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. Z

    B Single photons and expanding spheres of light

    This question has been bothering me for decades: Imagine a point source in space that emits one photon per second. Would the photon expand in a globe in all directions until it strikes an object or would the photon shoot off in a random direction? Suppose you have one target ten meters away...
  2. F

    The electrostatic potential energy of two spheres

    Homework Statement Homework Equations The Attempt at a Solution Is my answer correct ?
  3. shintashi

    I Equidistance of Points in a Sphere?

    I've been trying to wrap my head around equidistant points, like platonic solid vertices inside a sphere where the points touch the sphere surface. This led me to the strange and unusual world of mathematical degeneracy, henagons, dihedrons, and so on, along with the lingering question of...
  4. J

    A Anamolous Aerodynamic behaviour of small spheres?

    This refers to the behaviour of cricket balls. Every cricketer in the world believes that a cricket ball "swings" more when the atmospheric conditions are cool and damp (as in the UK) as opposed to hot and dry (as in Australia). I have watched a bit of baseball and I have never heard...
  5. S

    Two spheres of are dropped to ground while in contact.

    Two spheres of different masses are dropped to ground.They are in contact as one above the other and are of masses, let’s say m and 2m.They are dropped with velocity v - My question is if we can conserve momentum and if we can why?And how to find the final velocity of upper ball after collision...
  6. M

    Electric field of two conducting concentric spheres

    Homework Statement Two conducting hollow spheres are are placed concentrically, the inner sphere have a radius ra = 5 cm and the outer sphere have a radius rb = 15 cm. The charge on the inner sphere is qa = 4 · 10−7 C and qb = −4 · 10−7 on the outer sphere. (a) Use Gauss’s law to find the...
  7. fresh_42

    Insights What Defines a Local Lie Group in A Journey to The Manifold - Part I?

    fresh_42 submitted a new PF Insights post A Journey to The Manifold - Part I Continue reading the Original PF Insights Post.
  8. Pushoam

    Current due to metal spheres kept far away in the sea

    Homework Statement Homework EquationsThe Attempt at a Solution I solved the first part. I = 4πσV/(1/a - 1/b) Here, it is solved assuming that both the shells have positive charges and the charge flows from the inner shell to the outer shell . So, in the part c, it is assumed that each...
  9. Z

    Angle between 2 charged spheres hanging from string

    Homework Statement Two positively charged metal spheres are suspended from the same hook by light strings of equal length, making an angle of 10.0◦ with each other. The charges carried by the spheres are as shown in the diagram. After that, the spheres are brought in contact briefly, then...
  10. L

    I Can 2 spheres orbit each other say inside ISS?

    I was thinking about two spheres of lead, 1 Kg and if I remember right would be about 3 cm radius. So inside the ISS in microgravity could the gravitational attraction of the two spheres allow them to orbit one another? I calculated an orbital time, if 2 cm apart of about one hour per orbit...
  11. I

    Connecting three spheres with wires redistributes charge

    Homework Statement There are three identical conducting spheres, A, B and C. They are initially charged as q_A = 0, q_B = 0, q_C = +Q. Initially, A and B are connected by a wire. Then the spheres are connected (by a wire) as follows: 1) A to C (while A is still connected to B) 2) Connection...
  12. S

    Charge distribution on spheres

    Homework Statement Two conducting spheres having same charge density and with radius “R” & “2R” are brought in contact and separated by large distance. What are their final surface charge densities ? Homework Equations No equation in question. The Attempt at a Solution Tried using the fact...
  13. Pushoam

    Change in electrostatic potential energy of two spheres

    We have two conducting spheres of radius r1 and r2 far away from each other. The first sphere has a charge Q. What is the change in electrostatic potential energy when they are connected together? Before the connection , Ube = ## \frac{Q^2}{8\pi\epsilon_0 r_1} ## After the connection , Uaf = ##...
  14. F

    Electric potential of charged concentric spheres

    Homework Statement Two conducting concentric spheres of negligible thickness. The radii of the spheres are R_1 and R_2, respectively, with R_2>R_1. A charge q_2 is placed on the external sphere. A charge q_1 is placed on the internal sphere. Assume that the electric potential is zero...
  15. X

    I Relativity Paradox w/ Charged Spheres

    There is a similar thought experiment I imagined to help me begin to understand the Bell's spaceship paradox: Consider two positively charged spheres, placed side-by-side inside a frame S' with a string stretched to the point where it balances the repulsive electrostatic force between them. For...
  16. R

    Equivalent capacitance of a system of 2 spheres

    Homework Statement : [/B]Two conducting spheres of radii R1 and R2 are kept widely separated from each other. what are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combiation?Homework Equations Capacitance of a sphere of radius...
  17. Marcus95

    Change in electrostatic energy on two spheres

    Homework Statement We have a spehere of radius ##r_1## and on of ##r_2## far away from each other. The first sphere has a charge ##Q##. What is the change in electro static energy when they are connected together? Homework Equations Potential of a charged sphere: ## V = \frac{Q}{4\pi\epsilon_0...
  18. B

    How to distribute the charge between two spheres to minimize the potential?

    Homework Statement We have two metal spheres of radii ##R_1## and ##R_2## placed far apart. Given total amount of of charge ##Q## to distributed between the two spheres, how should you do it so that the potential of given distribution is as small as possible. Homework EquationsThe Attempt at a...
  19. Kara386

    Potential between concentric spheres

    Homework Statement A particle charge q and mass m moves in a circle radius r between two concentric spheres which are a distance d apart, where d<<r. There's a potential V between spheres. Find an expression for this potential. Homework EquationsThe Attempt at a Solution Can I assume that...
  20. M

    MHB Proving Perpendicular Motion of Two Colliding Spheres

    Two smooth spheres of masses km and m collide obliquely. the sphere of mass m is brought to rest by the impact. the coefficient of restitution for the collision is 1/k (k greater or equal to 1) Prove before the impact the spheres were moving perpendicular to each other. i have worked out k=-1...
  21. E

    Finding electric potential between two concentric spheres.

    Homework Statement A spherical shell with inner radius A and outer radius 3A which has a uniform charge density, i.e charge per unit volume, p0. Find difference in electric potential between the center of the shell and a point a distance 2A from the center. Homework Equations The answer given...
  22. ikihi

    Two uncharged metal spheres

    Homework Statement X and Y are two uncharged metal spheres on insulating stands, and are in contact with each other. A positively charged rod R is brought close to X. Sphere Y is then physically moved away from X. What are the final charge states of X and Y? Homework Equations N/A The...
  23. W

    Concepts regarding Electric Potentials of Spheres

    Homework Statement My questions are just related to part a of this problem. Homework EquationsThe Attempt at a Solution I know that potential inside a conductor is equivalent to potential on the surface of the conductor and potential at any point is an algebraic sum of potential...
  24. Alanay

    B Are black holes perfect spheres?

    Since it is practically impossible to artificially create a perfect sphere, are black holes the closest thing?
  25. peroAlex

    Capacitance of two unequal spheres

    Assume that we have two charged spheres with unequal radii and which do not overlap. How cold we express their capacitance?
  26. RoboNerd

    Energy in system of two conducting spheres

    1. Homework Statement Hi everyone. I am having trouble figuring out how to solve this problem. The right answer is E Homework Equations Well, we do have the law of conservation of charge. I also know that Work by a conservative force = - change in potential energy The Attempt at a Solution...
  27. D

    A simple angular velocity with two spheres problem

    Homework Statement Two masses have same mass m, both of them are tied by a string and put in a hollow cylinder. When the cylinder start to rotate until the angular speed is ω. The tension in the string is T and the string breaks, both masses move away from the axis in the hollow cylinder...
  28. I

    Solving Charge Distribution for Spheres with Different Material Properties

    Hey all, So the question in Jackson 1.4 is that I have 3 spheres that all have a total charge Q on them, but each sphere has different material properties. For instance, I have a conducting sphere, a sphere with a uniform charge distribution, and one with a charge distribution that has a...
  29. Abwi

    Electric force between two spheres

    Homework Statement [/B] Find the electric force between the two spheres. Sphere r=b-a has a volumetric density of p=K, where K is a constant Sphere r=a has a volumetric density of p=θ*r Homework Equations As you can see the sphere of radius 'a' doesn't have a uniform electric field because...
  30. Misha Kuznetsov

    Voltage applied to urchin-like iron spheres in salt water?

    Hello, if I had salt water and put microscopic spheres with iron spikes in (a lot of them, say 1,000). Then if a high static charge was applied to the water (say 500,000 volts), what would happen? My intuition tells me that the electric field would concentrate on the tips of the spikes, making...
  31. E

    Determine the location of the center of mass of spheres

    Homework Statement All three disks are made of sheet metal of the same material, and the diameters are 1.0 m , 2.0 m , and3.0 m . Assume that the x-axis has its origin at the left-most point of the left-most object and it points to the right. Part A) Determine the location of the center of mass...
  32. C

    Time of collision of two lead spheres

    Homework Statement Two uniform lead spheres each have mass 5000kg and radius 47cm. They are released from rest with their centres 1m apart and move under their mutual gravitational attraction. Show that they will collide in less than 425s. Homework Equations By Gauss' Law, force on a sphere...
  33. Gummy_Bear

    What is the heat produced when two charged spheres are connected by a wire?

    Homework Statement A solid metal spheres of radius a surrounded by a concentric thin metal shell of radius 2a. Initially botb are having charge Q each. When the two are connected by a conducting wire , then the amount of heat produced in process will be : Homework Equations Heat = E2 - E1...
  34. S

    Radiant heating of air trapped in hollow glass spheres....

    I'd posted more of a real world version of this question, involving greenhouses, a few days ago at... https://www.physicsforums.com/threads/is-greenhouse-interior-much-cooler-if-reflective-inside.875575/ ...but with no responses after 130 reads, I'm reducing it down to a barer and much better...
  35. F

    A Proof for Close Packing of Congruent Identical Spheres

    I developed two algorithms for calculating the density of close packed congruent identical spheres in two different arrangements: A tetrahedron with four equilateral triangular faces, and A square pyramid with a square base and four equilateral triangular faces, as shown below. Figure...
  36. F

    Volume enclosed by two spheres using spherical coordinates

    Homework Statement Use spherical coordinates to find the volume of the solid enclosed between the spheres $$x^2+y^2+z^2=4$$ and $$x^2+y^2+z^2=4z$$ Homework Equations $$z=\rho cos\phi$$ $$\rho^2=x^2+y^2+z^2$$ $$dxdydz = \rho^2sin\phi d\rho d\phi d\theta$$ The Attempt at a Solution The first...
  37. G

    I Questions about Vsauce's Banach-Tarski video

    Hi, I have some questions about the video about the Banach-Tarski Paradox from the YouTube channel Vsauce: 10:09: Is this really a valid way of constructing the hyperwebster? In this order, one will never get past sequences of only "A". Shouldn't one follow an order like A, ... ,Z, AA, ... ...
  38. kolleamm

    I Perfect Spheres: A Theoretical Possibility or an Impossibility?

    I've been wondering about this for a while. If you were to take a perfect sphere and cut it in half so that you would see a circle and then use a magnifying glass to zoom in closer and closer on part of the circle, the arc would approach near flatness but it would never reach it so therefore...
  39. JulienB

    Maximal repellence between charged spheres

    Homework Statement Hi everybody! I just started electromagnetism, and I'd like to make sure I get the concepts correctly before going further. I got this homework: A charge is shared between two spheres. How big must the share of charge relative to one another be, so that there is the maximal...
  40. U

    Electric charges and fields: Charged conducting spheres touching then separated

    Homework Statement Two charged metallic spheres of same size repel each other by a force F. They are now touched with each other and are then separated to same initial distance. Now the force of repulsion is F'.Homework Equations On touching the spheres will reduce their charges... So the new...
  41. M

    Finding eigenvalue energy between two spheres

    Homework Statement there are two spheres with radius a and b that b > a.they don't have the same center and the distance between their centers is d . how can I find eigenvalue and eigenfunction of energy spacing between two spheres... I don't have any idea. please help me . Homework...
  42. akshay86

    Rotating & Moving Spheres: What Causes Torque & Force?

    if a central force acts on a sphere it will rotate and move and also a angular momentum is given to that body it will also move in the same manner.What provide torque in first case and net force in second case.is it friction then how?
  43. C

    Why Does a Rolling Sphere Climb Higher Than a Sliding Particle?

    Homework Statement A uniform sphere and a particle are sent one-by-one with the same initial speed up the same incline. Each rises to a maximum height before falling back towards the starting point. The sphere rolls without slipping; the particle slides without friction. Use conservation of...
  44. C

    B Do curves, circles and spheres really exist?

    Obviously, they exist as mathematical concepts, and those concepts are real, but in physical reality, everything is made up of subatomic particles and, if the theory is ever verified, strings. So if you try to construct a curve, circle or sphere, you are necessarily stacking a bunch of subatomic...
  45. V

    Distribution of charge on two spheres

    Homework Statement Homework EquationsThe Attempt at a Solution I believe the entire charge Q has to be given to any of the sphere such that one charge is neutral ,while the other has charge Q . In this way there would be no electric force between the two spheres and only attractive force...
  46. SarahAlbert

    Flux Through Concentric Spheres with Varying Charge Density

    Homework Statement A sphere of radius a has its center at the origin and a charge density given by p=Ar^2 where A=constant. Another sphere of radius 2a is concentric with the first. Find the flux through the larger sphere. Homework Equations Flux=E*da The Attempt at a Solution According to...
  47. SarahAlbert

    Gauss Law: Concentric Spheres

    Homework Statement Two concentric spheres have radii a and b with b>a. The region between them is filled with charge of constant density. The charge density is zero everywhere else. Find E at all points and express it in terms of the total charge Q. Do your results reduce to the correct values...
  48. M

    What Happens to Sphere Velocities After an Elastic Collision?

    Homework Statement Two solid spheres hung by thin threads from a horizontal support (Figure 1) are initially in contact with each other. Sphere 1 has inertia m1 = 0.040 kg , and sphere 2 has inertia m2 = 0.10 kg. When pulled to the left and released, sphere 1 collides elastically with sphere 2...
  49. I

    Electric Field of Concentric Spheres and Opposite Charges

    Homework Statement The figure to the right shows two concentric spheres made from insulators. One has radius and the other has radius R1, and the other has radius R2. The inner sphere has a positive charge density, +ρ, while the insulator region between the inner and outer spheres has a...
  50. K

    Electric field through the intersecting part of two spheres

    Homework Statement Consider a pair of spheres of radius R with uniform charge densities ρ > 0 and −ρ located respectively at ~r+ = (0, 0, d/2) and ~r− = (0, 0, −d/2), with d < R. a)Find the electric field at all points in the region of overlap of the spheres for arbitrary d < R. Homework...
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