see how the cursor changes?) and click on the position of the point (you may want to zoom in for accuracy). Every time you click the mouse, the video automatically moves forward to the next frame, so you can mark the new position. Mark all successive positions in your video clip. You can adjust them afterward by dragging them. Just don’t skip any frames!

When you mark a position, it is automatically added to the plot and table views. In our case, we are interested in the vertical (y) position, not in the default horizontal (x) position, so in the plot view click on the axis label and choose “position y-component”.

## Step 15: Plot the Variables

Now that the measurements have been taken you must extract information from the data. The first step is to plot the variables of interest. You already have the plot of vertical position (y) versus time (t)—a very nice parabola, as expected.

Let’s see how the speed of the rocket changes. Tracker calculates the instantaneous speed of the object at each position, so click again on the vertical axis label in the plot view and choose “velocity y-component”. Look at the graph. The speed seems to be increasing at a steady rate, doesn’t it?

## Step 16: Fit the Data to a Function

The plots give a fairly good idea of the type of movement of the rocket, but you need more information. To further analyze the measurements, you could copy the data from the table view and paste them in a spreadsheet. But Tracker provides a very useful tool for data analysis: the Data Tool. This Data Tool provides statistical analysis for the data like, for example, curve fitting.

To open the Data Tool, double-click the plot on the plot view. Alternatively, you can access this tool in the View item of the menu bar.

Let’s analyze how the vertical position of the rocket changes. Once you have opened the Data Tool, make sure that the first column of data (the so-called “horizontal axis”, which has a yellow heading) contains the values of time, t, and the second column (the vertical axis, in green) contains the values of the vertical position. If this is not the case, just drag the columns to the correct place. Uncheck the markers and lines of any other variables that may appear in the table. To fit the data to a function, click on the Analyze button above the graph and select both Statistics and Curve Fits. The default fitting function is a straight line. But for an accelerated motion like this we now that the y-t curve is a parabola, so you will have to change the fit equation accordingly.

## Step 17: Obtain the Acceleration

The program calculates the parameters A, B, and C of the chosen fit equation y=A·t^2+B·t+C. Let’s compare this equation to the position-time equation of a rectilinear accelerated motion:

y=y0+v0·t +½ a·t^2

Comparing these two equations it is obvious that A (the coefficient multiplying time squared) is equal to ½ of the acceleration of the rocket, so the acceleration is 2A:

A = ½ a ⇒ a = 2A

Taking into account that the program gives a value of A=1.678, the acceleration of the rocket is:

**a = 3.356 m/s^2**

## Step 18: Gather All the Data

Let’s put together the information we need to solve the problem.

**Acceleration of the rocket**

From the video analysis, we have obtained a value of **a = 3.356 m/s^2**.

**Mass of the rocket**

From the given online references we learn that:

- The Soyuz rocket has a mass of 308 tons (Soyuz - The medium launcher: http://www.arianespace.com/vehicle/soyuz/)
- The launcher carries a total payload of 2,105 kg including 2,034 kg for the Gaia satellite (Soyuz Flight VS06 with Gaia - Launch kit: http://www.arianespace.com/wp-content/uploads/2015/10/VS06-launchkit-GB2.pdf)

So the total mass of the rocket m is the mass of the rocket itself plus the mass of the payload it carries:

m = mSoyuz + mPayload = 308,000 + 2,105 ⇒ **m = 310,105 kg**

## Step 19: Calculate the Thrust

Two forces are acting on the rocket:

- The thrust of Soyuz’s four boosters, which produces the vertical upward force for lifting off.
- The weight of the rocket, which is also vertical but points towards the Earth.

As these two forces act in opposite directions, the resultant or net force Fnet acting on the rocket is calculated by subtracting both forces:

Fnet = Thrust − Weight

According to Newton’s second law, the acceleration a with which the rocket lifts off is directly proportional to this net force and inversely proportional to its mass m. So:

Fnet = m·a

Substituting this expression in the previous equation and then solving for thrust we obtain:

Thrust − Weight = m·a ⇒ Thrust = m·a + Weight

Taking into account that the weight of a body is its mass times the acceleration of gravity g, the thrust of the rocket can be expressed this way:

Thrust = m·a + m·g ⇒ **Thrust = m·(a + g)**

So to calculate thrust we need the value of these magnitudes (which we have obtained in the previous steps):

- m: mass of the rocket → m = 310,105 kg
- a: acceleration of the rocket → a = 3.356 m/s^2
- g: acceleration of gravity → g = 9.81 m/s^2

Then the thrust of Soyuz’s boosters is:

Thrust = m·(a + g) = 310,105·(3.356 + 9.81) = 4,082,842.43 N ⇒ **Thrust = 4082.8 kN**

There it is! This is the value of the thrust of the Soyuz rocket at lift-off. You could as well have calculated the thrust using the impulse-momentum theorem, which would obviously lead to similar results.

## Step 20: Evaluate the Result

We have obtained a value of 4082.8 kN for the thrust of the boosters. But does this result make sense? Is that a reasonable force for the engine of a rocket? The students should be asked to check the validity of the value of the thrust they obtain.

In Soyuz User’s Manual (http://www.arianespace.com/wp-content/uploads/2015/09/Soyuz-Users-Manual-March-2012.pdf) we can find that the first stage of the rocket has four boosters and that each one has a thrust of 838.5 kN at sea level (SL) and 1021.3 kN in a vacuum (Vac).

As we are neglecting the effect of air on the rocket, we can take this second value as a reference:

Thrust (one booster) = 1021.3 kN

Four boosters make four times that force, so the overall thrust is:

**Thrust (four boosters)** = 4 x 1021.3 kN = **4085.2 kN**

Comparing this value with the 4082.8 kN that we obtained experimentally we conclude that we can be really happy with our result!

## Step 21: Going Further

Solving problems like this can be initially a challenge both for teachers and students. But once you are familiar with the video analysis tools, solving real-life problems becomes a very rewarding experience, not to mention all the critical thinking skills that students must develop to be successful in the task. So go ahead and adapt this activity to your needs and your student’s knowledge and skills. You will both benefit from a different approach to learn Physics!