By Rhett Allain

The Automated Transfer Vehicle (ATV) doesn’t just bring supplies to the International Space Station. It can also be used for ISS reboosts. What is a reboost? In short, during a reboost, the ISS velocity is increased by a small amount to bring the space station up to a slightly higher orbit.

Why is this needed? Well, although the ISS is in space, there is still stuff up there (gas from the atmosphere) that exerts a small drag force on the Station, decreases its velocity. The reboost are there just to keep it where it needs to be.

This video shows the inside of the ISS during an ATV reboost, i.e. when the ATV's main thrusters were firing. Let’s see if we can estimate the ATV thrust based on the acceleration of astronauts inside the space station.

*Editor's note: In addition to having a knack for science communication, Rhett Allain is Associate Professor of Physics at Southeastern Louisiana University. He writes regularly for Wired's Dot Physics blog and is a bit of a physics fanatic who spends more time than many pondering how daily life intersects with science. With the recently announced development of ATV in cooperation with NASA for Orion, we're delighted to feature a few posts from the far side of the Atlantic. Enjoy! – DGS*

There are a couple of different ways you can measure the acceleration in NASA astronaut Mike Fossum's YouTube video, but I am going to use one of the astronauts themselves (*we think this is the first scientific use of an astronaut's floating body as seen in a YT video to calculate ATV acceleration – Ed*).

Basically, I will use a video analysis program (in this case, the free Tracker Video Analysis). With video analysis, you can get position and time data from each frame of a video. If the motion of the astronauts had been recorded from a side view, position vs. time would obviously be the best choice. As you can see in Mike's video above, however, Mike, astro Satoshi Furukawa and cosmonaut Sergy Volkov are moving away from the camera, so I will measure the angular size of a person.

As things move farther away from a camera, they also appear steadily smaller. Here is a diagram that shows the relationship between angle, size and distance.

If you know the angle theta (θ) and the length of the object, you can find the distance (which I call r) with the formula:

*r = L / θ*

With this, I can mark a point on each side of one of the receding astronauts as he accelerates away from the camera. With some basic estimations for the angular view of the camera (and size of an astronaut), I get the following plot of distance from the camera for one of the astronauts.

Since the graph of motion appears to be quadratic, I can compare the polynomial coefficients with the kinematic equation for constant acceleration.

This says that the astronaut’s acceleration (with respect to the camera) was 0.034 m/s^{2}. Since the astronaut's body is in free flight orbit, this also means that the ISS had an acceleration of 0.034 m/s^{2} in the opposite direction.

This means that the ISS had an acceleration of 0.034 m/s

^{2 }

So far, so good. But remember, this isn’t the official acceleration due to ATV's thrust – this is just an estimate.

Although this video analysis method is fun, there are other ways to get the acceleration of the ISS during a reboost. For this particular reboost, the change in speed of the ISS was 5.75 m/s.

(*Editor's note: The YT video used in Rhett's calculations was recorded during the ATV-2 reboost conducted on 15 June 2011, or possibly on 12 June; click on dates for details.*)

I'm not sure exactly how long this reboost lasted, but the video was 2:13 long. If we assume that is the time for the change in velocity, then we can calculate the acceleration.

That's not exactly the same value from my video analysis, but it is close enough for me.

**Thrust from ATV**

The ATV thrusters have to exert a force on the ISS in order to obtain this acceleration. What magnitude of thrust would this require? If this is the only force acting on the ISS (it isn't), then we can say:

*F _{thrust} = ma*

The ISS has a mass of about 4.5 x 10^{5} kg. So, the amount of acceleration calculated above would require a thrust with a magnitude around 1.5 x 10^{4} (15 000) Newtons.

That might seem like a large force, but it isn't. Just as a comparison, this would be about the same as the gravitational force on two adults on the surface of the Earth. If you want some serious thrust, you could look at one of the Solid Rocket Boosters that were used during the launch of the Space Shuttle. Each of these rockets had a thrust around 14 million Newtons.

*Editor's note: ATV's actual Orbital Correction System thrusters provide 4 X 490N, for a total of 1960N. ATV flight dynamics engineer Laurent Arzel, at ATV-CC, says that ATV only uses two thrusters in parallel at one time, so the thrust during reboosts is fixed at around 2X490 or about 1000N. *

*One reason why Rhett's thrust estimate above, 15 000N, is much higher is due to the fact that he assumed the reboost ran only during Mike's 2:13 video. It actually ran about 40:12, or 2412 seconds. Plugging this back into the equations gives a thrust estimate for ATV of about 1073N, much closer to the actual 1000N. This shows that Rhett's calculations are correctly done, but just off a bit in the burn duration.*

Here is the cool part: What does this thrust say about the motion of the ISS? Let's just approximate that the ISS needs a similar reboost about once a month. That would mean that this reboost takes the space station from some speed to some value that is around 5 m/s greater in magnitude. If you know the increase in speed during a reboost, you know the decrease in speed over the month in between reboosts.

This means that on a typical day, the ISS has a (negative) acceleration of about:

Since this is an estimate, let's just call it -2 x 10^{-6} m/s^{2}.

Now I can use this acceleration to estimate the daily drag force on the ISS. Using the same mass as mentioned above, this acceleration goes with a drag force of about 0.9 Newtons.

This is about the force you would exert by pushing on something with your finger. It's not a large drag force, but it is always there so that it eventually slows down the space station enough to cause a problem, which is 'fixed' by the periodic reboost provided by ATV or the Station's owe engines.

**Why do astronauts accelerate backwards?**

This is the real interesting question!

Just about all of the introductory physics textbook examples you see are in an 'inertial reference frame'. What does that even mean? It means that the view point for the motion is from a frame that does not accelerate. In an inertial reference frame, our Newtonian physics models work. In particular, we can say that the net force on an object equals the mass of that object times its acceleration. More importantly, all of the forces on any particular object are due to interactions with other objects.

You are probably sitting somewhere that is very close to an 'inertial frame' right now. In this frame of reference, you could see something like a book sitting on a table. The acceleration of this book is zero which implies that all the forces on it have to add up to zero. But what forces are there? There is the gravitational force – which is an interaction with the Earth – and then there is the force of the table pushing up on the book. Each force is an interaction with an object.

But what if you aren't in an inertial frame of reference? What if your frame is accelerating? A great example is when you are in a moving car that is turning.

If the car turns to the left, you can feel that something is different – you feel a force pushing you to the right.

Things seem to behave differently because we want to use our ideas of physics for inertial frames (the book sitting on a table) even though you moving in a car is a non-inertial frame. In the case of a car turning to the left, you feel like you have a new force pushing you to the right.

But what object is this right-pushing force an interaction with? The answer: nothing! This is the 'fake' force we call the centrifugal force.

So, a fake force is a force you need to add in an accelerating frame. This fake force is not an interaction with another object – I guess that's why you would call it 'fake'.

There is one more thing. The fake force can be written as: If the reference frame accelerates one way, you would feel a fake force in the opposite direction.

Now back to the astronauts in the ISS. The cool thing is that there are more than one fake forces on these astronauts in the YT video. Suppose that we looked at an astronaut at some point before a reboost. In this case, the astronaut would just 'float' at any location. Here is a diagram showing the forces on an astronaut:

In this frame, the fake force and the gravitational force have the same magnitude. This makes the net force on the astronaut zero, so that he or she just floats there. Of course, if you were able to observe the astronaut from outside the ISS (and in an inertial frame), you would see that the astronaut actually is accelerating. His or her acceleration would be the acceleration corresponding to only the gravitational force acting on the astronaut's body.

During the ATV reboost, the ISS accelerates two ways at the same time. It accelerates as it orbits the Earth (because it is moving in a circle) and it accelerates because of the thrust from the ATV. This would make another fake force that pushes the astronauts in the opposite direction of the acceleration of the ISS. So, what is the difference between the acceleration of the ISS due to the gravitational force and the thruster? Why does one make the astronaut float and one does not? The difference is gravity.

The gravitational force on the Space Station (from the Earth) also pulls on the astronaut. This gives both the astronaut and the space station the same acceleration and in a reference frame of the accelerating ISS, it makes a fake force that cancels the gravitational force. The thrust from the ATV, on the other hand, does not also exert a force on the astronauts. This means that there will be a fake force on the astronaut, but not a real force to cancel it, and they will float slowly to the rear.

Note from Astro Mike Fossum:

We shared a copy of this post with Mike, who sent in a couple of comments – Ed.

*I'll never forget this day and am excited you find it interesting! This is hard, but very cool, stuff! Thanks for helping tell the story!!*

Mike also adds that they did, in fact, record, the side-looking video that Rhett mentions above during this reboost as well. If we get a chance, we'll ping our NASA friends to see if a copy can be provided.

Note on Rhett's companion post in Wired:

Rhett's also done a great companion post in Wired based on reboost acceleration, namely 'an estimation of the density of air in orbit on the ISS based on the acceleration during reboosts' via Wired Science.

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