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Think of firing a canon sideways: it takes a while for the cannon ball to drop and hit the earth. Now imagine firing it faster and faster, till eventually it's

Think of firing a canon sideways: it takes a while for the cannon ball to drop and hit the earth. Now imagine firing it faster and faster, till eventually it's dropping at the same rate as the earth curves. That is essentially what the ISS is doing at a height of about 400km above the surface.

aurailious 8y ago
And the important part about orbits is that wind resistance won't slow it down significantly. At a low orbit like the ISS it touches the atmosphere ever so slightly and needs a boost every now and then.
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oliveshell 8y ago
It’s worth noting that if you shoot a cannonball dead horizontally, it hits the ground at the same time as it would if dropped from the same height [1]. It just has more horizontal speed, so it travels sideways a decent amount during its fall. Anyways, yes, the ISS is scooting sideways so fast that, in the time it would have taken to fall straight down, the ground beneath it has dropped away by an amount equal to its initial height, so the thing stays at the same altitude. [1]: *This hurt my brain when I first heard it, but I promise it’s true: it’s just that cannons are normally fired at an upward angle, giving them upward velocity and thus “hang time.”
- ethbro 8y ago
  > It’s worth noting that if you shoot a cannonball dead horizontally, it hits the ground at the same time as it would if dropped from the same height Do you have a citation for this? I'd expect, as with all physics questions, there's a caveat. In this case, "... over sufficiently small distances." If you fire, say, the main guns of a battleship "over the horizon" (from your initial vantage point), I'd strongly suspect this doesn't hold. In order for it to, the gravitational force vector, integrated over flight path, would have to perfectly counter the curvature of the Earth... which doesn't seem like it would line up so neatly. In reality, air friction and maximum muzzle velocities probably render most of these concerns moot for practical purposes.
  - JumpCrisscross 8y ago
    > there's a caveat Air.
  - sonnyblarney 8y ago
    "Do you have a citation for this?" This is Newtonian physics. Obviously, air, other things, friction mess it up. But essentially that's it. Horizontal motion of a body won't affect gravitations vertical pull.
    - plaguuuuuu 8y ago
      in a completely Newtonian universe (ignoring relativity), if you shoot the ball at high enough speed it will never hit the earth. horizontal motion doesn't affect the vertical pull, but the direction of the vertical pull changes by the time the ball's traveled well over the horizon.
      - dragonwriter 8y ago
        > in a completely Newtonian universe (ignoring relativity), if you shoot the ball at high enough speed it will never hit the earth. Right. Assuming a perfectly spherical earth, at below orbital velocity, it hits the ground somewhere; at orbital velocity up to (but excluding) escape velocity it (assuming the cannon gets out of the way) orbits with the low point at (and opposite) the firing position, and beyond escape velocity it takes a curving path getting ever farther away.
    - ethbro 8y ago
      Aka orthogonal vectors won't affect each other. Does this hold true as an object's ballistic trajectory approaches significant fractions of a planet's diameter? Granted, the object is constantly being accelerated towards the center of the planet. But that force vector's direction changes with respect to the initial "horizontal" launch vector as the object continues on a straight path, until they're longer orthogonal.
      - 8y ago
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- dragonwriter 8y ago
  > It’s worth noting that if you shoot a cannonball dead horizontally, it hits the ground at the same time as it would if dropped from the same height No, it doesn't, because the Earth is curved, and air resistance. With a relatively dense, aerodynamic shell and energy sufficient for only a short flight time, both of these effects are minimal, so it's approximately true, but lose any of those and it stops being a good approximation.
- jefftk 8y ago
  > It’s worth noting that if you shoot a cannonball dead horizontally, it hits the ground at the same time as it would if dropped from the same height I think this is assuming the ground is flat, which isn't a good assumption when talking about orbits.
  - oliveshell 8y ago
    It’s a perfectly fine assumption when talking about cannons, which are typically earthbound and have low projectile speeds. I discuss orbits in the next paragraph, where I hope it’s evident I don’t assume a flat plane :)

aurailious 8y ago

And the important part about orbits is that wind resistance won't slow it down significantly. At a low orbit like the ISS it touches the atmosphere ever so slightly and needs a boost every now and then.

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oliveshell 8y ago

It’s worth noting that if you shoot a cannonball dead horizontally, it hits the ground at the same time as it would if dropped from the same height [1]. It just has more horizontal speed, so it travels sideways a decent amount during its fall. Anyways, yes, the ISS is scooting sideways so fast that, in the time it would have taken to fall straight down, the ground beneath it has dropped away by an amount equal to its initial height, so the thing stays at the same altitude. [1]: *This hurt my brain when I first heard it, but I promise it’s true: it’s just that cannons are normally fired at an upward angle, giving them upward velocity and thus “hang time.”

ethbro 8y ago
> It’s worth noting that if you shoot a cannonball dead horizontally, it hits the ground at the same time as it would if dropped from the same height Do you have a citation for this? I'd expect, as with all physics questions, there's a caveat. In this case, "... over sufficiently small distances." If you fire, say, the main guns of a battleship "over the horizon" (from your initial vantage point), I'd strongly suspect this doesn't hold. In order for it to, the gravitational force vector, integrated over flight path, would have to perfectly counter the curvature of the Earth... which doesn't seem like it would line up so neatly. In reality, air friction and maximum muzzle velocities probably render most of these concerns moot for practical purposes.
- JumpCrisscross 8y ago
  > there's a caveat Air.
- sonnyblarney 8y ago
  "Do you have a citation for this?" This is Newtonian physics. Obviously, air, other things, friction mess it up. But essentially that's it. Horizontal motion of a body won't affect gravitations vertical pull.
  - plaguuuuuu 8y ago
    in a completely Newtonian universe (ignoring relativity), if you shoot the ball at high enough speed it will never hit the earth. horizontal motion doesn't affect the vertical pull, but the direction of the vertical pull changes by the time the ball's traveled well over the horizon.
    - dragonwriter 8y ago
      > in a completely Newtonian universe (ignoring relativity), if you shoot the ball at high enough speed it will never hit the earth. Right. Assuming a perfectly spherical earth, at below orbital velocity, it hits the ground somewhere; at orbital velocity up to (but excluding) escape velocity it (assuming the cannon gets out of the way) orbits with the low point at (and opposite) the firing position, and beyond escape velocity it takes a curving path getting ever farther away.
  - ethbro 8y ago
    Aka orthogonal vectors won't affect each other. Does this hold true as an object's ballistic trajectory approaches significant fractions of a planet's diameter? Granted, the object is constantly being accelerated towards the center of the planet. But that force vector's direction changes with respect to the initial "horizontal" launch vector as the object continues on a straight path, until they're longer orthogonal.
    - 8y ago
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dragonwriter 8y ago
> It’s worth noting that if you shoot a cannonball dead horizontally, it hits the ground at the same time as it would if dropped from the same height No, it doesn't, because the Earth is curved, and air resistance. With a relatively dense, aerodynamic shell and energy sufficient for only a short flight time, both of these effects are minimal, so it's approximately true, but lose any of those and it stops being a good approximation.
jefftk 8y ago
> It’s worth noting that if you shoot a cannonball dead horizontally, it hits the ground at the same time as it would if dropped from the same height I think this is assuming the ground is flat, which isn't a good assumption when talking about orbits.
- oliveshell 8y ago
  It’s a perfectly fine assumption when talking about cannons, which are typically earthbound and have low projectile speeds. I discuss orbits in the next paragraph, where I hope it’s evident I don’t assume a flat plane :)