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. 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...
  2. C

    Identical Hollow and Solid Spheres

    Homework Statement Two spheres look identical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is which. Homework Equations mgh= ½ m v^2 + ½ I ω^2 where I= 2/3 mr2 for a hollow sphere I=2/5 mr2 for a solid sphere The Attempt...
  3. A

    Two spheres with a conducting wire

    Homework Statement 1. Two solid metal spheres are very far apart: sphere A (radius 44.1 cm) is charged to potential +2,346 Volts; sphere B (radius 63.6 cm) is charged to potential +8,848. Now, a long conducting wire connects the two spheres. When the charge has stopped moving, find the new...
  4. I

    Optics Question -- small glass spheres to couple to fiber optic cables

    Homework Statement Homework Equations I know that yin = 0.7mm, y2 = 0mm, the index of refraction for the sphere is 1.8 and the indices of refraction for the air surrounding it is 1. The Attempt at a Solution Not sure how to even begin with the given information. I was thinking I could...
  5. Rene Manzano

    Need some help with this homework -- Conducting Spheres and Charge

    Hi, I need some help with this homework from my Electromagnetism course. I hope this is the correct place to post this. (Please excuse any potential english mistake I made trying to translate this). Problem 1: Copper (conductor) sphere of radious R with an spheric bubble inside placed at...
  6. Xsnac

    [E&M] Concentrical metalic spheres

    Homework Statement I two concentric metalical spheres r1 =/= r2. What to do to have: a) potential energy = 0 and electric charge =/= 0 b) potential energy =/= 0 and electric charge =0. In eighter one of the spheres. Relevant equations Gauss law. The Attempt at a Solution a) If I charge the...
  7. quantumfunction

    How many Hubble Spheres are in the universe?

    From what I understand, our Hubble's sphere is just relative to Earth and has a diameter of 93 billion light years putting the edge of the observable universe at 46-47 billion light years away. So every object in space will essentially have it's own Hubble's sphere and objects near the edge of...
  8. J-dizzal

    Gravity and superpostion of two spheres

    Homework Statement The figure shows a spherical hollow inside a lead sphere of radius R = 4.6 m; the surface of the hollow passes through the center of the sphere and “touches” the right side of the sphere. The mass of the sphere before hollowing was M = 245 kg. With what gravitational force...
  9. toforfiltum

    Proving magnitude of impulse on either spheres

    Homework Statement A sphere of mass m is moving with a speed V along a horizontal straight line. It collides with an identical sphere of mass m moving along the same straight line with speed u (u<V). Show that the magnitude of impulse on either sphere is ½m(1+e)(V-u), where...
  10. E

    Electric Potential and charge flowing between 2 spheres

    Homework Statement A large hollow metallic sphere A is charged positively to a potential of 100 V and a small sphere B to a potential of 50 V. Now B is placed inside A and they are connected by a wire. In which direction will the charge flow? Homework EquationsThe Attempt at a Solution A is at...
  11. SanEng02

    Finding if two sphere's intersect method

    Hi I was just curious if this method of solving whether or not two spheres intersect is a viable method that will give me the correct answer. Say if I am given the two equations of the sphere's is it viable to: Find the centre and radius of each sphere. Find the magnitude of the distance of...
  12. S

    Atoms as spheres in packing fraction of crystal lattice

    Why are atoms taken to be spheres, and not of some other shape, in the calculation of the packing fraction of different crystal lattices? In other words, what experimental evidence and theoretical reasoning motivates this form of the atomic shape?
  13. I

    Electrostatics- Charged Identical Spheres

    In electrostatics, why is it that identical spheres that are touched for a brief moment or connected by a conducting wire (wire not gaining any charge) should have an equal charge? Why is that they come in an equilibrium of charge? For example - If we take 2 identical spheres one bearing a...
  14. D

    Surface joining two points in a family of concentric spheres

    Hi, What's the surface joining two points in a family of concentric spheres? Shown below is the general idea; it's actually optical. Two rays meet at P from P1 and P2, respectively, where each point comes from a different sphere. How do I find surface S if I know the coordinates of P1 and P2...
  15. B

    Exploring Gauss' Law: Understanding Spheres and Flux in Closed Surfaces

    Flux through a closed surface is zero due to external charge but why it is not so in case of sphere
  16. Y

    Electric field due to 2 charged spheres

    Homework Statement The first part is to calculate the electric field everywhere in space given a body of 2 spheres of radius R and distance d apart (d<R), located on the z-axis, with charge density ρ and -ρ. Of course when r>>R this is essentially a dipole. The second part is to approximate the...
  17. S

    How did Coulomb charge his spheres to verify Coulomb's law?

    We are doing an experiment to verify coulomb's law, and we are currently using a stable voltage source. However, we were assigned to do it using static electricity, and we were wondering how to establish inverse r^2 dependence if the amount of the charge on the ball isn't the same every time we...
  18. A

    Electrostatic induction in different size spheres

    if we have a charged sphere with charge Q and radius r, the voltage on it's surface is calculated by gauss's law, what if we approach to it another sphere with radius R , R>r, Earth it, remove earth, basically charging by induction, will the sphere have the same charge, which means less voltage...
  19. carllacan

    Electric potential on concentric spheres

    Homework Statement A metallic sphere at ##\phi = 0 ## is surrounded by a spherical layer with charge density ##\rho ##. Find the potential at every point...
  20. G

    Gravitational Potential Energy and Oscillations of a Bead Attracted by Spheres

    Homework Statement A bead of mass m slides without friction on a smooth rod along the x axis. The rod is equidistant between two spheres of mass M. The spheres are located at x = 0, y = ± a, and attract the bead gravitationally. (a) Find the potential energy of the bead. (b) The bead is...
  21. J

    Velocity of two spheres under gravitational attraction

    Homework Statement Two solid copper spheres of radii 1 and 2 cm are released from rest in free space, their centers being 20 cm apart. Estimate the velocity with which they collide Homework Equations density =mass/volume F=GMm/r^2 The Attempt at a Solution Find mass of each from density of...
  22. Q

    Moment of Inertia of a rod and two spheres

    Homework Statement A barbell that consist of a long thin rod of mass M and length L is attached to two uniform spheres on each end. Both spheres have mass M and (1/3)L. The sphere on the left is hallow (spherical shell) and the sphere on the right is solid. What is the moment of inertia for...
  23. W

    Solving 2-Sphere Collision Problem: M, 2M, R, & 2R

    Homework Statement Two spheres having masses M (sphere 1) and 2M (sphere 2) and radii R and 2R, respectively, are released from rest when the distance between their centers is 8R. How fast will sphere 1 be moving when they collide? Assume that the two spheres interact only with each other...
  24. J

    Two spheres mass of inertia multivariable calculus problem

    Homework Statement Let R be the solid region that is bounded by two spheres x^2 + y^2 + z^2=1 and x^2 + y^2 + z^2=2. Determine the moment of inertia of R around the x-axis if the mass density per unit volume of R is u=sqrt(x^2 + y^2 + z^2). Homework Equations Moment of Inertia around the...
  25. C

    Packing fraction of spheres in a HCC structure

    Homework Statement Show that the ratio of atomic sphere to unit cell volume in HCP (hexagonal close packing) is 0.74. Homework Equations volumes of spheres, geometry The Attempt at a Solution I did the same problem for FCC and BCC and it was fine. My unit cell structure is that...
  26. F

    Close Packing of Spheres in Regular Tetrahedral vs. Square Pyramidal C

    The full title of this post is "Close Packing of Spheres in Regular Tetrahedral vs. Square Pyramidal Container" I'm not sure where this post belongs, but Greg Bernhardt suggested I just post it where I thought best, and he would find a place for it. So here goes: In 1611, Johannes Kepler...
  27. D

    Charge Leakage in Suspended Spheres with Varying Approach Velocity

    Two small eqlly chrged spheres ech of mass m, are suspnded frm same point by silk threads of length l. The distnce betwen sphres x<<l. Fnd dq/dt wth whch the charge leaks off each sphere.. If their approach velocity varies as v=a/root ovr x where a is a constnt. ***** My ques is; how can the...
  28. R

    How Does Gauss' Law Apply to Charged Spheres?

    Hi everyone, I am struggling with gauss law. I understand the basic concept , but I can not relate it to other physics problems. I have this physics problem. I want to really understand physics, but I can't. I have watched a lo of videos but I still don't understand. I am going to give my...
  29. R

    What is the potential between 2 concentric spheres?

    Homework Statement Consider two concentric spherical conducting shell. The inner sphere has radius r1, potential V1, while the outer sphere has radius r2, potential V2. Find the potential at the center of these two sphere, at r0=(r1+r2)/2. 2. The attempt at a solution I tried to use method...
  30. M

    Calculating Angle and Distance of Separation for Repelling Charged Spheres

    [b]1. Homework Statement [] Two spheres each of 5g, tied to 1.0m strings, repel each other after being charged to +91nC of the two spheres . What is the angle θ they form with the vertical after repulsion Homework Equations (1) F = mg...m=5.0g, g= 9.8m/s^2 (2) F = Kq1q2/r^2...
  31. J

    Charge distribution on spheres with varying radii

    Homework Statement Basically, I'm told that two insulated metal spheres, one positively charge (+20uc, sphere A) and one negatively charged (-10 uc, sphere B) come into direct contact (so obviously conduction is the method of charge), and that sphere A's radius is twice the size of sphere...
  32. B

    A electric charge question for two spheres

    Homework Statement A metallic sphere A of radius 1.00 cm is several centimetres away from a metallic spherical shell B of radius 2.00 cm. Charge 450 nC is placed on A, with no charge on B or anywhere nearby. Next, the two objects are joined by a long, thin, metallic wire, and finally the...
  33. H

    Visualizing higher dimensional spheres

    Visualizing a higher-dimensional sphere seems impossible to me. The best that can be done is to come up with several different representations, each of which is inaccurate in a different way. A property of n-spheres is that they have n/2 planes of rotation, each at right angles to the other...
  34. A

    Help with Contact Mechanics Between two Spheres

    Homework Statement Hello. Me and my partner are in Grade 7, and are currently doing an inquiry project in Math. We were told to take a question, and calculate theoretical probability of both outcomes. In this case, it would be surviving or dying. Our question is: What is the probability...
  35. U

    Spheres placed in an electric field

    Homework Statement Two neutral metal spheres of radius r and mass m each are connected by a light flexible conducting string of length L. The spheres are placed in a uniform electrostatic field E directed along the line connecting the centers of the spheres. Initially, the spheres are at rest a...
  36. R

    Derive the van der Waal interaction between 2 spheres.

    Hi guys, I need some help on this question: Derive the van der Waal interaction potential between 2 spheres of radius R_1 and R_2 using the Hamaker approach. Take the distance between the center of each sphere to be D. Thank you very much for your help!
  37. W

    Angular momentum of concentric spheres immersed in magnetic field

    Homework Statement Two concentric spherical shells carry uniformly distributed charges +Q (at radius a) and -Q (at radius b>a). They are immersed in a uniform magnetic field \vec{B}=B_0\hat{z}. (a) Find the angular momentum of the fields (with respect to the center). (b) Now the...
  38. Saitama

    Force between two spheres connected by wire and battery

    Homework Statement There are two alike initially uncharged spheres of radius r at a distance of d>>r, as shown in the figure. a) Switch ##K_2## is closed. What is the force exerted between the two spheres? b) What would be the force between the two spheres, if in the previous experiment...
  39. Saitama

    Charge on capacitor connected between spheres

    Homework Statement Two metallic spheres, each of radius R having charges 2Q and Q are joined through a capacitor of capacitance C as shown in the figure. Assuming R<<d, the charge on the capacitor long time after the key K is closed is: (Ans: ##\dfrac{Q}{2+\frac{4\pi \epsilon_0 R}{C}}##)...
  40. S

    Building a Coilgun for Shooting Steel Spheres: Need Help!

    Hey guys! Not sure if this is the correct place to post this, but this seemed the most relevant... So I'm working on a coilgun to shoot 45mm steel spheres, but I need to figure out how long [diameter, gauge, etc] my coil needs to be. I want to generate a force of about 5 Joules or more...
  41. I

    Non-uniform electric field and conducting spheres

    Homework Statement Q1. A non-uniform electric field is given by the expression E=3yi+2zj-k. Determine the electric field flux through a rectangle in the xy plane, extending from x=0 to x=20 cm and y=0 to y=15cm Q2. A point charge q1 = +5nc is placed at the center of a non-conducting sphere...
  42. T

    Two Conducting Spheres connected by a wire

    Homework Statement Two conducting spheres of radii rA and rB are connected by a very long conductive wire. The charge on sphere A is Qa and rA < rB. What is the charge on sphere B? Which sphere has the greater electric field strength immediately above its surface. Homework Equations...
  43. Rugile

    Charge of three small spheres when connected to a big one

    Homework Statement Three small metal solid uncharged spheres are put on vertexes of an equilateral triangle. Then they all one by one are connected to a big conducting solid sphere, which is at the same distance from all the small ones, by a wire. Thus the first sphere is charged to q1 and the...
  44. I

    Draw the field for two concentric conducting spheres

    Homework Statement We are given two concentric conducting shells centered around a common origin. Within the inner shell there is a positive point charge q and somewhere outside the two shells is another positive point charge q. The question wants the field lines for this system and then again...
  45. S

    University physics - conducting concentric spheres

    Homework Statement Two hollow conducting spheres are connected electrically, and are charged to a potential V. The connection is then removed and the outside sphere is grounded, find the charge and potential of the inner sphere after the grounding. 2. The attempt at a solution I'm not...
  46. G

    Find charge and radius of conducting spheres given voltage and electr

    The electric potential immediately outside a charged conducting sphere is 200 V, and 10.0 cm farther from the center of the sphere the potential is 150 V. Determine (a) the radius of the sphere and (b) the charge on it. The electric potential immediately outside another charged conducting sphere...
  47. S

    Electric Field & Potential for Three Concentric spheres

    Homework Statement Three volumes bounded by three concentric spheres with radii a, b ​​and c. The innermost volume r<a, consists of vacuum. Next volume, a<r<b, is filled with a material having a constant volume charge density ρ1 and a relative dielectric constant ε1. The external volume...
  48. T

    Finding density for identical spheres

    Homework Statement Two identical spheres of diameter 8.55m are on the surface of the earth. The spheres are touching each other. What is the minimum density the spheres must have such that the gravitational force between them is at least equal to the weight of one of the spheres. Homework...
  49. J

    Understanding Planetary Spheres: The Role of Gravitational Compression

    Why planets are "spheres" I was reading the specifics on why large bodies in space, such as planets, are pulled into spherical shape and they had a very technical term for the process. Does anyone know what I'm talking about?
  50. E

    Force between Two Conducting Spheres

    Homework Statement Two tiny conducting spheres are identical and carry charges of -19.4 μC and +49.3 μC. They are separated by a distance of 2.55 cm. What is the magnitude of the force that each sphere experiences? Homework Equations Coulombs Law: F=kelq1q2l/r2 Ke = 8.99E9 The Attempt...
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