Just to make one thing clear from the start – I know the difference between mass and weight, and I know the Earth’s *mass *is about 6x10^24 kg.
However, the Earth is in the Sun’s gravitational field, and has a *weight *in that context, distinct from its mass.
I used to think the Earth, being in free fall, is weightless – so the Earth’s weight is zero. But now I’m not so sure. The Earth can only truly be in free fall if there is no resistance to its motion through space. Space is not a perfect vacuum, though it’s very close; and an object falling through any medium, however thin, ought to experience some resistance to its motion, and hence not be quite weightless.
I think that the use of the term “weightless” to refer to an object in orbit is a misnomer perpetrated by the popular media. An object in free fall is no more weightless than an object sitting on the ground. The weight is not realized by something pushing back, it is the pull of gravity on the object. A skydiver in free fall is not weightless, and neither is an object in orbit. A person in an orbiting spacecraft or a free-falling aircraft just has the *illusion *of weightlessness since his container is falling at the same rate.
In the case of your question, as Squink has so elegantly answered, the weight is the force of gravity exerted by the Sun. Of course, that’s just the predominant source of gravitational pull; the Moon exerts gravity on Earth as well (so do other planets).
BTW
I would assume this implies that the sun also imparts 0.0006 g on all of us on the planet as well. So during the day time I weigh a little more than I do at night…
Wouldn’t it be the opposite? During the day the gravitational force of the sun on you is opposed to the gravitational force of the earth (you are between them), resulting in a lower apparent weight. At night the forces are in the same direction and you appear to weigh a little more.
Probably just a shorthand way of not having to explain the difference between free fall and weightlessness, since, once you’re outside of the noticeable effects of gravity, you are weightless, even though you’re not in free fall.
I seem to recall free fall being used appropriately in some type of printed matter – maybe in science fiction or technical-oriented magazines (I don’t mean the book by that name).
That looks like it should be measurable. Are there any super sensitive experiments that have to take in account the position of the sun relative to the experiment?
The weight of an object as we normally use the term is the force of the gravitational attraction between that object and the earth. It is simply calculated using the formula F=Gm1m2/r^2.
If we want to calculate the weight of the Earth with respect to the Sun’s gravity we use:
G=6.673x10^-11 m^3Kg^-1S^-2
M(sun) =1.989x10^30 Kg
M(earth) =5.974x10^24Kg
r=1.544x10^10m
I get a weight of 3.326x10^24 Newtons or 7.477x10^23 pounds
If so, it’s fooled brighter people than me - I read the statement that the Earth is weightless because it’s in free fall many years ago in one of Isaac Asimov’s science essays. He was describing how Henry Cavendish determined the mass of the Earth, and in passing he pointed out that Cavendish hadn’t “weighed” it, explained the difference between weight and mass, and went on to ask “so what *is *the weight of the Earth?” His answer was zero, for the reason given.
Actually, the idea that “things in orbit are not really weightless” is a misconception perpetrated by folks who don’t know relativity. Really, learning relativity is more about unlearning Newtonian ideas and going back to what’s obvious to common sense, than it is about learning new concepts.
Okay, now I’m confused. Doesn’t Newtonian physics dominate at the orbital speeds we’re talking about? Sure, we’ve got to slightly compensate our trajectory when we aim at the moon due to relativistic effects, but isn’t it less than 1%? Can’t we disregard them as insignificant for the purposes of the discussion?
The pressure your butt feels from body above is from the Earth accelerating it against the chair.
If you go to the moon there’s less acceleration from gravity so your butt won’t be presed into the seat as hard. You weigh less
In orbit you’re experience no acceleration so the chair will drift away from your butt. You weigh nothing.
Why? IANAP but as I understand it matter (such as the Earth) bends space. when you’re in orbit you’re following a straight path through curved space. There’s no change of path relative to you so there’s no acceleration/nothing to shove your butt in the chair.
General Relativity is not a set of add-ons to the Newtonian theory that apply in extreme circumstances. General Relativity is (so far as we can tell) the actual, fundamental behaviour of gravity, and always applies. Newtonian theory is just an approximation that can be used in some situations.
In other words, an object in orbit has no forces acting on it and is not accelerating, but as long as certain conditions are met, we can approximate its behaviour by pretending that it does have a force on it and is accelerating.
That’s not true at all. An object in orbit certainly has a force on it, the vector points to the center of the orbit. It’s also always accelerating towards the center of the orbit, since acceleration is a change in the velocity or direction. How is that pretending? If it didn’t have a force on it, it’d be going in a straight line. Objects in motion tend to remain in motion, etc.
Or are we saying that the gravity bends space so it is actually going in a straight line?
I think he meant in the sense that an orbiting body is perceived to go in a straight line, but it only ends up being an orbit because space is curved. In that sense, no, his mind isn’t blown. Gravity curves space, but not into a 360° arc around an object the mass and size of Earth.
An object in orbit certainly has a force on it, the vector points to the center of the orbit. It’s also always accelerating towards the center of the orbit, since acceleration is a change in the velocity or direction. How is that pretending? If it didn’t have a force on it, it’d be going in a straight line. Objects in motion tend to remain in motion, etc.