Let’s say I have a one-meter sphere weighing, say, 1000kg. I’m out in deep DEEP space – as in, light years away from the nearest star or what have you. I also have a one-millimeter sphere weighing, say, one milligram. If I held the smaller sphere a few centimeters from the larger one and let go of it, would the larger sphere’s gravity be enough to pull it towards its center, the way the Earth does with, well, anything? If I moved it laterally just so, would the smaller sphere orbit the larger one?
Let’s say I have the same sphere with me on the ISS. If I tried to move it, would I essentially just be pulling myself towards the sphere, since its mass is so much greater than my own? If the floor of the ISS were at my feet, and I was scrunched down between the floor and the sphere, would I be able to lift it?
It’s my understanding that you could “lift” it, it would just be slow to start and hard to stop. As for pulling on it, the answer is that you both move; you’d just move somewhat more. Just as if you jump into the air here on Earth, you move the Earth an infinitesimal bit in the opposite direction because you are pushing on it.
Lifting it would involve overcoming inertia. I think measuring the inertia would be a way to
‘weigh’ something on the ISS since weight would generally be a measurement taken at 1G here on earth, so it’s not clear what you mean by 1000kg sphere in this case.
In theory yes the smaller sphere could orbit the larger sphere. In practice, it would depend on the gravitational influence of nearby planets and stars.
The second paragraph is easier to answer. On the ISS objects don’t have weight but they still have mass. Imagine that you were on Earth and there was a 1000 kg sphere suspended above ground on a rope attached to the ceiling. Could you brace yourself and push it away from you? Maybe a little, but it wouldn’t be easy. Smilar to moving the sphere on the space station
This is an interesting question and I think one that physicists would love to experiment with: in the absence of any other gravitational bodies do small objects behave in the same way as massive objects? Certainly if you get really small than absolutely not. The electromagnetic force is 40 orders of magnitude larger than gravity between two atoms. That’s a 1 with 40 0s at the end. The reason why we experience gravity in our everyday life is that the Earth is so huge it contains enormous numbers of atoms, and this is where the large gravitational force then builds up.
So undoubtably, small objects behave differently from large objects and the smaller they get the bigger that difference gets. At the sort of size you’re describing I’m not sure we’d see much difference though. However someone more knowledgeable than me might have a better idea.
Yes. Very, very, slowly. But if you nudged the smaller sphere at all while releasing it, it would probably be traveling beyond escape velocity.
The gravitational force between the two objects (at 10 cm seperation) would be 6.674 x 10 -9th newton. (The gravitational force between the Earth and moon is 1.933 × 10 to the 20th newtons.)
Yes, they do, but “The same way” would look very counter-intuitive to our lived experience.
There’s an orbital calculator you can play with here:
For the masses in the OP, and a circular orbit with a diameter of 2 m (1 m radius from center of the large mass), the orbital speed would be 0.00018268 m/s, and it would have an orbital period of 19.1 hours. So it will (or at least, could) orbit, but so slowly you’d have to observe it for many hours to be able to determine that.
Gravity is so weak that measuring it accurately is difficult because almost anything exceeds the gravitational pull. Shining light on the experiment pushes it harder than the gravitational pull. Even third-order magnetic or electrostatic forces within the test objects outweigh it.
Regarding the ISS hypothetical the answers are correct for a “flat” space, but which a close orbit around the Earth is not. In fact low Earth orbit is the most sharply (but not deeply) curved spacetime in the solar system, with an orbit time less than any other body. Being just a few centimeters closer or farther away from the Earth introduces microgravity tidal forces.
And one I’ve actually done as a student. As I mentioned, the biggest part of the experiment was walking away for a few hours while it settled down enough to show the effect.
And it was very sensitive. The apparatus we used was in its own room in the lab, and when they first set it up, they kept getting weird results. They finally figured out that they had a solid wall on one side of the apparatus, but just a plain door on the other. The difference in mass threw everything off. They fixed it by buying a super-heavy metal door to replace the lighter one. That balanced the gravity of the room enough to get good measurements.
The kilogram is a unit of mass, and mass is different from weight. A 1000kg object will unambiguously be a 1000kg object everywhere in the universe, irrespective of local gravity. The force by which some other object attracts this sphere will be dependent on local gravity (the mass of that other object and the distance to its centre of gravity), but this force is different from mass, and it’s not measured in kilograms.
Yes and it’s assumed the mass is the weight for a given system such as the OP. Whatever the unit of measure, the larger object (1000 kg) is a thousand thousands times more massive than the smalle (1 milligram).
Yes, I assumed he was talking about something that weighed 1000kg on earth. I was commenting on another post mentioning the effort it took to move such an object even on the ISS. I don’t know much about physics and have try to clarify everything in discussions. Don’t want to sidetrack things but I remain confused about why mass and inertia are different since they’re directly proportional to each other.
I have only a hobbyist’s understanding of orbital mechanics, so others can correct me, but if I got my equations right then for a sphere of 1000kg and a radius of 60 centimetres (50 centimetres radius of the sphere itself, and an object orbiting 10 centimetres away from the surface of the sphere), orbital velocity will be 0.333 millimetres per second, and escape velocity will be √2 times that, so 0.47 millimetres per second. If the smaller object is moving tangentially to the larger sphere at 0.333 mm/s (0.013 inch/second) at that distance, it will orbit it; if it’s slower, it will fall towards the larger sphere; if it’s faster but slower than 0.47mm/s (0.019 inch/s), it will rise to a higher orbit; and if it’s faster than 0.47 mm/s it will fly away into infinity.
But how would that affect my efforts to move the sphere around, for example moving it further away from the center of earth? Tidal forces act to elongate an object along the line of gravitational pull, but they do not affect the center of mass of that object.
Well, of major solar system bodies, at least. Orbital time just above the surface of a spherical object depends only on the object’s density, and the Earth’s density is higher than that of the Sun or any of the other planets. But there are probably some asteroids that are denser.
“Weighed 1000 kg on Earth” is actually meaningless, since nothing ever weighs any number of kilograms anywhere. It makes no more sense than me saying that I weigh six feet. Kilograms are a unit of mass, and a 1000 kg sphere will be a 1000 kg sphere anywhere. An object’s weight will be different, in different gravitational fields, but kg are not a unit of weight. Pounds or (in SI units) newtons are units of weight.
This makes sense when you think about it - the OP was asking if it behaved in the same way as a much larger body. This would be evidence that is does behave at least similarly.
I don’t think that type of distinction is helpful to OP. Weighing is how we determine mass (for 1000 kg spheres) and it’s assumed by convention that the measurement was performed here on the surface of Earth.
This sort of confusion is precisely the reason why there is a non-SI but useful unit of weight, the kilopond, defined as the weight of one kilogram on the surface of the Earth - but with a name that clearly sets it apart from the kilogram as a unit of mass.