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. O

    Gap between two displaced spheres

    This was out of a physics book, but since it's just geometry, I thought this would be the best forum to ask about it. I was reading through a derivation of the far electric field of a uniformly polarized sphere, and the author used a trick where he modeled the sphere as two displaced spheres...
  2. X

    Speed of two charged, insulated spheres?

    Homework Statement Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.450 kg and 0.700 kg, and uniformly distributed charges of -2.00 µC and 3.00 µC. They are released from rest when their centers are separated by 1.00 m. (a) How fast will each be moving when they collide...
  3. Feodalherren

    Attraction of two spheres in deep space

    Homework Statement A solid led sphere of radius 10m has a mass of about 57 million kg. If two of these spheres are floating in deep space with their centers 20m apart, the gravitational attraction between them is only 540N. How large would this gravitational force be if the distance between...
  4. D

    Change in Electric Energy of Spheres

    Homework Statement A heavy nuclei can be approximately considered as a spherical ball with uniform volume density  = 4/3 * 10^ 25 C/m3. If a nuclei with total charge Q = 92e splits into 2 equal spherical piece and they fly away. What will be the total electric energy change during this...
  5. N

    How to Calculate Energy Lost in a Rolling Sphere?

    Homework Statement There is a tube attached to a board in a fashion that a ball can be dropped in the top and the tube curves to the right 90°. If a ball of mass 7.6g is dropped into the top of the tube, what is the minimum height the exit point of the tube needs to be in order for the ball to...
  6. S

    Calculating Initial Potential and Heat of Metal Spheres Collision

    We have a metal sphere of radius R in the space and resistivity p. At a distance d>R from it we have antoher sphere of metal of radius r<<R and charge q. The 2 spheres intially are at rest. What is the initial potential energy between them? Now the sphere accelerate and collide anelastically...
  7. D

    Light Scattering by (Transparent) Spheres: Mie Solution

    Homework Statement Hello everyone, I've been struggling to understand the relationship between two algebraic forms of the scattering function used in the Mie solution for light scattered by (transparent) spheres. I think there's some use being made of Legendre function identities, but I've...
  8. D

    Collision between hard spheres

    The wikipedia article on collisions says "collisions between hard spheres may be nearly elastic". It doesn't elaborate nor give a source on the statement. I was wondering about those two conditions. Hardness I understand, but is the spherical shape necessary? Is it about there being a single...
  9. Y

    Natural Frequency of Solid Spheres

    Dear Physics Forum community, I am posting here as a last resort, so any guidance/references would be much appreciated. As a small part of my project, I need to calculate the natural frequency of metallic solid spheres. All I have been able to find on the web is the Schummann Resonance...
  10. 1

    Two charged spheres are connected

    Homework Statement Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.108N when their center-to-center separation is 50 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with...
  11. X

    Finding the Optimal Ratio for Two Concentric Spheres in a Capacitor

    Homework Statement It's desired to build a capacitor which has two concentric spheres separated by a dielectric of high permittivity, low loss, and high dielectric strength. Calculate the ratio of sphere b's radius to sphere a's radius which produces the lowest electric field between the...
  12. D

    Can Two Repelling Spheres Be Solved?

    Solved.
  13. I

    Velocity of two insulating charged spheres at collision

    Homework Statement Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.200 kg and 0.700 kg, and uniformly distributed charges of -2.00 µC and 3.00 µC. They are released from rest when their centers are separated by 1.00 m. (a) How fast will each be moving when they collide...
  14. W

    Resonance of antennas (rods, spheres etc)

    How can you find the resonant frequency of an antenna whether it is a rod shape or an irregular shape or a sphere? I understand they have a capacitive reactance and you may need an inductive load but can someone explain it all in detail and include which formulas to use. I have a radio antenna...
  15. A

    Capacitance of two tangential spheres

    Hi, Question: Consider two conducting spheres with radius R, which are tangential each other (i.e. they touch right at one point) If C = Q/V, where V is the potential at the surface, find the capacitance of this configuration...
  16. S

    How Many Electrons Are in Aluminum Spheres?

    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.) The attempt at a solution I said that there are 6.02*10^23...
  17. E

    Oblique Collision Between Two Spheres : Incomplete info?

    Two smooth spheres of masses 4 kg and 2 kg impinge obliquely. The 2 kg mass is brought to rest by the impact. (i) Prove that, before impact, they were moving in directions perpendicular to each other. (ii) Show that, as a result of impact, the kinetic energy gained by the 4 kg mass is...
  18. S

    Gauss' law and conducting spheres

    Homework Statement A conducting sphere of radius R2 has a central cavity of radius R1 that holds a charge q in its centre. Determine the electrical field for r > R2, r < R1 and R1 < r < R2 and determine the charge density induced by q. I'm not allowed to include a link to my figure, but I'm...
  19. R

    Measuring volume of spheres using triple integrals

    Homework Statement I'm just interested in knowing where the 4 comes from in front of the integral.
  20. binbagsss

    What Is the Angle of Deflection in Sphere Collisions?

    What exactly do we mean by the angle of deflection? Is the ‘angle the velocity is turned through equivalent’? - does it tak into account the direction of the impulse , I ask because if it does, I am struggling to see how, I have attached an example where the impulse is in the direction of the...
  21. 5

    Electric potential of concentric spheres

    Homework Statement attached image http://sphotos.xx.fbcdn.net/hphotos-snc7/148934_353406858048194_100001366491698_897020_688558166_n.jpg Homework Equations V = integral of E * dr The Attempt at a Solution I do not completely understand the solution to part B. I was able to solve it...
  22. B

    Electricity Problems - conductive spheres

    Homework Statement Initially, metal sphere X is charged to an electric potential of 10,000 volts, with a total charge on its surface of +Q. Metal spheres Y and Z are initially uncharged. Spheres Y and Z are the same size as sphere X. All three spheres are held by insulated stands. 6...
  23. M

    Paschen's Law and E-field between spheres

    I am reading up on Paschen's Law and came across some papers measuring breakdown voltage between two identical spherical electrodes. I've read in a couple places that the electric field is uniform when the gap distance is no larger than the radii. Why is that? It seem to me that the field...
  24. F

    Electric Field Strength Inside Concentric Uniformly Charged Spheres

    Homework Statement The graph in the figure shows the electric field strength (not the field lines) as a function of distance from the center for a pair of concentric uniformly charged spheres. Which of the following situations could the graph plausibly represent? (There may be more than one...
  25. V

    Static Electricity, Spheres question

    Homework Statement Suppose you have two isolated conducting spheres that are both neutral. You move 2mC of charge from one to the other. a. What is the charge now on each sphere? My solution: One sphere is positively charged with 2mC more protons, while the other is negatively charged with...
  26. A

    Calculating charge transferred between metal spheres

    Suppose I have two metal spheres, radius 1 metre and 1 cm. I charge the small one to 100V. The self-capacitance of the sphere is 4µϵR, so the charge Q = CV = 4µϵ coulombs Then I touch the two spheres together. I assume charge flows between them so that the voltage equalizes. As charge builds on...
  27. A

    Metal Spheres; Interaction between conductors; induction

    Homework Statement Initially the three spheres are uncharged; then sphere A is dragged across a t.v. screen with an excess charge, giving (A) an excess negative charge. Then (A) is placed next to (B) and all three spheres lie on a line. There is a wire connecting (B) and (C). We want to...
  28. O

    Charges on two small spheres suspended from a thread

    Homework Statement Two small spheres, each with mass m = 5.0 g and charge q, are suspended from a point by threads of length L = 0.30 m. What is the charge on each sphere if the threads make an angle θ = 20° with the vertical? Homework Equations F=k|q1q2|/r2 The Attempt at a Solution I found...
  29. S

    What is the equation for the circle formed by the intersection of two spheres?

    Homework Statement In the space, consider the sphere S1 of radius 3 whose center is the point A (1, -1, 1) and the sphere S2 of radius 2 whose center is the point B(t, 1 - t, 1 + t). a. Find the range of values of t in order the two spheres S1 and S2 have common points b. Find the value of...
  30. E

    Electric Potential of three concentric spheres

    Hey, i have a conceptual doubt. Suppose there are three concentric conducting spheres A,B,C having radius a,b,c (a<b<c). We put charge q1, q2 and q3 on these three surfaces A,B,C respectively. Now using gauss law, we can prove that Charge on inner surface of A is 0 Charge on...
  31. K

    How Does Grounding Affect Charge Distribution in Nested Spherical Shells?

    Hi, I'm a physics student, preparing for an exam (it happens to be tomorrow heh), and I'm having trouble with induction of conductors. I need to get it right so i can solve more difficult problems, but the more i try the worse it gets. Basically i'd like to know how things work in sets of shells...
  32. S

    Overlapping Charged spheres: solve Electric Force of point charge (Q) locations

    I need help understanding how to calculate various Electric Field Strengths of several point charges (Q) both inside and along two OVERLAPPING identical spheres BUT with on NON-UNIFORM VOLUME CHARGE DENSITIES (-1p non-overlap density on the outside with -4p density overlapping internally) with...
  33. D

    Tension in a rope connecting charged spheres.

    Homework Statement Two positive charged spheres, with masses m = 2.0 g and with the same charge 2 µC are connected by a rope that is a distance of 5 cm. The charged spheres are at rest and the system is in static equilibrium. Homework Equations N/A. The Attempt at a Solution The...
  34. V

    Comparing Cooling Rates of Solid and Hollow Spheres

    There are two sphere of same radius but one is solid and other is hollow. Both are heated to same temperature(greater than room temperature). which will cool at faster rate? I think both the spheres will cool at same rate since hollow sphere can't loose it's heat inside it (because internal...
  35. M

    Finding equation for potential between concentric charged spheres

    Homework Statement A metal sphere with radius r_a is supported on an insulating stand at the center of a hollow, metal spherical shell with radius r_b. There is charge +q on the inner sphere and charge -q on the outer spherical shell. Take the potential V to be zero when the distance r from the...
  36. S

    Oblique Impact of Smooth Spheres

    Hey, I'm struggling with this question, any help would be great. 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 My attempt...
  37. C

    Electric Potaential of two spheres

    Homework Statement Electric charge can accumulate on an airplane in flight. You may have observed needle-shaped metal extensions on the wing tips and tail of an airplane. Their purpose is to allow charge to leak off before much of it accumulates. The electric field around the needle is much...
  38. N

    Electric field on two charged spheres

    Homework Statement Two tiny spheres of mass m = 7.90 mg carry charges of equal magnitude, 72.0 nC, but opposite sign. They are tied to the same ceiling hook by light strings of length 0.530 m. When a horizontal uniform electric field E that is directed to the left is turned on, the spheres hang...
  39. M

    How Does Charge Distribution Affect Electric Field Inside a Hollow Sphere?

    Homework Statement A total charge Q is spread uniformly over the surface of one hemisphere of a hollow insulating spherical hull of radius R. The magnitude of the electric field at the centre of the ball(point C) will be? The Attempt at a Solution The answer was less then that KeQ/R^2, was...
  40. D

    Two spheres hanging, find charge.

    Homework Statement Two identical, small spheres of mass 2.0g are fastened to the ends of a 0.6m long light, flexible, insulating fishline. The fishline is suspended by a hook in the ceiling at it's exact center. The spheres are each given the same electric charge. They are in static...
  41. B

    Finding the number of spheres in a graduated cylinder

    Homework Statement This is from a worksheet. I had to find the volume myself "A large number of spheres are poured into a graduated cylinder and gently vibrated until the occupy a minimum volume of 40 mL (or 40 cm^3). Use the information about close packing and the data you found to...
  42. M

    Two identical small metal spheres 3 cm apart

    Homework Statement Two identical small metal spheres 3 cm apart attract each other with a force of 150N electrical module. They are temporarily connected by a conducting wire, which is then removed, making both charges equal. a) Determine the initial electrical charges if they now repel each...
  43. J

    What Does the Product of Spheres Look Like?

    Hi all, I would really appreciate if someone can explain to me what is meant by a product of spheres. What would for example S1 x S0 look like? The first being a circle and the second being a pair of boundary points... So what kind of "object" is their product? And how about S1 x S1 or...
  44. S

    The property of spheres that gravity acts on the shape as one component?

    I'm wondering if there's a term for the property of spheres that makes gravity pull equally on all aspects of the sphere's mass. The wording for what I'm asking is tricky, so I'll give an example of a shape that wouldn't have this property, a long prism. If you drop a long prism on an angle...
  45. P

    Exploring Gauss' Law of Flux & Newton's Shell Method for Hollow Spheres

    While I do see how this makes sense using Newton’s Shell method, I don’t see how Gauss’ Law of Flux for a closed surface proves the same thing. Both Gauss’ Law of Flux and Newton’s Shell method make perfect sense to me in showing that when dealing with a point outside the hollow conducting...
  46. S

    Cooling of Spheres: Why is it Different?

    Why is it that two spheres,one hollow and other solid having same material and size and heated to same temperatures cool differently? Precisely,why does hollow sphere cool faster than solid sphere?
  47. D

    Comparing Surface Areas of Two Water Balloons Using a Formula

    Homework Statement The question wants me to use this formula: ((4pi)^(1/3))((3v)^(2/3)) You have filled two round water balloons with water. One balloon contains twice as much water as the other balloon. Compare the surface areas of the two water balloons using the given formula...
  48. D

    How Do You Calculate the Kinematics of Touching Spheres Under External Force?

    Homework Statement My physics classes were a long time ago, and I can't for the life of me remember how to solve this problem: If I have two spheres s1 and s2 touching, of mass m1 and m2, with radii r1 and r2, and centers c1 and c2, and I have a force Fout normal to the surface of s1, how do I...
  49. S

    Moment of inertia tensor of three spheres

    Hi everyone Homework Statement I want to find out the moment of intertia tensor of the graphic below. Homework Equations parallel axis theorem The Attempt at a Solution We know the moment of inertia for one sphere, that's given, so I don't have to calculate it...
  50. S

    Concept/Derivation for total electric potential energy of two concentric spheres

    What will be the total electric potential energy of two concentric spheres. Will it be = [P.E. of Inner sphere] + [ P.E. of Outer sphere] + [ Energy required to bring outer sphere from infinity to the present position(i.e. position concentric to inner sphere) ] OR it Will...
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