# What is Spheres: Definition and 503 Discussions

The Synchronized Position Hold Engage and Reorient Experimental Satellite (SPHERES) are a series of miniaturized satellites developed by MIT's Space Systems Laboratory for NASA and US Military, to be used as a low-risk, extensible test bed for the development of metrology, formation flight, rendezvous, docking and autonomy algorithms that are critical for future space missions that use distributed spacecraft architecture, such as Terrestrial Planet Finder and Orbital Express.Each SPHERES satellite is an 18-sided polyhedron, with a mass of about 4.1 kg and a diameter of about 21 cm. They can be used in the International Space Station as well as in ground-based laboratories, but not in the vacuum of space. The battery-powered, self-contained units can operate semi-autonomously, using CO2-based cold-gas thrusters for movement and a series of ultrasonic beacons for orientation. The satellites can communicate with each other and with a control station wirelessly. The built-in features of the satellites can be extended using an expansion port.From 2006, three SPHERES units are being used in the International Space Station for a variety of experiments. The SPHERES Guest Scientist Program allow scientists to conduct new science experiments using SPHERES units, and the Zero Robotics Program allow students to participate in annual competitions that involve developing software to control SPHERES units.The SPHERES program is expected to continue until 2017, and possibly further.The SPHERES project lead to a newer project called Astrobee.

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1. ### I Higher Dimensional Spheres viz. Cubes

This is about Euclidian geometry in n dimensions. On this subject it is often noted that the volume of the unit sphere goes to zero as n increases. However this has more to do with the unit cube getting larger than the sphere growing smaller. As n increases the diagonal of the unit cube...
2. ### Find the magnitude of the electric field at point P

There are two identical spheres with the same charge that are the vertices of an equilateral triangle. ##+3 \mu C## will exert an outward electric field, which is drawn in the FBD below (see the attached pic), Since the horizontal force components (1x and 2x) are equal and opposite at point P...
3. ### 2-D Momentum Problem -- Elastic collision of two spheres

Hi, Here is the problem What is required to answer this question is two assumptions. Firstly, the component of the momentum normal to the centre line is the same before and after. Therefore, secondly, A must recoil entirely in the horizontal plane. This is the only way to answer this question...
4. ### Normal Forces on a Sphere in a Non-vertical Groove

neglect friction and motion (sliding) and G(sphere)=20N. In this question I reached two different result with two different solving method.But one of them is false according to answer key. My question is why first solving way is false? Because the first solution way makes sense to me. If we...
5. ### Charge of 2 conducting spheres separated by a distance

First assuming only one sphere at a potential of 1500 V, the charge would be q = 4πεrV = 4π(8.85×10 −12C2/N · m)(0.150 m)(1500 V) = 2.50×10−8C. The potential from the sphere at a distance of 10.0 m would be V =(1500V)(0.150m)/(10.0m) =22.5V. I don't understand the reasoning of the...
6. ### Balance of forces for two charged spheres hanging from the ceiling

I think if we don't consider electron's/proton's mass then we can say that the amount of charge doesn't need to be equal according to Newton's 3rd Law. I mean having q on one ball and 2q on another ball , still makes the angles having the same size. Is it true ? What if we consider proton's...
7. ### Induced polarization for collision between conducting spheres

For this part (b) of this problem, The solution is, However, would a better explanation be: As the spheres are conductors, there will be free electrons within and on the surface of the conductors that will be polarized by the external electric field between the conductor. This will decrease...
8. ### POTW What is the Relationship Between Fiber Bundles of Spheres?

Prove that if there is a fiber bundle ##S^k \to S^m \to S^n##, then ##k = n-1## and ##m = 2n-1##.
9. ### Two charged spheres hitting each other

Since the forces involved (gravity and electric force) are conservative we can use conservation of energy. The initial energy is ##E_i= k\frac{q_1q_2}{r_0}-G\frac{m^2}{r_0} ## and the final ##E_f=mv^2+k\frac{q_1q_2}{2r}-G\frac{m^2}{2r} ## so from ##E_i=E_f ## we get...
10. ### I Triangles on Spheres: Isosceles and Shortest Distance Inferences

If I have a triangle on a sphere with two of its angles 90 degrees each, do I conclude that it's isosceles and that the shortest distance (on the sphere) beteeen the base and the vertix of the thid angle is 1/4 the circumference of a great circle on the sphere? This is the picture I have in...
11. ### I Elastic collision between two spheres

Suppose I have two spheres in 3 dimensions of equal mass. In cartesian coordinates, sphere A is traveling with velocity uAi, and sphere B travels with vBi. They will collide elastically. I want to find the final velocities after the collision, ie uAf and vBf. Am I correct in saying that...
12. ### Volume of pyramid formed by center of 5 spheres inside a hemisphere

Let the radius of the small sphere = r 3r = 1 → r = 1/3 ##x=\sqrt{4r^2-r^2}=r\sqrt{3}## Volume of pyramid: $$=\frac{1}{3} \times (2r\sqrt{3})^2 \times r$$ $$=\frac{4}{27}$$ So m + n = 31, but the answer is 29. I guess my mistake is assuming line AB is tangent to the top sphere. How to do...
13. ### Two conducting spheres a distance d away with charges +q and -q

you can treat the center of two conducting sphere's like two point charges. Therefore it should be equal to ##k_e q^2/d^2##, but the answer is greater than ##k_e q^2/d^2##. Can someone explain how? Thank you
14. ### Microstates for a gas of hard spheres in a box

Hi, I have to found the number of microstates for a gas of N spheres of radius r and volume v in box taking into account the reduced volume after each sphere. V sphere << V box. I'm struggling to find the microstates in general. I don't see how to find the number of microstates without knowing...
15. ### Inverse square law of gravitation and force between two spheres

I recently encountered this problem on a test where the solution for the above problem was given as follows: $$F= \frac{Gm_1m_2} {r^2}$$ (1) but $$m=\frac{4}{3}\pi R^3$$ substituting in equation (1) $$F= \frac{{G(\frac{4}{3}\pi R^3\rho})^2 }{2R^2}$$ where r=radii of the two spheres m=mass...
16. ### B Coulomb pressure and concentric spheres

Suppose you have a sphere of radius a of positive charge, and a concentric shell from a to b of negative charge. The positive charge is equal to the negative charge. (non-conducting, uniform density) Is there an outward pressure at a of kqq/a2/(4πa2) - with pressure decreasing with radius...
17. ### Engineering Calculating the flux through a certain radius (concentric charged spheres)

Question My attempt for the 1st part, when r = 1.5 m Could someone confirm my answer?
18. ### Electric field problem -- Repulsive force between two charged spheres

I attempt to solve the problem in the picture below.
19. ### 2 Spheres of Charges and their Interaction

I can understand what happens with the conductor... (induction effects). But how can induction happen in insulators ? Is it due to the the induced dipole moment?
20. ### Charge on two spheres related to Earthing

Before grounding (left picture), X will be positively charged and Y will be negatively charge. After grounding, I think electrons from Earth will flow to sphere Y and then move to sphere X so X will be neutral and Y will be negatively charged (answer C). But the answer key is D. Why? Thanks
21. ### How do I calculate the ratio of forces between two conducting spheres?

Here are the answer choices: a) F1 = 2F2 b) F1 = 8F2 c) 2F1 = F2 d) F1 = 4F2 e) F1 = F2 I figured that Coulomb's law would tell us the magnitude of the forces are identical, so I answered E, but that was incorrect. (Screenshot of question attached)
22. ### Understanding the Electric Field of Two Spheres: A Scientific Approach

I am not quite sure how to present my answer in the form of a function with relation to the distance from the centre. What I got so far is the E1 and E2, for the internal and external sphere respectively. For internal sphere, the charge is volume * 𝜌, so it is $$\frac{4\pi r^{3}}{3} * 𝜌$$...
23. ### Dyson Spheres & Rings - Better Alternatives Exist?

I seriously doubt that any of these things exist. For one thing there’s something better. Assuming the civilization has the technology to build a Dyson sphere or ring, would they? With that technology and resources it seems to me it would be much simpler to strip the rocky parts of a large...
24. ### Hollow and solid spheres floating in liquid

The two situations are shown in the figures alongside. The hollow sphere has a thick heavy rim that compensates for the air inside it - both spheres have the same mass ##m_B## and radius ##r_B##. Since the bodies have the same mass ##m_B##, the mass of liquid displaced is the same ...
25. ### B Newton's experimental law -- Questions about the collision of two spheres

The following is from the 2018 AQA AS Further Maths/Mechanics Paper 2 exam: 'Two smooth spheres A and B of equal radius are free to move on a smooth horizontal surface. The masses of A and B are m and 4m respectively. The coefficient of restitution between the spheres is e. The spheres are...
26. ### Charge rearrangement on conducting spheres

Hi, I think this problem is solved in exactly as a similar problem where the two spheres are very far apart and connected by a very long thin conducting wire. I'm trying to explain this in words, since LaTeX does not seem to work any more (for some reason LaTeX syntax is not replaced by maths in...

41. ### Electric Field Inside Concentric Spheres

Homework Statement Homework EquationsThe Attempt at a Solution I am having trouble figuring out why the answer is A) the electric field points radially between A and B. I think it is because since the point between A and B is mostly negative, the electric field would point outwords more...
42. ### Electric Potential at Radius R of Concentric Spheres

Homework Statement Homework Equations V=kQ/R The Attempt at a Solution The answer is B)kQ/R. It is because V= k(2Q)/R. I don't understand why Q=2Q in this case. Isn't the point on the inside of the outer shell, so the Q for the equation is just Q?
43. ### Charge distribution on concentric spheres

Homework Statement Two thin conducting spherical shells have radii R1 and R2.Outer shell is charged to q and inner shell earthed.Find charge appearing on both the shells. Homework Equations The Attempt at a Solution Isnt the charge on inner shell 0 and charge on outer shell remains Q as it...
44. ### Rank charge density of spheres

Homework Statement Sphere 1 has net positive charge Sphere 2 has net negative charge Sphere 3 has net positive charge The ranking of net charge magnitudes are SPHERE 3 > SPHERE 2 > SPHERE 1 All spheres are conductors Sphere 2 is moved away from Sphere 1 and toward Sphere 3 so that 2 and 3...
45. ### Effect of density on downward rolling spheres

Homework Statement If two balls, being identical in volume, but different in density (one ball is made of iron, the other of aluminum) roll down from an inclined plane, which will reach the bottom first and which will cover a larger distance after having reached the bottom? IMPORTANT NOTE...
46. ### Rank charges in spheres (Physics 2)

Homework Statement Homework Equations None (conceptual) The Attempt at a Solution My logic here is this, Sphere 3 has a net positive charge so it is repelling the positives in sphere 2 and attracting the negatives in sphere 2. This means that D has negative charge and C has positive charge...
47. ### Flow of charge between two spheres

Lets say I have two spheres of equal dimensions, one charged and one uncharged. Now I connect them with a conducting wire. They will now very quickly reach equal potential. Can it be said that the total charge on each sphere remains almost unchanged?
48. ### I Largest sphere in the space between dense packed spheres

If I consider a tetrahedron of four densely packed spheres of unit radius, what it the radius of the largest sized sphere that can fit in the space in between?
49. ### Without integrating, show two metal spheres collide in <425s

Homework Statement Two identical uniform metal spheres of radius 47 cm are in free space with their centers exactly 1 meter apart. Each has a mass of 5000 kg. Without integrating, show that gravity will cause them to collide in less than 425 seconds. [/B] Source: Classical Mechanics, R...
50. ### Capacitance and field of 2 eccentric spheres

Homework Statement Hi there! So I have found trouble with the following problem. I have a system of two eccentric spheres, where one is inside another. The Attempt at a Solution I have found this answer: https://physics.stackexchange.com/questions/16939/capacitance-of-non-concentric-spheres...