# Is there a change in altitude when "falling around earth"?

This just blew me away: What Is Microgravity?

The page says the reason astronauts (in the International Space Station, ISS) experience microgravity is not because they're in "space" but because they're falling. Gravity at the ISS altitude is 90% of on the surface of Earth.

What I don't understand is that they don't say how much altitude they're losing? Are they losing any at all?

It looks like I'm missing something here. Could someone shed light into this please?

• Obligatory XKCD what-if.xkcd.com/58, also you have posted a number of questions without accepting any answers, could you go back and check if you want to accept any of the answers as useful/correct please. Commented Jul 6, 2021 at 23:06
• You should read "How Can Spacecraft Fall Around Earth?" carefully. They say they're falling around the Earth loosing no altitude.
– Uwe
Commented Jul 7, 2021 at 0:21
• There may be nevertheless an abusive use of terminology. "fall" means to go from "high" to "low". But, where is "high" and where is "low"? Note that you can "fall" from a higher orbit to a lower orbit while never ever touching the Earth surface. What is even more counter-intuitive is that you are accelerating when going down to a lower orbit. Commented Jul 7, 2021 at 9:07
• @NgPh: The last part of that isn't counterintuitive at all. Everything speeds up as it falls down (neglecting atmosphere). Commented Jul 7, 2021 at 21:10
• @Vikki, you meant perhaps everything speeds up VERTICALLY as it falls down. I should have been more precise: what is counter-intuitive is when you have to speed up perpendicularly to your "downward" direction as you "fall". Commented Jul 8, 2021 at 13:44

In a ideal / non real world / perfect circular orbit situation, they wouldn't lose altitude. They're falling but missing the planet due to their "sideways" velocity.

In the real world aerodynamic drag and other factors cause them to lose speed and therefore altitude.

(Image from https://physics.stackexchange.com/q/67012)

• Newton's Mountain Cannon was the first thing I thought of. Commented Jul 8, 2021 at 20:29

Orbits don't have to be circular. If someone is orbiting in a non-circular (i.e. elliptical) orbit, their altitude will change, as in the yellow orbit in this picture:

(credit: Søren Peo Pedersen via Wikimedia Commons)

On the right side of the planet, the yellow satellite doesn't have enough speed to maintain its altitude, so its altitude decreases. By the time it gets around to the left, the situation reverses - it has a lower altitude and higher speed, and it has too much speed to maintain its altitude. Another half-orbit later, and it's back to its original situation with too much altitude and too little speed. The satellite continues oscillating between these extremes, and the orbit forms an ellipse instead of a circle.

If you balance the speed and altitude just right, then you get a circular orbit. Otherwise, you get an elliptical orbit. (Unless you're going way too fast, in which case you get an escape trajectory)

• Perhaps worth noting that an object in an elliptical orbit is still in freefall the entire time, meaning that it is accelerated by gravity alone and experiences an apparent zero-G environment. The object could be described as "falling" the entire time, even though its altitude is increasing for half the orbit! Commented Jul 7, 2021 at 13:02
• It falls while going upwards. That is to say, its upwards velocity decreases by 9.8m/s/s just as it would increase by that if going down. The rate at which it goes up gets less and less until it reverses direction. Like a thrown ball. Its falling as soon as it leaves your hand, but isnt necessarily going down to start with Commented Jul 7, 2021 at 20:32

I think "falling" here is just a euphemism for "following the natural trajectory of inertial forces", in the sense that a bullet exiting the barrel is (apart from air drag) falling from the moment it leaves the muzzle, even if you point it straight upwards and a person jumping up is falling from the moment he stops touching the ground.

It's probably not the best word to use when trying to talk in generally accessible terms.

• Yeah. My brain want to see a height change if I'm falling ... lol. It is hard to wrap my head around gravity being 90% but not really because your falling but not really changing altitude. Maybe someone can use vectors to show what happens.
– Rodo
Commented Jul 7, 2021 at 20:03
• Think of shooting a bullet horizontally. It falls towards the ground. But if that bullet is going at hypersonic speeds, the curve of the earth becomes relevant. The ground is curving downwards under the bullets path. Go fast enough, and the ground falls away at the same speed as the bullet falls, so its distance from the ground doesn't change. Commented Jul 7, 2021 at 20:34

One way of thinking about it, is considering that the Space Station is circling the Earth at 28000 kilometers per hour.
circling the Earth. Like a bucket on a rope, being swung around your head.

If the Earth did not have gravity, and you tied a rope to the ISS, it would be pulling very hard on that rope. This force results from Centrifugal Force Effect.

The Earth's gravity provides the "rope" keeping the space station near it.
The space station's circling provides the apparent outward force which exactly matches this pull from the Earth.
The end result is that the inhabitants of the space station experience exactly balanced forces, which feel (almost) exactly like zero gravity.

As for changing altitude? Due to the balance of forces the space station circles the Earth in an ellipse. But a very round-ish ellipse. The average altitude over the course of one orbit does not change at all, and the specific altitude differs very very little at different stages of the orbit, due to the very low eccentricity of the ellipse of the orbit. For all practical purposes you can consider the ISS's orbit to be a perfect circle around Earth, at a constant altitude.

Maybe it will help to try and extrapolate from something intuitive.

When cresting a hill on a rollercoaster, you will often feel "Zero-G", where you feel no force from anything touching you (i.e. you lift off the seat slightly, but aren't being pulled down by the restraints either). Obviously the roller coaster isn't somehow turning off gravity for you alone, so what's happening to make you feel weightless?

What we often refer to as "Zero-G" actually has another name: free-fall - the difference is that when you jump out of a plane, you know you're falling. When you're in a roller coaster your perception will often be a little bit different; because the vehicle is moving in relation to the Earth (i.e. falling), but you're not moving in relation to the vehicle, it may feel a bit like when you're floating in water - you're not moving, but nothing is actively keeping you in place.

This effect is achieved through careful engineering, such that the parabolic arc of the track follows the parabolic arc of gravity. Notably, this is the exact same arc that a canon ball would follow, if you launched it at the same speed as the roller coaster.

Now, instead of thinking on rollercoaster speeds, let's go a little faster - if you imagine the parabolic arc of your roller coaster hill, and add more horizontal speed (but kept the vertical speed the same), the parabola would stretch out wider and wider. Eventually, it would reach the point that the two ends (the points where the parabola intersects the Earth) would actually be behind the horizon from each other - and at that point, something interesting happens: you're going so fast horizontally that the amount of time it takes you to reach the ground increases, because the ground is actually pulling away from you a little bit, due to the curvature of the Earth (being a sphere).

Now add even more speed! The faster you go, the further apart the ends of your parabola are going to get - at least until your parabola covers the Earth from end to end, allowing you to start at the South pole and land at the North pole. But what happens if we go even faster? The ends are going to continue to get farther away from the highest point of your arc (which could now reasonably be called an "apoapsis"), but will start getting closer to each other, towards the other side of the world.

Now you keep adding more and more speed, and pushing the ends of your parabola closer together until they touch... And you're in orbit. Any speed you "lose" on your ascent will be regained after passing your apoapsis, and you'll end up at the bottom going the same speed you started at, meaning you'll keep going around and around, never touching the ground.

If you add just a little bit more speed at this point, you can raise the bottom (now called "periapsis") to be equal to your apoapsis, and you'll have a circular orbit: you never get closer or further away from the Earth, and you'll just continue orbiting forever.

And all it takes is to fall sideways really fast.

The ISS looses height continuously due to the atmospheric drag.

As you can see, reboosts (sudden peaks in altitude on graphs) are done on average about once per month, but there can be many consecutive months during which no adjustment in orbital altitude to the station is done.

Image and blockquote from How often does ISS require re-boosting to higher orbit?

Look at December and January, a period without any reboosts, from 412 km down to 406 km.

So if we consider the atmospheric drag, there is a permanent change in altitude when falling around Earth.

Draw a circle, and then draw a line tangent to the circle. Let C be the center of the circle, and T be the point of tangency. Take another point P on the line. The distance from C to P will be larger than the distance from C to T.

This line represents the path a satellite would take without gravity. If gravity were to suddenly switch off, the satellite's distance from Earth would increase because it would fly off on a line tangent to its orbit.

Getting into a circular orbit means getting enough speed that the altitude that you would gain from this effect is enough to cancel out the altitude you lose from gravity.