The enormous velocity of the space station in orbit in a horizontal path can be thought of as a distance over ground velocity. Each second the space station will travel some amount of distance over ground, and each second gravity will bend that line vertically downward. So there is a horizontal speed per second and a vertical (falling) speed per second. The curve of the earth over the distance that the space station travels each second falls away the exact same distance that the space station falls in it’s vertical velocity (gravity).

This is why objects in orbit are considered to be constantly falling.

Larry

I do have one other area I would like to nitpick:

“While the rocket is firing, the ISS feels a force upwards.”

Firing a rocket “up” is generally a waste of energy and there are no applications I can think of at the moment in which you would ever deliberately design an orbit transfer that way. Raising an orbit requires an increase in VELOCITY. Since your velocity in orbit is already thousands of miles per hour in the “forward” direction, adding a couple of meters per second in the “upward” direction is not going to change that much.

You can show this with simple trigonometry.

Let’s say the ISS velocity is 8,000 meters per second and we’re going to do a burn with a delta-v (engineer speak for change in velocity) of 2 meters per second. If you burn the rocket in the direction of travel, your orbital velocity is simply now 8,002 meters per second. But if you were to do a radial burn, which Phil implies in his post above, your new velocity would be the hypotenus, or in trig terms that’s velocity = sqrt(8000^2+2^2) = 8,000.00025. I have thrown away that 2 m/s of rocket fuel.

this is why when the ISS does a reboost, we (generally) keep the pointy end forward, as they say, and fire the Service Module main engines tangential to the orbit. This clears up what some of the other commenters were asking about (@54 Peter B). A radial burn of course adds energy but its mostly wasted fuel.

The confusing thing about an orbital maneuver is that when you get to your new higher orbit, you are actually moving SLOWER than you were at the lower orbit… this orbital mechanics thing can be very confusing and is hard to simplify, as you can tell.

@6 Dr Sid
There are several reasons we don’t do a two burn maneuver (ie, a hohmann transfer) when reboosting the ISS orbit. Firstly, as others have pointed out, the ISS orbit is never perfectly circular. I am not in the trajectory design office, but my understanding is that we actually do our maneuvers at APOGEE to simply raise the low side of the orbit, making the orbit more circular. By doing the burn at apogee we in effect pull perigee out of the denser atmosphere, reducing the overall drag on the orbit and raising the average altitude of ISS. When you are only increasing your orbital velocity by less than a thousandth of a percent, a maneuver like a hohmann transfer becomes somewhat meaningless, from an efficiency perspective.

We do often do two reboosts within a few days or a week or two of each other. The logistics associated with planning and executing a reboost make it easier to do one reboost at a time, and do another one on another day. A hohmann transfer would mean doing a burn 90 minutes after the first burn which means the ISS systems would have to stay configured for the reboost for an additional 90 minutes or more. Part of configuring for reboosts includes parking the large solar arrays which may lead to degraded power generations, which can be hard to deal with depending on our position in the orbit.

The last thing to consider is the very difficult task that the TOPOs have (TOPO is the name for our trajectory officer) of planning our orbit to avoid orbital debris and other satellites as well as to keep us in the right location to link up with future Progress or Soyuz visiting spacecraft. I imagine there is something about that planning that leads them to prefer a single burn boost.

Hope that was enlightening!
Ad astra,
- Ben H.
Mission Control, Houston, TX

I think you are referring to the ‘Killer Tissue Box’ myth. In that a tissue box in an accident can fly forward with sufficient force to kill you. It was busted. (2005, S03E12)

My favorites that they have touched on lately have been taking the physics thought experiments and actually trying them out IRL to put them to the test. Like the bullet drop (2009, S07E12) and the moving vehicle ball drop. (2010, S08E04)

“As the ISS circles the Earth, all the forces on it are balanced.”

Umm…no, they’re not. Holy Haleakalā man, this is Physics 101. If they were balanced, then the station would be traveling in a straight line. This is a direct consequence of Newton’s laws: and object will maintain the same momentum unless acted upon by a net external force. Since the station’s trajectory is curved into an orbit (and, thus, its momentum is changing continuously), it’s clear that the forces aren’t balanced in any way, shape, or form – there’s undoubtedly a net external force at work.

“But,” you say, “centrifugal force is opposing gravity!” To which I say (and I know you’re going to kick and scream about this) there is no such thing as centrifugal “force”. It’s an artifact of choosing a non-inertial reference frame (in other words, a frame that’s accelerating and rotating along with the station). Sure, non-inertial frames are nice sometimes – in this case, the ISS is in a constant position in its LVLH reference frame, because it’s defined as such – but Newton’s laws don’t apply in a non-inertial frame. Because of this, you can’t choose to work in a non-inertial reference frame but then turn around and try to use Newton’s 1st and 2nd laws (F=dp/dt) in that frame to invent forces out of thin air…they don’t apply, remember?

To actually be able to do physics in a non-inertial reference frame, you have to do some work to figure out what the laws are that actually do apply to that frame…but, to do that, you end up having to apply Newton’s laws to figure out how the frame itself is rotating and accelerating relative to an inertial frame! “Centrifugal force” is a mathematical artifact of this process, nothing more.

Want to convince yourself that centrifugal force doesn’t exist? Newton’s third law, buddy: if centrifugal force is acting on the station, then the station must be exerting an equal and opposite force on something else. Where is that equal and opposite force?

“…every now and again low thrust rockets are used to push it up into a higher orbit. But that applies a force that is not balanced! ”

No, this isn’t it at all. We’ve already established that the forces were unbalanced before the rocket ever fired. The rocket isn’t suddenly “unbalancing” anything.

To figure out what’s actually going on here, let’s think about what forces are working on each object…

“Because there are no leftover forces on the ISS, it feels like it’s in free fall, what some people call weightlessness.”

I’m not even sure what the heck “leftover forces” is even supposed to mean, but, before the rockets fire, the ISS doesn’t just feel like it’s in free fall, it ***is*** in free fall…and so are the astronauts. Gravity works on all of them, and accelerates all of them equally (think back to the hammer and feather experiment on Apollo 15). There are other forces working on the station only – drag, solar pressure, etc. – and, while these forces are significant in the long term (as you’ve pointed out with the need for reboost), they’re insignificant enough compared to gravity in the short term that we can ignore them for this analysis. So, before the rocket fires, gravity is working on both the ISS and astronaut, so the astronaut experiences no acceleration relative to the ISS. Check.

Then the rocket fires. In this case, if the astronaut isn’t hanging on to the station, the rocket is applying a force to the ISS only. The astronaut is still in free fall, but the ISS is also being accelerated by the rocket, so the astronaut accelerates relative to the station…in this case, out of the Harmony node, through Destiny and Unity, and eventually hitting the slanted wall of PMA1.

So, that’s what this is illustrating. Gravity is working on everything, but the rocket is accelerating only the ISS and anything attached to it. Simple enough.

There’s an ad which appears occasionally on TV which I suspect is from the UK (in earlier screenings of the ad the two women spoke with English accents, but more recently their accents were Aussie) which illustrates this. Two women are in a car, and there’s an open packet of spherical chocolates (ah, can’t remember their name – I suppose it doesn’t matter) on the dashboard. The passenger is navigating for the driver, and constantly getting her to turn right. Each time the car turns another chocolate rolls out of the packet and down to the passenger…

Are you sure? It’s just that a prograde burn would add energy and raise apogee, and therefore a retrograde burn would do the opposite. I assumed a radial burn would be half way between the two, and thus have no effect on total energy (and thus period).

Fortunately, I don’t do this for my job.