# Spheres Definition and 10 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. ### Normal Forces on a Sphere in a Non-vertical Groove

neglect friction and motion (sliding) and G(sphere)=20N. In this question I reached two different result with two different solving method.But one of them is false according to answer key. My question is why first solving way is false? Because the first solution way makes sense to me. If we...
2. ### Inverse square law of gravitation and force between two spheres

I recently encountered this problem on a test where the solution for the above problem was given as follows: $$F= \frac{Gm_1m_2} {r^2}$$ (1) but $$m=\frac{4}{3}\pi R^3$$ substituting in equation (1) $$F= \frac{{G(\frac{4}{3}\pi R^3\rho})^2 }{2R^2}$$ where r=radii of the two spheres m=mass...
3. ### Lubrication theory for two spheres -- Finding the resisting force

Homework Statement Show that the force resisting change of the minimum distance h between the surfaces of two rigid spheres of radii a and b which are nearly touching is: $$6\pi\frac{\mu}{h({a^{-1} + b^{-1}})^2}\frac{dh}{dt}$$ provided $$\frac{\rho h}{\mu}\frac{dh}{dt}$$ Homework Equations...
4. ### I Largest sphere in the space between dense packed spheres

If I consider a tetrahedron of four densely packed spheres of unit radius, what it the radius of the largest sized sphere that can fit in the space in between?
5. ### I Equidistance of Points in a Sphere?

I've been trying to wrap my head around equidistant points, like platonic solid vertices inside a sphere where the points touch the sphere surface. This led me to the strange and unusual world of mathematical degeneracy, henagons, dihedrons, and so on, along with the lingering question of...
6. ### Insights A Journey to The Manifold - Part I - Comments

fresh_42 submitted a new PF Insights post A Journey to The Manifold - Part I Continue reading the Original PF Insights Post.
7. ### Finding electric potential between two concentric spheres.

Homework Statement A spherical shell with inner radius A and outer radius 3A which has a uniform charge density, i.e charge per unit volume, p0. Find difference in electric potential between the center of the shell and a point a distance 2A from the center. Homework Equations The answer...
8. ### Energy in system of two conducting spheres

1. Homework Statement Hi everyone. I am having trouble figuring out how to solve this problem. The right answer is E Homework Equations Well, we do have the law of conservation of charge. I also know that Work by a conservative force = - change in potential energy The Attempt at a Solution...
9. ### I Questions about Vsauce's Banach-Tarski video

Hi, I have some questions about the video about the Banach-Tarski Paradox from the YouTube channel Vsauce: 10:09: Is this really a valid way of constructing the hyperwebster? In this order, one will never get past sequences of only "A". Shouldn't one follow an order like A, ... ,Z, AA, ... ...
10. ### 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...