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. F

    Two Insulating Spheres in Each Other's Electric Field

    Hi, I'd like to ask the good people of this forum for some help. Here's a problem I've been working on for a while, and I'm seriously at my wit's end. I guess there's something I'm missing here... Homework Statement Two insulating spheres have radii r1 and r2, masses m1 and m2, and...
  2. F

    Insulating Spheres in Electric Fields

    Hi, I'd like to ask the good people of this forum for some help. Here's a problem I've been working on for a while, and I'm seriously at my wit's end. I guess there's something I'm missing here... Homework Statement Two insulating spheres have radii r1 and r2, masses m1 and m2, and...
  3. G

    Calculating Force Between Two Magnetized Spheres with Unlike Poles Touching

    Hi ... how can I calculate the force between two permanent magnetized spheres(each r in radius) and has a magnetization (M) when they are magnetically stuck together with unlike poles touching?? I tried to think about it and found the following: 1) I can treat it like Earth magnetic field...
  4. D

    Charge Sharing between two metal spheres

    Two small metal spheres are located 3.0 m apart. One has radius 0.48 cm and carries charge 0.15 uC. The other has radius 0.95 cm and carries charge 0.090 uC. If the two spheres were suddenly connected by a thin wire, how much charge would move along it? This is a question that I have been...
  5. A

    Electric Field in Gaussian Spheres: Equilibrium and Charge Distribution

    Homework Statement Consider a metal sphere and spherical shells. The innermost one is solid with radius R_1. A spherical shell surrounds the sphere and has an inner radius R_2 and an outer radius R_3. The sphere and shell are again surrounded by a shell of inner radius R_4 and outer radius...
  6. S

    Circular motion of identical spheres in space

    Hey everyone, I have this question that does not make much sens to me and I can't find any clue on the internet. Find the shortest possible periode of revolution of two identical gratitating solid spheres which are in circular orbit in free space about a point midway between them. (You can...
  7. N

    Exploring the Relationship Between Parallel Capacitor Plates & Spheres

    This isn't a problem out of my book, just something I noticed while *doing* a problem on parallel capacitor plates. The problem gave me an area for each plate (1 m^2)and a desired capacitance (1 F)and prompted me to find the distance between the plates. C = q/v (capacitance = charge/potential...
  8. K

    Electric Charge on spheres suspended from an angle

    There is a picture for this question so I will try to describe it to my best ability. Two small spheres, each with mass m=3g and charge q, are suspended from a point by threads of length L=.22m. What is the charge on each sphere if the threads make an angle of 15 degrees with the vertical...
  9. U

    Gauss' Law: Net Electric Field of Two Spheres

    Homework Statement Two nonconducting spheres, of r1=3.0cm and r2=2.0cm, are placed of an x-axis. They have surface charge densities of +6.0mC/m2 and +4.0 mC/m2, respectively, on their outside surfaces. The center of sphere r1 is on the origin and the center of sphere r2 is 10 cm away. What is...
  10. K

    Potential between 2 concentric spheres

    The problem: Find the potential between 2 concentric spheres, of radii a & b, where the potential of the spheres are held at Ca*P3(cos(t)) & Cb*P5(cos(t)), where P3 & P5 are the 3rd & 5th Legendre functions, t is theta & Ca & Cb are constants. The general solution to Laplace with azimuthal...
  11. A

    Question on Proportionate spheres (Help )

    Question on Proportionate spheres (Help!) A spherical balloon is partially blown up and its surface area is measured. More air is then added, increasing the volume of the balloon. If the surface area of the balloon expands by a factor of 9.4 during this procedure, by what factor does the radius...
  12. S

    How are the number of ball bearings in a roller bearing determined?

    Six circles fit tightly around one all of equal length, 12 spheres fit tightly around one sphere all of equal diameter. How many circles can fit around one which is 6 times the other circles diameter? How many spheres can fit around one sphere which is 6 times the diameter of the others?
  13. N

    Resonant frequency and circumference of spheres

    Does the electromagnetic or acoustic resonant frequency of a hallow spherical object ever equal the circumference of that object? If not what are the formulas to calculate this? Thanks in advance.
  14. Y

    Calculating Electric Field of Concentric Spheres

    We have two thin concentric conducting spheres r1 and r2. THe spheres are connected with a power source which supplies emf of epsilon_0. The smaller sphere is connected to the positive pole of the power supply and the larger sphere is connected to the negative pole. Using Gauss Law find the...
  15. A

    Capacitance of parallet plate with dielectric spheres in between

    I want to calculate the capacitance of a system consisting a parallel plate and dielectric spheres of different radius and dielectric strength in between the plates. please give some mathematical derivation. I really need to know it,my career depends on it. Please help me. :) thanks &...
  16. S

    Ratio of potentials and charges on two spheres

    Homework Statement Consider two "solid" conducting spheres with radii r1= 4 and r2= 1. I.E., r2/r1= 1/4. The two spheres are separated by a large distance so that the field and the potential at the surface of sphere #1 only depends on the charge on #1 and the corresponding quantities on #2...
  17. M

    Moment of Inertia and two uniform solid spheres

    Homework Statement Two uniform solid spheres of mass M and radius R0 are connected by a thin (massless) rod of length 1.6R0 so that the centers are 3.6R0 apart. (a) Determine the moment of inertia of this system about an axis perpendicular to the rod at its center...
  18. B

    Finding Electric Forces Between Identical Spheres

    Homework Statement Two identical conducting small spheres are placed with their centers 0.300m apart. One is given a charge of 12.0 nC and the other a charge of -18.0 nC. a) Find the electric force exerted by one sphere on the other. b) Next, the spheres are connected by a conducting wire...
  19. K

    Universal Gravitation and spheres

    Two spheres are released from rest when the distance between their centers is 12R. Sphere 1 has mass M and radii R while sphere 2 has mass 2M and radii 3R. How fast will each sphere be moving when they collide? Assume that the two spheres interact only with each other. (Use G for gravitational...
  20. C

    Electric Potential and Spheres

    Two unequally sized metal spheres are each charged. A wire is connected from one sphere to the other. When the wire is removed, the spheres will have the same potential. T/F? The answer is true (I looked up the key), but I do not understand why. I know that the spheres, due to being...
  21. G

    Gravitational force among 4 spheres

    Homework Statement Four 7.5kg spheres are located at the corners of a square of side 0.70 m. Calculate the magnitude of the gravitational force exerted on one sphere which is in left and down corner of the square by the other three. Homework Equations F_tot = F_2 + sqrt(2) * F1 The...
  22. V

    Two small insulating spheres with radius

    Homework Statement Two small insulating spheres with radius 5.50×10−2 m are separated by a large center-to-center distance of 0.510 m. One sphere is negatively charged, with net charge -2.20 \mu C, and the other sphere is positively charged, with net charge 4.05 \mu C. The charge is...
  23. N

    Two nonconducting spheres problem

    Homework Statement Two nonconducting spheres have a total charge of 13.4 μC. When placed 0.362 m apart. the force of repulsion is 2.777 N. What is the value of the greater charge (Give your answer in coulombs)? Homework Equations The Attempt at a Solution
  24. A

    Two thin conducting spheres

    Homework Statement two thin conducting spheres, one inside the other. They are both centered about the same point. The outer sphere has a total charge Q and radius R2 and the inner sphere has a total charge -Q and radius R1. The magnitude of the charges is Q = 500 nC, and the radii are R1 =...
  25. R

    Finding the charges on surfaces (hollow spheres)

    Dear all, Two hollow conducting spheres have a common center O. The dimensions of the spheres are as shown (attached above). A charge of −200 nC is placed on the inner conductor and a charge of +80 nC is placed on the outer conductor. The inner and outer surfaces of the spheres are...
  26. P

    How Do Cube Root Numbers Relate to the Fraction 1/8 in Determining Pitch?

    Dose anyone know the relationship of cube root numbers and the fraction of 1/8 "Assuming a body of a size represented by X has a pitch of 1024 per second, then a pitch of 2048 (double 1024) per second will be produced by a body having a volume of some mean between 1/8 of X and the cube root of...
  27. tony873004

    Electric field from concentric spheres

    Two concentric spherical surfaces with radii R1 , R2 each carry a total charge Q. What is the electric field between the two shells? I don't know what kind of answer they are expecting. Do I just describe it? Here's my attempt: The field lines from the inner shell will point away from...
  28. G

    Solving for Electron Transfer Between Charged Spheres

    [SOLVED] Charged Spheres Homework Statement Two small aluminum spheres, each of mass 0.0250 kilograms, are separated by 80.0 centimeters. How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude 1.00x10^4...
  29. L

    Are the ions at the edge of an ionic crystal complete spheres?

    or are they 1/8 of a sphere at the corners and 1/4 of a sphere at the edge?
  30. H

    Gravitational Tendency of Disks & Spheres

    Hi! Can someone illuminate why there are gravitational tendency in larger scale to form disks (galaxies, solar systems, accretion disks) whereas all smaller scale bodies (planets etc.) are spherical? What about the spherical halos in the galaxies, is just "unorganized matter" which will...
  31. H

    Oblique impact of smooth spheres?

    1. A sphere of mass m impinges obliquely on a sphere of mass M, which is at rest. The coefficient of restitution between the spheres is e. Show that if m=eM, the directions of motion after impact are at right angles 2. Coefficient of restitution - 3. I really don't think I have a...
  32. S

    What is the repulsive force pushing these two spheres apart?

    Homework Statement At the point of fission, a nucleus of 235U with 92 protons is divided into two smaller spheres, each with 46 protons and a radius of 5.9x10^-15m. What is the repulsive force pushing these two spheres apart? Homework Equations F = k(qi)(q2)/d^2 The Attempt at a...
  33. P

    HELP Gravitational force and spheres. (prob easy)

    So I'm completely lost...here's the problem. There's a small ball inside an empty sphere. How can I prove this sphere doesn't attract the small ball gravitationally, independently of the position of the ball inside the sphere?? Also, how can I use the result from above to find the gravity...
  34. L

    Two Conducting Spheres Connected

    When a charge is applied to a conducting sphere and connected to another conducting sphere by an ideal thin wire (infinite distance apart), the potential at the surface of each sphere is the same. However, that means (for spheres of different radii) that the charge density on each sphere...
  35. A

    Gauss's Law/Energy Problem with Concentric Spheres

    Hi there. I'm new to PF, so please correct me on any mistakes in presenting my question. I'm just hoping to get some direction in doing this problem right. Homework Statement Concentric spherical shells of radius a and b, with b > a, carry charge Q and -Q, repsectively, each charge uniformly...
  36. M

    Capacitance of concenctric spheres

    The figure below shows six concentric conducting spheres, A, B, C, D, E, and F having radii R, 2 R, 4 R, 6 R, 7 R, and 9 R, respectively. Spheres B and C are connected by a conducting wire, as are spheres D and E. Determine the equivalent capacitance of this system. I understand that spheres...
  37. X

    Two uniformly charge spheres are firmly fastened

    Two uniformly charge spheres are firmly fastened to and electrically insulated from frictionless pucks on an air table. The charge on sphere 2 is three time the charge on sphere 1. Which force diagram correctly shows the magnitude and direction of the electrostatic forces: Explain <...
  38. M

    System of conducting spheres

    Was curious how some of you guys would solve this problem... Three conducting spheres of radii a, b and c are connected by negligibly thin conducting wires. Distances between the spheres are much larger than their sizes. The electric field on the surface of a is measured to be E_{a}. What is...
  39. B

    Charged Aluminum Spheres: Determining Number of Electrons

    [SOLVED] Charged Aluminum Spheres Homework Statement Two small aluminum spheres, each of mass 0.0250 kilograms, are separated by 80.0 centimeters. How many electrons does each sphere contain? (The atomic mass of aluminum is 26.982 grams per mole, and its atomic number is 13.) Homework...
  40. G

    Charged Aluminum Spheres: Calculating Electrons and Attractive Force

    I'm having difficulty with a problem on MasteringPhysics (such wonderful software...) and as a last resort I'm posting on here. This is, I'm sure, a really simple problem but I'm getting no kind of feedback from MP and there isn't an example problem like this in the book. Homework Statement...
  41. G

    Solving for Charge Distribution on Charged Aluminum Spheres

    I'm having difficulty with a problem on MasteringPhysics (such wonderful software...) and as a last resort I'm posting on here. This is, I'm sure, a really simple problem but I'm getting no kind of feedback from MP and there isn't an example problem like this in the book. The Problem Two...
  42. malawi_glenn

    Max Packing Fraction of Hexagonal Unit Cell Volume w/ Hard Spheres

    Homework Statement Calculate the maximum packing fraction of the unit cell volume that can be filled by hard spheres in the Hexagonal structure Relevant eq: Volume of spheres is number of lattice points multiplied with the maximum volume of one sphere. The Attempt at a Solution I...
  43. K

    Gravitation of two iron spheres homework problem

    Consider two iron spheres, each of diameter 100mm, which are just touching. At what distance r from the center of the Earth will the force of mutual attraction between the contacting spheres be equal to the force exerted by the Earth on one of the spheres? Here's my work... d = distance...
  44. R

    Net Electric Force on Charged Spheres

    Homework Statement Three spheres, each with a negative charge of 4.0 X 10^6 C, are fixed at the vertices of an equilateral triangle whose sides are 0.20 m long. Calculate the magnitude and direction of the net force on each sphere. Homework Equations Fe = kq1q2 / r^2 The Attempt at...
  45. P

    Two Conducting Spheres Problem - Applying

    Homework Statement 9. Two identical conducting spheres, fixed in place attract each other with an electrostatic forces of 0.108 N when their center-to-center separation is 50.0 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each...
  46. F

    Coulomb's Law and spheres Problem

    Homework Statement Of the charge Q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated as particles. For what value of q/Q will the electrostatic force between the two spheres be maximized? Homework Equations...
  47. A

    Calculating Buoyancy and Tension in a 2-Sphere System in an Ocean

    Homework Statement Two spheres, with volume 0.1m^3, and masses M1=200kg and M2=15kg, are connected by a thin wire. They are dropped into the ocean (assume Rho=1000kg/m^3) and allowed to sink Homework Equations The Attempt at a Solution I know buoyancy = Rho * g * V Buoyancy +...
  48. H

    Two spheres with given potential, what's their charge?

    Hi This shouldn't be very difficult: I have two spheres (made of Cu -> conductors) with given radius a (both), the distance of their centers is h. Now I know that the potential on the first sphere is zero and on the other 1000 Volts (the potential at infinity is zero). I must determine the...
  49. J

    Two charged suspended spheres

    Homework Statement Two small charged spheres (S1 and S2) are suspended from a common point P by cords of equal length l, as shown in the figure below, and make small angles, a1 and a2, with the vertical through P. The charge on S1 is Q and the charge on S2 is 2Q (same polarity). The mass of S1...
  50. W

    Electrostatic potential energy for concentric spheres

    Two concentric metal spheres have radii r_1 = 10 cm and r_2 = 10.5 cm. The inner sphere has a charge of Q = 5 nC spread uniformly on its surface, and the outer sphere has charge -Q on its surface. (a) calculate the total energy stored in the electric field inside the spheres Hint: You can treat...
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