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Comment by marcosscriven | Hacker News Reader

This all seemed reasonable except this paragraph:

"The reason they are floating around is that they have no net acceleration. The outward acceleration of (apparent) circular motion, which wants to sling them out into deep space, exactly balances the inward acceleration of gravity that wants to pull them down to Earth."

There is no "outward acceleration". The weightlessness is because the craft they are in is accelerating towards Earth with exactly the same acceleration. The reason they don't hit the ground is that they have a suitably high tangential velocity.

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Both you and the article are right - you are analyzing it in the frame of reference where the center of the earth is stationary, while the article analyzes in the frame of motion where the center of the rocket is stationary.

Since the frame where the center of the rocket is stationary is a non-inertial frame, Newton's law doesn't apply [1]. However a modification of Newton's law that includes a so-called "ficticious force" applies [2] (I don't think this modification has a name). This is why the article says there's an outward acceleration, because in the frame where the center of the rocket is stationary, the outward acceleration is caused by the ficticious force.

[1]: https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion begins the laws with "when viewed in an inertial reference frame"

[2]: https://en.wikipedia.org/wiki/Non-inertial_reference_frame quotes, "One might say that F = ma holds in any coordinate system provided the term 'force' is redefined to include the so-called 'reversed effective forces' or 'inertia forces'."

Right, of course I understand that - but two points.

1) The whole original post appears to be worded for the layman to try and dispel myths around what orbit is. I don't think the layman is going to think about inertial frames of reference, rather I genuinely think the common misconception that there's really something 'pulling' the astronauts up will continue, much like many people think a car is throwing them out of a bend in the road, rather than the vehicle pushing them away from a straight line.

2) In any case, even if Musk implies the frame of reference, there's a reason a 'centrifugal force' is also referred to as a 'fictitious force' [1]

[1]: https://en.wikipedia.org/wiki/Fictitious_force

It's describing the dynamics in the (non-inertial) reference frame of the satellite (the reference frame in which the astronauts can be described as "floating around"). In this reference frame, the centrifugal force balances the gravitational force, leading to zero net acceleration.

Is "tangential velocity" not just another way of saying "outward acceleration"?

I'm not sure if that's a question or a statement.Firstly, velocity and acceleration are different things. Velocity is change of distance with time (km/s), acceleration is change of velocity with time (km/s per second or km/s^2).

Secondly, an acceleration on a mass requires a force. Supposing there were an 'outward acceleration', where do you propose the 'outward force' is?

... We are talking a tangent on a circle that is changing every second.

So that is a change of velocity, which is acceleration. Outwards is clearly "out" of the circle. The tangent (on the curve) would be a snapshot of that "outward" velocity.

As a said: Tangential velocity is the same as saying outward acceleration. Unless you were referring to just that single "snapshot" in a frozen time scenario.

That "outward" force usually comes from a massive rocket... It is then maintained by the inward force of gravity.

Nothing is accelerating outward. There's only one acceleration here, and that's towards the centre of the mass of Earth.

If that were the case then you could get into orbit by simply going straight up. Why do they go laterally up to 8km/s then? (if not to generate an 'outward' force?).

There are two vectors being added here. One is gravity. The other is a tangental/outward vector. When added together, they form an orbit. Ignore one, and you leave orbit, either by going into space, or smashing into earth. But there are clearly two forces/vectors. And one of them, is having it's direction changed by the other, and thus is acceleration... I don't know what other words I can use to describe it. But I fail to see where I'm wrong :\

The only force, and therefore the only acceleration, when you're in orbit is the force of gravity. And therefore, the only acceleration is towards the center of Earth.

The thing in orbit is already moving with a high enough velocity that it isn't able to get closer to the Earth.

I guess maybe what you're saying, is if you take the velocity vector and apply the acceleration vector over time, that changes the velocity at the same rate as the curve of the Earth.

Either way, there is exactly one force vector (which causes exactly one acceleration vector), not two.

Accidentally up voted you :)

They get to that vast 8km/s veloctiy you mention with huge rocket engines. Then they turn them off.

At that point the astronauts and their craft are in freefall.

You mention an outward 'vector'? You can only talk about forces and their effects on masses really. There's an intertia that resists the downward acceleration, but that's not a force.

Pretty sure inertia IS a force. But I think this point has been laboured enough.

Tomayto...Tomarto.

A force is the product of mass and acceleration. Its SI units are kg.m/s^2

Inertia is an inherent property of mass. If it were the same as a force its units would be the same.

So it's really not tomayto...tomato I'm afraid. It's right and wrong.

You are right the point has been laboured, but it upsets me to think you would go on under this misconception.

Gravity is also an inherent property of mass... It's also a force.

Crazy huh?

No, not crazy. Not all properties of mass are force. For example, inertia. Also, really we should be talking matter, not mass.

A laughable claim, mister Bond, perpetuated by overzealous teachers of science.

:) https://www.explainxkcd.com/wiki/index.php/123:_Centrifugal_...

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