Spheres Definition and 504 Threads

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. R

    Why are spheres and triangles so important?

    I've notice that our eye balls are spheres, our Earth is a sphere and our sun is a sphere.. Now that makes me wonder. If our universe is a sphere, i already know scientist think so, but its still something to even think more into. Now this is the big part, triangles are important as well. Like a...
  2. R

    Two Spheres Launched Horizontally

    Homework Statement Two spheres are launched horizontally from a 1.1 m-high table. Sphere A is launched with an initial speed of 4.5 m/s. Sphere B is launched with an initial speed of 1.5 m/s. -What is the time for the sphere A to hit the floor? -What is the distance that sphere A...
  3. B

    Capacitance of a body versus capacitance of inscribed and circumscribed spheres

    just out of curiosity - it seems evident to me that the capacitance of a conductive body should be between the capacitance of an inscribed sphere and the capacitance of a circumscribed sphere. But I can't figure out how to prove this. If you prove this, it follows that the energy required to...
  4. C

    Charged concentric metal spheres

    Homework Statement Two concentric metal spheres have radii R1 =10cm and R2=10.5cm. The inner sphere has a charge of Q=5 nC spread uniformly over its surface, and the outer sphere has charge −Q spread uniformly over its surface. Calculate the total energy stored in the electric field...
  5. N

    What is the charge ratio between two equipotential spheres?

    Homework Statement A spherical potential conductor of radius R1 is charged to 20kV. When it is connected by a long, fine wire to a second sphere faraway. its potential drops to 12kV. What is the radius of the second sphere. Homework Equations V=kq/r The Attempt at a Solution So...
  6. P

    Solving GRE Spheres: Find h0 from h

    "Two small spheres of putty, A and B, of mass M and 3M, respectively, hang from the ceiling on strings of equal length l. Sphere A is drawn aside so that it is raised to a height h0 and then released. Sphere A collides with sphere B; they stick together and swing to a maximum height h equal to "...
  7. S

    Why do planets of our solar system orbit in rings not spheres?

    I was looking at this link: http://en.wikipedia.org/wiki/File:Universe_Reference_Map_%28Location%29_001.jpeg" and wondered to myself why the asteroid belt just outside of Mars is a ring...as opposed to a sphere. Then I thought, why do all the planets seem to orbit the sun on a similar plane...
  8. B

    Two Spheres connected by a wire.

    Charge is placed on two conducting spheres that are very far apart and connected by a long thin wire. The radius of the smaller sphere is 5 cm and that of the larger sphere is 12 cm. The electric field at the surface of the larger sphere is 830 kV/m. Find the surface charge density on each...
  9. T

    Balancing Charges on Identical Spheres

    Homework Statement Two identical small metal spheres initially carry charges q_1 and q_2. When they're x=1.0m apart, they experience a 2.5N attractive force. Then they're brought together so charge moves from one to the other until they have the same net charge. They're again placed x=1.0m...
  10. C

    Volumes of Spheres around a Box

    Homework Statement Let B be a solid box with length L, width W, and height H. Let S be the set of all points that are a distance at most 1 from some point of B. Express the volume of S in terms of L,W, and H. Homework Equations 4/3(pi)r The Attempt at a Solution I have gotten to...
  11. T

    How many apples can I fit in a box using close packing of spheres?

    1. How many apples can you put into a box in the following dimensions: Width: 1.25 meters Length: 3 meters Hight: 2.1 meters 2. Close packing of spheres 3. All I could find is the efficiency of close packing of spheres in face-centered cubic, which is 0.74048. Is there an...
  12. M

    What is the volume between two intersecting spheres with given equations?

    Homework Statement Find the volume of the solid that lies inside both the spheres x^2+y^2+z^2=4 x^2+y^2+z^2+4x-2y+4z+5=0 Homework Equations none The Attempt at a Solution I completed the square on the 2nd equation to get (x+2)^2 + (y-1)^2 + (z+2)^2 = 4 So I have the two...
  13. C

    Potentials of Hollow and Solid Spheres

    A hollow spherical conductor of radius 3.00 cm has 6.00 nC of charge distributed uniformly over its surface. (a)What is the electric potential at the center of the sphere(in volts)? (b) If the conductor is solid rather than hollow, what is the potential at the center of the sphere? I know...
  14. A

    Force between two oppositely charged conducting spheres

    ...if the spheres are separated by a large distance - one with charge Q, the other with charge -Q - isn't the force between them just the same as the force between two oppositely charged point charges, since the electric field produced by one of the spheres "looks like" the field of a point...
  15. D

    What Happens to the Speed and Proximity of Two Charged Metal Spheres in Motion?

    Homework Statement A small metal sphere, carrying a net charge of q_1 = -2.60 \mu C, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q_2 = -7.70 \mu C and mass 1.40 g, is projected toward q_{1}. When the two spheres are 0.800 \rm m...
  16. A

    Capacitance of two conducting spheres

    Homework Statement We're supposed to find the capacitance of a system of two conducting spheres, one of radius r_1 and charge Q, the other of radius r_2 and charge -Q, separated by a distance L (this is the distance between their centers) that's very large compared to either r_1 or r_2.Homework...
  17. T

    What Is the Electric Field in the Overlapping Region of Two Charged Spheres?

    Homework Statement Two spheres, each radius R and carrying uniform charge densities +rho and -rho are placed so that they partially overlap. Call the vector from the positive center to the negative center dhat. Show that the field in the region of overlap is constant and find its value.Homework...
  18. O

    What is the net electric field at a point between two charged spheres?

    Homework Statement Figure 23-30 shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +6.0 µC/m2 on its outer surface and radius 3.0 cm. Shell 2 has uniform surface charge density -3.8 µC/m2 on its outer surface and radius 2.0 cm. The shell centers...
  19. J

    Vectors, Planes, and Spheres, OH MY (Help mep lease)

    Homework Statement Find an equation of the plane that contains both the center and "south pole" of the sphere (x-3)^2+(y-2)^2+(z-3)^2 = 400 and is parallel to the line given in vector form by r(t) = [-43*t-82, -44*t+39, -84*t+94]. Write your answer in the form ax + by + cz = d Homework...
  20. D

    Two identical like-charged conductive spheres are placed very close

    Homework Statement Two identical like-charged conductive spheres are placed very close to each other, the charges willl redistribute themselves on the sphere's surface with an effective center-to-center distance rc so as to approximately satisfy the Coulomb's law, F = ke q1 q2 / (rc)^2. Is the...
  21. L

    EM field between 2 superimpose spheres

    Homework Statement Problem: 2 spheres each one of them with a radius R and uniformly charged with ro+ and ro-, are situated in a way they superimpose partially ( see figure). Let be "d" the vector from the positive center to the negative center...
  22. U

    Modeling a lense using the intersection of two spheres

    Hi everybody! I am trying to model a lense shape using two circles of radii R and r, with one at the origin and the other offset upwards vertically by distance D. D must be less than R + r, but it must be greater than the larger of R or r. Thus, I have two equations, and the region of their...
  23. Nabeshin

    Maximizing Spheres: How Many Can Fit Around One?

    Suppose I have a bunch of spheres, all with the same radius r. Now, take one sphere and set it aside in R3. The question then, is, how many spheres can I place around this sphere such that at least one part of them is touching the central sphere? I've arrived at a very strict upper bound of...
  24. I

    Volume of intersection of spheres

    Homework Statement Find the volume of the intersection of two spheres of radius 2, give that the center of each sphere lies on the surface of the other. The Attempt at a Solution I was trying to do this problem with volumes of revolution. I drew two circles, one with a center at -1, the...
  25. A

    What Was the Initial Charge on Sphere A in the Conducting Spheres Problem?

    Homework Statement Figure 21-36 shows four identical conducting spheres that are actually well separated from one another. Figure 21-36 Sphere W (with an initial charge of zero) is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B (with an initial...
  26. M

    Moment of Inertia of Solid and Hollow Spheres using Disks and Rings Respectively

    Whilst following my textbooks advice and "proving to myself that the inertia listed are true" I considered the Moment of Inertia of a hollow sphere by adding up infinitesimally thin rings: dI = y^2 dm = y^2 \sigma dS = y^2 \sigma 2\pi y dz = 2\pi y^3 \sigma dz This didn't work...
  27. S

    Charged Spheres +quadratic equation

    Homework Statement Two small, positively charged spheres have a combined charge of 14.0 × 10-5 C. If each sphere is repelled from the other by an electrostatic force of 0.9 N when the spheres are 1.7 m apart, what is the charge (in Coulombs) on the sphere with the smaller charge? Homework...
  28. O

    Currents and charge between spheres

    Homework Statement Consider two small conductive spheres in radius a and b located far from each other. In t=0 "a" sphere charged with Q and "b" sphere neutral. We connect the spheres by wire with resistance R. Find the charge on each sphere as a function of time. Homework Equations...
  29. O

    Repulsion between two small spheres

    Homework Statement Calculate the force of electric repulsion between two small spheres placed 1.0 m apart if each has a deficit of 1.0 x 10^8 electrons. Homework Equations N = q/e qe = mg q = mg / e q = mgr / Vb e = 1.602 x 10^-19 C. k = 9 x 10^9 - not sure if relevant or not. Fe = qe...
  30. S

    Probability of finding an electron betweeen two spheres of radii?

    Homework Statement For a hydrogen atom in a state with n=2 and l=0, calculate the probability of finding the electron between two spheres of radii r = 5.00a0 and r = 5.01 a0. Homework Equations As stated above, calculate the probability of finding the electron in the given spheres of...
  31. S

    Reaction diffusion problem concentric spheres

    Hello, I am trying to (numerically) solve the following reaction-diffusion equation for the probability density of the a pair, \rho (\vec{r}_1,\vec{r}_2): \dot{\rho} (\vec{r}_1,\vec{r}_2,t) = D_1 \nabla^2_1 \rho (\vec{r}_1,\vec{r}_2,t) + D_2 \nabla^2_2 \rho (\vec{r}_1,\vec{r}_2,t) - k...
  32. Z

    Classification of Vector Bundles over Spheres

    This is a question from Hirsch's Differential Topology book: show that there is a bijective correspondence between K^k(S^n) \leftrightarrow \pi_{n-1}(GL(k)) , where K^k(S^n) denotes the isomorphism classes of rank k vector bundles over the sphere. The basic idea is that any vector bundle...
  33. S

    Concentric spheres and electrostatic induction

    Homework Statement There's three thick, conducting concentric spheres with radii R1, R2, R3 (R1 < R2 < R3) with charge Q1, Q2, Q3 respectively. a.- The middle one is now wired to the ground. Find its net charge b.- The internal and external spheres are now wired. Find the distribution of all...
  34. E

    Surface Homeomorphism Between Cubes and Spheres?

    Is it true that the surface of a (hyper)cube in Rn is homeomorphic to Sn-1? Or only for particular n?
  35. quasar987

    Homology of spheres from the M-V sequence

    Hi everyone. Take the open sets A=S^1 - N and B=S^1 - S, that is, the circle minus the north and south pole resp.. Noting that AnB=S^0 and that A and B are contractible, the Mayer-Vietoris sequence in reduced homology for this decomposition writes, \ldots \rightarrow...
  36. B

    Properties of 6 Dimensional Spheres

    It occurred to me that most unification theories propose at least 6 dimensions, and that the 6th dimension would look like a sphere or a doughnut. For the sake of greater simplicity, I will use a sphere for my question. My question is, if an object were traveling in the 6th dimension, would...
  37. V

    Three spheres attached by conducting wire

    Homework Statement Three conducting spheres of radii a, b and c, respectively, are connected by negligibly thin conducting wires as shown in figure 4. Distances between spheres are much larger than their sizes. The electric field on the surface of the sphere of radius a is measured to be...
  38. E

    How Do You Calculate the Work to Assemble Concentric Charged Spheres?

    I have a problem that I am not sure I am working correctly. There are 2 concentric spheres, the inner of charge -q and radius Ra and outer of charge +q and radius Rb. I am to find the work that is required to put together these two spheres in such a way. Is it enough to find the energy...
  39. S

    Electrical Field of a Charged set of Spheres

    Homework Statement Two spherical shells have a common center. A -1.37 x 10-6 C charge is spread uniformly over the inner shell, which has a radius of 0.0422 m. A +5.86 x 10-6 C charge is spread uniformly over the outer shell, which has a radius of 1.60 m. Find the magnitude of the electric...
  40. D

    Charge on spheres connected by wire

    Homework Statement A total charge of 2.600 C is shared by two metallic spheres A (radius 7.00 cm) and B (radius 5.00 cm) that are connected by a thin wire of length 1.00 m. Find the charge on sphere A. (Note that the influence of sphere B is not negligible.) Homework Equations I...
  41. B

    Two conducting hollow spheres, a point charge and electric field prob

    Homework Statement A point charge is at the center of a conducting hollow sphere, with radius 0.011m, that is within another conducting hollow sphere of radius 0.041m. The point charge is Q0=+4.30e-6 C, the inner sphere has a net charge of Q1=-1.70e-6 C, and the outer sphere has a net charge...
  42. A

    Two spheres, solve for electric field strength

    Homework Statement Two 2.0-cm-diameter insulating spheres have a 6.50 cm space between them. One sphere is charged to + 89.0 nC, the other to - 95.0 nC. What is the electric field strength at the midpoint between the two spheres? Homework Equations Esphere = KQ/r^2 k = 8.99 * 10^9...
  43. S

    Calculating Charges on Uniformly Charged Spheres

    Homework Statement Suppose that the magnitude of the charge on the yellow sphere is determined to be 2q. Calculate the charge q_red on the red sphere. Express your answer in terms of q , d_1 , d_2 , theta and . Hi Guys iv done the first two bits to this problem the sign of the...
  44. A

    Resolving the Problem: Charging Spheres A and B

    Homework Statement Initially, sphere A has a charge of –10e and sphere B has a charge of +20e. The spheres are made of conducting material and are identical in size. If the spheres then touch, what is the resulting charge on sphere A? a) +10e, b) -10e, c) -5e, d) +5e The attempt at a...
  45. P

    Translational friction coefficient of spheres: Biophysics

    Homework Statement Prove that the translation friction coefficient for a sphere (protein) with a molecular weight of 25 kiloDaltons is approximately 60% the translation friction coefficient for a 100 kiloDalton protein sphere. Homework Equations Stoke's Law: f = 6πηr where f =...
  46. B

    Buoyancy of Spheres: max mass added without sinking

    Homework Statement Styrofoam has a density of 300 kg/m3. What is the maximum mass that can hang without sinking from a 40-cm-diameter Styrofoam sphere in water? Assume the volume of the mass is negligible compared to that of the sphere. Homework Equations FB=poVog Volume of sphere...
  47. B

    Solving for Charge Distribution on 2 Conducting Spheres & Rod

    Homework Statement 2 conducting spheres with radii 2 & 3m are connected with a conducting rod of thickness 0.1m & length 0.5m. 500C charge is put on the 2m radius sphere. Find the amount of charge on each sphere & on the rod. Homework Equations The Attempt at a Solution By...
  48. J

    Surface charge distribution of two metal spheres

    Homework Statement A total charge Q is shared by two metal spheres of small radii R1 and R2, that are connected by a long thin wire of length L. Fin (a) the charge on each sphre and (b) the tension in the wire. Source: Haliday 4th edn chapter 26 q. 91, p. 738 The Attempt at a Solution...
  49. W

    How Do You Solve for tanB in an Elastic Collision Problem?

    Homework Statement A sphere of mass m1 traveling at velocity u1 collides elastically with a stationary sphere of m2. The particles move away with v1 and v2 respectively. I'm at part 4, of 5. It asks us to resolve the conservation of momentum equations normal and tangential to the...
  50. C

    Elastic Collision in 2D between 2 Hard Spheres

    Homework Statement By resolving the momentum equations parallel and perpendicular to the incident beam direction, show that α is related to the speed v2 of the recoiling particle by: cos α = m2*v2/(2μ*u1) where μ=m1m2/(m1+m2) Homework Equations See attachment for diagram...
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