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. K

    How Do You Calculate the Intersection of Two Spheres in 3D Integrals?

    Hello, I am calculating some integrals in 3 dimensions. However, the difficulties of such integrals lie in the determination of the boundaries of the variables integrated over. \int_{C} d^{3}\vec{t} e^{-\vec{s}.\vec{t}} For example, if we consider (C) as the region of the intersection of 2...
  2. J

    Tough Concentric Spheres with mixed Dielectrics and a air-gap Problem

    1. Homework Statement 1. Homework Statement I have concentric spheres with mixed dielectrics. There is an air-gap between the spheres which consist of a permittivity ε0. The radius' are a, b and c and the permittivities of the dielectric portions are ε1 and ε2. An image is attached! What...
  3. J

    Tough Concentric Spheres with mixed Dielectrics and a air-gap Problem

    Homework Statement I have concentric spheres with mixed dielectrics. There is an air-gap between the spheres which consist of a permittivity ε0. The radius' are a, b and c and the permittivities of the dielectric portions are ε1 and ε2. An image is attached! What are the potentials in the 4...
  4. O

    Field between 2 conducting spheres in electric field

    Hi, I tried to make some simulations of two conducting spheres in a constant electric field. The simulations seem to indicate that the electric field in the gap increases with increasing diameter of the spheres at a constant gap distance. Does this make sense? I expected just the reverse. What...
  5. PeterDonis

    Family of nested spheres in Schwarzschild spacetime

    On the Wikipedia page on Schwarzschild coordinates... http://en.wikipedia.org/wiki/Schwarzschild_coordinates ...it talks about a "family of nested spheres": each surface of constant t and r is a 2-sphere (i.e., setting dt = dr = 0 and r = constant in the metric results in a Euclidean...
  6. H

    Why Is Thermal Expansion the Same for Solid and Hollow Spheres?

    Explain why the thermal expansion of a spherical shell made of a homogeneous solid is equivalent to that of solid sphere of the same material. I guess these equations would be of some help. (ΔA)=A*2α*(ΔT) α→ Coefficient of linear expansion. A→ Area T→ Temperature (ΔV)=V*3α*(ΔT)...
  7. L

    Two conducting spheres connected by conducting wire.

    Homework Statement Two spherical conductors of radii r1 and r2 are separated by a distance much greater than the radius of either sphere. The spheres are connected by a conducting wire. The charges on the sphere are in equilibrium are q1 and q2 respectively, they are uniformly charged. Find...
  8. Z

    Conservation of Energy with Metal Spheres

    Homework Statement Two small metal spheres with masses 2.0g and 4.0g are tied together by a 5.4-cm-long massless string and are at rest on a frictionless surface. Each is charged to +2.1 μC . The string is cut. What is the speed of each sphere when they are far apart? Homework Equations...
  9. E

    Electric field of concentric conducting spheres

    Why is the Qenclosed zero if there's a charge inside the shell? Homework Statement A solid conducting sphere of radius a is placed inside a conducting shell which has an inner radius b and an outer radius c. There is a charge q1 on the sphere and a charge q2 on the shell. Find the...
  10. V

    Calculating Drag Force on Spheres for Airsoft/Paintball

    I maintain a small piece of software for the Airsoft/Paintball community. I include some basic energy and velocity calculations but I have also as of a few versions back started including more "theoretical" calculations like how far a BB will travel and that sort of thing. I want to improve the...
  11. Telemachus

    Concentrical conducting spheres with charge distribution and dielectric

    Hi. I have this problem, which I must solve. It says: two concentric conducting spherical shells, of radius a and b (a<b), are charged at Q and -Q respectively. The space between the spheres is filled at its half by an hemisphere of dielectric with dielectric constante ε. a)Find the field for...
  12. Telemachus

    Electrostatics, potential between and outside concentric spheres

    Hi there. I have this problem which I was trying to solve, but I couldn't fit the boundary conditions. The exercise says: Two conducting spherical shells with radii a and b are concentrically disposed and charged at potentials φa and φb respectively. If rb>ra, find the potential between the...
  13. G

    Adding Spheres: How to find the new radius?

    Okay this seems like a really simple question. Basically I'm adding together 8 spheres (like raindrops coalescing into one bigger drop) and I'm getting two different answers for the new radius. Each individual drop is identical. I start by expressing the new volume in terms of the...
  14. N

    When two spheres intervine - very hard 3d geometry and vectors problem

    Homework Statement Sphere with P as centre has equation (x-5)^2 + (y-9)^2 + z^2 -100 = 0 Sphere with Q as centre has equation (x-1)^2 + (y+3)^2 + (z-3)^2 -49 =0 These spheres intervine with each other. Find the surface area of the object limited by the two spheres. The Attempt at a Solution...
  15. R

    Touching Conducting Spheres of Different Size

    Homework Statement Two uncharged conductors A and B are of different sizes. They are charged as follows: 1. A is charged via an electrostatic generator to charge q 2. A is briefly touched to B. 3. Steps 1 and 2 are repeated until the charge on B reaches a maximum value. If the...
  16. C

    How to find energy stored between two spheres?

    Homework Statement A spherical conductor of radius 7.00 mm carries a surface charge density of 9.00 μC/mm2. A second hollow, concentric, spherical conductor has an inner radius of 7.09 mm. How much stored energy is there between the spheres? Homework Equations C=Q/V A=4pi(r^2)...
  17. T

    Gravitational Force on three spheres

    Homework Statement Three uniform spheres are located at the corners of an equilateral triangle. Each side of the triangle has a length of 0.550 m. Two of the spheres have a mass of 2.85 kg each. The third sphere (mass unknown) is released from rest. Considering only the gravitational forces...
  18. R

    Need some clarification on conducting spheres

    Question: Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.141 N when their center-to-center separation is 67.0 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an...
  19. F

    Finding the initial and final charge of two spheres

    Homework Statement Two identical small metal spheres with q1 > 0 and |q1| > |q2| attract each other with a force of magnitude 70.2 mN, as shown. The spheres are then brought together until they are touching. At this point, the spheres are in electrical contact so that the charges...
  20. C

    Can someone answer a quick question for me about e field by spheres.

    So let's say a sphere has radius R and you want to find the e field where R>r and R is equal to or greater than r. would the e field for R>r just be 0? Wouldn't that also mean it's 0 for R is equal to or greater than r, or does it change because it's EQUAL or greater?
  21. R

    Flux through concentric spheres

    Homework Statement Charge of uniform surface density (4.0 nC/m2) is distributed on a spherical surface (radius = 2.0 cm). What is the total electric flux through a concentric spherical surface with a radius of 4 cm? Homework Equations \Phi = E 4 \pi r^2 = \frac{q}{\epsilon_0}...
  22. R

    Finding Charge of Two Charged Spheres

    Homework Statement Two hard rubber spheres, each of mass m = 15.1 g, are rubbed with fur on a dry day and are then suspended with two insulating strings of length L = 4.90 cm whose support points are a distance d = 2.97 cm from each other as shown in the figure below. During the rubbing...
  23. P

    Electrostatic potential of two spheres

    Homework Statement Two identical conducting spheres, with a radius of 15.0 cm, are separated by a distance of 10 m. What is the charge in each sphere, if the potential of one sphere is +1500 V, and the potential of the other one is -1500 V? Which assumptions did you make? Homework Equations...
  24. S

    Solving Ellipses on Spheres: Finding Point Sources in Galaxies

    I have galaxies in the shapes of ellipses, and I have point sources around these galaxies. I need to find a formula to determine whether or not the point sources are within a specific galaxy or outside. It would be extremely simple with circles, but I can't figure it out with ellipses...
  25. A

    Failing point of a lexan spheres?

    Hi I'm a newby and have a project way out of my depth where a wrong calculation will be fatal... I need calculations of : 1.how far a 2500mm and 3000mm sphere of lexan plastic 50mm thick can be submerged in sea water before it will implode/fail (in meters)? See data below. 2.From what...
  26. E

    Find Equations for 2 spheres that are tangent to the planes

    Homework Statement Find the equations for two spheres that are tangent to the plane x+y-z=3 and x+y+z=9 and the line x=t , y=2t, z=3t passes through its center. Preface: This problem was on a test I took yesterday. My professor handed it back today. The relevant equations and work are what...
  27. A

    Two Spheres, Two Humans: Who is Older?

    Let there be two spheres in free space. Also there are two humans on each of them. Now the spheres move apart and come together again(like a harmonic oscillator), When they move apart , wrt one human the other is moving into lesser grav field and when he comes back he should have aged less...
  28. O

    Electrostatic force between to spheres

    given to solid half charged sphere Insulators. In which state the mutual net force is bigger: A/B/the same
  29. M

    Integration Over Spheres in R^d

    Homework Statement I'm a bit confused at a single step in a proof. Let \phi \in L^1(\mathbb{R}) \cap C(\mathbb{R}^d) be a function such that for any \omega \in \mathbb{R}^d , \phi(\omega) = \psi(||\omega)|| . That is, the function depends solely on the norm of the vector input, so it is...
  30. F

    Problem on distribution of charges between charged/uncharged spheres

    Homework Statement 2 Spherical conductors B and C having equal radii and carrying equal charges repel each other with force F. Another conductor A having same radius as B but uncharged is brought into contact with B, and then C and then removed from both. Find the new force of repulsion...
  31. R

    Final velocity of 2 spheres attracted by gravity and electrostatic charge

    Homework Statement Two insulating spheres having radii 0.22 cm and 0.42 cm, masses 0.16 kg and 0.47 kg, and charges −4 μC and 5 μC are released from rest when their centers are separated by 1 m. How fast is the smaller sphere moving when they collide? Answer in units of m/s...
  32. L

    A simple question regarding spheres and spherical shells

    Moved my question to Intro Physics. Mods feel free to delete.
  33. B

    Conducting spheres Gauss's law

    Homework Statement There are two conducting spheres, one hollow outer sphere which originally had +60nC of charge on it, and a smaller inner sphere enclosed by the hollow outer sphere which contains +20nC of charge. Homework Equations INT(E.DA) = Qenclosed/epsilon0 The Attempt at a...
  34. A

    Mathematician Wins Abel Prize for Exotic 7-Dimensional Spheres

    Hey guys I heard an interesting segment on NPR today regarding a mathematician that received the Abel prize for his work in explaining and proving "the existence of exotic seven-dimensional spheres". http://www.npr.org/2011/03/24/134832727/American-Mathematician-Wins-Abel-Prize Any...
  35. E

    What is the constant density of a solid sphere given its radius and mass?

    Homework Statement The density of a solid sphere of radius R=10cm and mass M=15kg varies with distance from the center according to the equation p=po*e^(r/R). Determine the constant po. Homework Equations density= mass over volume. The Attempt at a Solution Change density to...
  36. M

    Van der Waals and electrostatic force between polystyrene spheres

    Homework Statement Compare gravitational, electrostatic and van der Waals forces between two 100nm polystyrene spheres which are separated by a) one micrometer b) one millimetre and c) one centimetre Homework Equations Gravitation and electrostatic equations are standard. The...
  37. P

    Calculating Charge of Two Spheres in Equilibrium

    Homework Statement Two plastic spheres each of mass 100.0 mg are suspended from very fine insulating strings of length 85 cm. When equal charges are placed on the spheres, the spheres repel and are in equilibrium when 10 cm apart. (a) What is the charge on each sphere? Homework Equations...
  38. J

    How Does Connecting Two Spheres Affect Charge Distribution?

    Homework Statement In the figure, r1 = 2 and r2 = 8 cm. Before the conducting spheres are connected by the wire a charge of 6.0×10-7 C is placed on the smaller sphere while the larger sphere is uncharged. Calculate the charge on the smaller sphere after the wire is connected. Assume that the...
  39. L

    Potential Energy of two spheres

    Homework Statement Two small metal spheres, A and B, of mass mA = 5.5 g and mB = 9.4 g have equal positive charges of 8 μC. The spheres are connected by a non-conducting string of negligible mass and with length d = 1 m, which is much greater than the radii of the spheres. a) What is the...
  40. N

    Concentric Spheres: Learn About Shapes

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  41. S

    Consider two metal spheres of radii

    Homework Statement Consider two metal spheres of radii r1 = R and r2 = 2R, both charged to the same potential V0. a) What is the ratio n1/n2 of their surface charge densities?Homework Equations n(eta) = charge/area Er = -dV/drThe Attempt at a Solution a) n1/n2 = Q/(4*pi*R2) / Q/(16*pi*R2) = 4...
  42. S

    Tracking the motion of spheres

    Hi, I'm looking to do random, silly stuff with the Coriolis effect, mainly just confirming what theory predicts, using a simple rotating turntable. My hope in doing that was to use a typical, average consumer camera, film the motion in question from above, with markers for frames of...
  43. R

    Surface point of collision of two spheres?

    Hi! I need to calculate the point (or average point) of actual collision between any two spheres of any size and mass in any orientation in space. I understand that I can zero things out a bit by assuming that one sphere is centered at (0,0,0). OK, I know how to calculate collision...
  44. B

    Two Hanging Spheres: Calculating Electrical Force

    Homework Statement Two tiny conducting spheres with a mass of 14 gm each are hanging from non-conducting threads of length 60 cm such that they are 6 cm apart. What is the electrical force between the spheres? Homework Equations f = m*g*tan(theta) The Attempt at a Solution 0.6^2...
  45. jegues

    What Happens When Identical Charged Spheres Make Contact?

    Homework Statement See figure attached from problem statement. Homework Equations The Attempt at a Solution I've never really done a question of this type so I'm slow to get going. I'm not sure what is happening when he touches the spheres with the others. He first touches...
  46. N

    How Do Suspended Charged Spheres Behave?

    Homework Statement This is a long one... Two small spheres with mass m are suspended with insulating threads of length L from a common point. Uncharged, the spheres hang so they touch each other. When given the same charge q they repel each other and hang d distance apart. Assume d is...
  47. R

    Rotational Motion - Two spheres orbiting around a common barycenter

    Homework Statement Two spherical bodies with equal mass m1=m2=1000 kg are orbiting around a common barycenter in a weightless environment because of the gravitational attraction. A: Show how the frequency of orbiting is related to the distance between two bodies. B: We connect two...
  48. M

    Question on charged spheres and shells

    Homework Statement Suppose we are given a metallic sphere with charge Q1 and electric potential V1 and radius a. Then it is surrounded by a metallic spherical shell with charge Q2 and electric potential V2 with inner and outter radius b and c. What is the charge and the electric potential...
  49. C

    Two cocentric conducting spheres

    Homework Statement Two concentric conducting spheres of radii a and b (a < b) are separated into four hemispheres by a nonconducting sheet. The upper ( 0 < θ < π / 2 ) outer (radius b) and lower ( π / 2 < θ < π ) inner (radius a) hemispheres are kept at potential +V. The upper inner and lower...
  50. I

    Two spheres falling through water..terminal velocity?

    Homework Statement A glass sphere of diameter 1.75 cm and density 2.5 g/cm^3 falls through water with a terminal velocity of 0.3m/s. A wooden sphere of the same diameter and density 0.85 g/cm^3 is released from the bottom of a tank of water. Determine the terminal velocity with which the...
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