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HeyHomie
09-12-2017, 01:33 PM
The circumference of the Earth is ~40,000km. Due to some scientific principle that I don't understand and can't explain, the ISS's orbit around the Earth is going to be larger, but by how much I can't tell.

I note that the ISS's altitude is ~408km, which I imagine will figure into the calculations somehow.

Also, how does this play out in linear distance? Like, if the ISS were to "cross" from the west side of Missouri to the east side (a distance of ~398km on the ground), how far would it have moved in space during that time?

Andy L
09-12-2017, 01:38 PM
The circumference of the Earth is ~40,000km. Due to some scientific principle that I don't understand and can't explain, the ISS's orbit around the Earth is going to be larger, but by how much I can't tell.

I note that the ISS's altitude is ~408km, which I imagine will figure into the calculations somehow.

You're already almost there. During each orbit, the ISS travels 40,000 km + 408 * 2 * pi km - so to a single significant figure, 40,000 km is still good enough. If not, call it 42.5 megameters...

naita
09-12-2017, 04:29 PM
The circumference of the Earth is ~40,000km. Due to some scientific principle that I don't understand and can't explain, the ISS's orbit around the Earth is going to be larger, but by how much I can't tell.

It's the principle of a circle having a circumference proportional to its radius. Increase the radius and you increase the circumference.

LSLGuy
09-12-2017, 05:13 PM
To put it another way, the circumference of the orbit is proportional to the orbit's radius measured from the center of the Earth.

In 'Merkin units the Earth's radius is roughly 3,950 miles. So as you sit on your couch, you're "orbiting*" the Earth's center from 3,950 miles away. The ISS orbit is roughly 250 miles higher than the surface. So it orbits about 4,200 miles above the center.

Which means the ISS' orbit is about 6% farther from the Earth's center than you are. So that 6 % factor applies to all the other distances.

Six percent more radius means 6% more circumference. And the distance to traverse over Missouri would be 6% more than the same path at ground level.

If you're keen on the ISS, this NASA cite/site (https://eol.jsc.nasa.gov/ESRS/HDEV/) has a really neat camera set mounted on the ISS and streaming continuously. Sometmes the camera is looking straight down and sometimes it's looking ahead or behind or sideways. In those latter shots you'll see how the ISS is really just skimming over the surface of a much larger sphere. The "sphere" knitted together from all the ISS orbits is only 6% bigger than the one made of rocks. And only 4ish percent bigger than the sphere formed by the "top" of the visible atmosphere.

One a human scale, 250 miles up is a long ways. On a planetary scale it's almost just a rounding error.

=======
* Sitting on your couch on the surface is not technically an orbit. But you're still circling the center at a predictable rate & radius, so it shares those 2 features with a true orbit.

snfaulkner
09-12-2017, 06:19 PM
To put it another way, the circumference of the orbit is proportional to the orbit's radius measured from the center of the Earth.

In 'Merkin units the Earth's radius is roughly 3,950 miles. So as you sit on your couch, you're "orbiting*" the Earth's center from 3,950 miles away. The ISS orbit is roughly 250 miles higher than the surface. So it orbits about 4,200 miles above the center.

Which means the ISS' orbit is about 6% farther from the Earth's center than you are. So that 6 % factor applies to all the other distances.

Six percent more radius means 6% more circumference. And the distance to traverse over Missouri would be 6% more than the same path at ground level.

If you're keen on the ISS, this NASA cite/site (https://eol.jsc.nasa.gov/ESRS/HDEV/) has a really neat camera set mounted on the ISS and streaming continuously. Sometmes the camera is looking straight down and sometimes it's looking ahead or behind or sideways. In those latter shots you'll see how the ISS is really just skimming over the surface of a much larger sphere. The "sphere" knitted together from all the ISS orbits is only 6% bigger than the one made of rocks. And only 4ish percent bigger than the sphere formed by the "top" of the visible atmosphere.

One a human scale, 250 miles up is a long ways. On a planetary scale it's almost just a rounding error.

=======
* Sitting on your couch on the surface is not technically an orbit. But you're still circling the center at a predictable rate & radius, so it shares those 2 features with a true orbit.

Re: bolding. It depends on what drugs you are on.

Xema
09-12-2017, 08:23 PM
Due to some scientific principle that I don't understand and can't explain, the ISS's orbit around the Earth is going to be larger ...
Attempts to orbit along a path shorter than the Earth's circumference have a poor rate of success.

LSLGuy
09-12-2017, 08:54 PM
Lithobraking: it never fails. :D

Bumbershoot
09-12-2017, 09:49 PM
The ISS does not follow the same path on each trip around the planet- e.g. directly above the equator, to keep it simple. As shown here (http://www.isstracker.com/) it is sometimes over the northern hemisphere and sometimes over the southern hemisphere. Would this orbital path add a lot to the distance traveled in one trip around the world?

Andy L
09-12-2017, 10:12 PM
The ISS does not follow the same path on each trip around the planet- e.g. directly above the equator, to keep it simple. As shown here (http://www.isstracker.com/) it is sometimes over the northern hemisphere and sometimes over the southern hemisphere. Would this orbital path add a lot to the distance traveled in one trip around the world?

The ISS follows the same path - the Earth just rotates below it. That wouldn't affect the distance the ISS moves through space.

Bumbershoot
09-12-2017, 10:24 PM
Thanks for that explanation, but it leads to another question- what causes the ISS to keep crossing the equator? Is it just the rotation of the Earth? I guess I don't understand why the Earth spinning on its axis would result in the orbital path which the ISS follows.

snfaulkner
09-12-2017, 10:26 PM
The orbit is at an angle to the equator. Even if the earth wasn't spinning, the ISS would still cross the equator twice per orbit. With the earth spinning, it crosses the equator at different points each orbit.

Andy L
09-12-2017, 10:30 PM
Thanks for that explanation, but it leads to another question- what causes the ISS to keep crossing the equator? Is it just the rotation of the Earth? I guess I don't understand why the Earth spinning on its axis would result in the orbital path which the ISS follows.

The orbit has to go around the Earth's center - so the orbit is either always above the equator, or it spends half its time on one side of the equator and half on the other.

Bumbershoot
09-12-2017, 10:36 PM
Thanks guys, that makes sense. However, I'm still not 100% clear on why the ISS follows the path it does. For example, right now the ISS has just crossed Australia and is looping around New Zealand before heading north again. But why does it turn north? Why doesn't it continue south, over Antarctica?

snfaulkner
09-12-2017, 10:42 PM
Because it isn't in polar orbit. Just like it isn't in equatorial orbit. It's at an angle that is in between.

Dr. Strangelove
09-13-2017, 12:19 AM
But why does it turn north? Why doesn't it continue south, over Antarctica?

This is just an artifact of the map projection. The ISS is in a circular orbit and doesn't change direction aside from the constant curvature needed to follow the surface. When you project the path out to a rectangular map, it looks like a sine wave, where it seems to veer away from the poles. But that's no more real than Greenland being larger than Africa.

Bumbershoot
09-13-2017, 06:59 AM
This is just an artifact of the map projection. The ISS is in a circular orbit and doesn't change direction aside from the constant curvature needed to follow the surface. When you project the path out to a rectangular map, it looks like a sine wave, where it seems to veer away from the poles. But that's no more real than Greenland being larger than Africa.

Thanks for clarifying that. I was having trouble visualizing the path on the two-dimensional map as a circular orbit in three dimensions.

LSLGuy
09-13-2017, 08:09 AM
Get yourself a globe. Or visit your library that probably has one you can fiddle with. Or imagine one. It's real obvious on a globe. As you say, it's not obvious if your mental picture of the Earth is a flat map, especially a Mercator one.

Now "draw" a circle around the globe set at, very roughly, a 45 degree angle between the equator & the poles. You'll see it goes down to the south, then levels off before it gets to the pole, then curves back up to the north, crosses the equator, then levels off before it gets to the other pole, then curves back down to the south & connects with itself, completing the circle.

Now rotate the globe under the circle. The net result is the orbit "wobbles" up and down from the northern mid latitudes to the southern mid latitudes while meanwhile sliding to the east the whole time. Because the earth is turning too, after one complete orbit circle a different part of the Earth is underneath the satellite at the moment the circle completes.

Another way to visualize it is to think of Saturn & the rings. Those rings are jillions of rocks in orbit that make the orbit visible. Here's https://en.wikipedia.org/wiki/Rings_of_Saturn some decent pix. The rings orbit a lot higher than does the ISS, so think something skimming the planet's cloud tops but oriented like the rings.

Bumbershoot
09-13-2017, 09:33 AM
Imagining the orbit as a circle around a globe helped a lot, LSLGuy (I have a globe but it's in storage right now). My problem was I kept looking at the map on the ISS Tracker website and I just wasn't seeing how the path on the map would translate to a complete circle around the planet. Ignorance fought!

howye
09-13-2017, 10:04 AM
Imagining the orbit as a circle around a globe helped a lot, LSLGuy (I have a globe but it's in storage right now). My problem was I kept looking at the map on the ISS Tracker website and I just wasn't seeing how the path on the map would translate to a complete circle around the planet. Ignorance fought!

This made me curious because I understood what is happening but have a hard time visualizing. So of course the internet provides: https://www.youtube.com/watch?v=8-mKLs2b3MM