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60-556: The STIS was installed on Hubble in 1997 during its second servicing mission ( STS-82 ) by Mark Lee and Steven Smith , replacing the High Resolution Spectrograph and the Faint Object Spectrograph . It was designed to operate for five years. On August 3, 2004, an electronic failure rendered STIS inoperable, ending its use 2 years beyond its predicted lifespan. In order to bring it back to operational status,

120-437: A closed system (where there is no net external torque), the total torque on the system must be 0, which means that the total angular momentum of the system is constant. The change in angular momentum for a particular interaction is called angular impulse , sometimes twirl . Angular impulse is the angular analog of (linear) impulse . The trivial case of the angular momentum L {\displaystyle L} of

180-450: A point particle is classically represented as a pseudovector r × p , the cross product of the particle's position vector r (relative to some origin) and its momentum vector ; the latter is p = m v in Newtonian mechanics . Unlike linear momentum, angular momentum depends on where this origin is chosen, since the particle's position is measured from it. Angular momentum

240-627: A unit vector u ^ {\displaystyle \mathbf {\hat {u}} } perpendicular to the plane of angular displacement, a scalar angular speed ω {\displaystyle \omega } results, where ω u ^ = ω , {\displaystyle \omega \mathbf {\hat {u}} ={\boldsymbol {\omega }},} and ω = v ⊥ r , {\displaystyle \omega ={\frac {v_{\perp }}{r}},} where v ⊥ {\displaystyle v_{\perp }}

300-429: A 52×52 arc-second field of view, covering the visible and near-infrared spectrum from 200 nm to 1030 nm. The other two detectors are Multi-Anode Multichannel Arrays , each with a 25×25 arc-second field of view. One is Cs 2 Te, and covers the near-UV between 160 nm and 310 nm. The other is CsI and covers the far-UV between 115 nm and 170 nm. On its 20th anniversary (1997-2017) NASA noted

360-447: A body in an orbit is given by L = 2 π M f r 2 {\displaystyle L=2\pi Mfr^{2}} where M {\displaystyle M} is the mass of the orbiting object, f {\displaystyle f} is the orbit's frequency and r {\displaystyle r} is the orbit's radius. The angular momentum L {\displaystyle L} of

420-409: A complex function of the configuration of the matter about the center of rotation and the orientation of the rotation for the various bits. For a rigid body , for instance a wheel or an asteroid, the orientation of rotation is simply the position of the rotation axis versus the matter of the body. It may or may not pass through the center of mass , or it may lie completely outside of the body. For

480-453: A magnitude, and both are conserved. Bicycles and motorcycles , flying discs , rifled bullets , and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes form spirals and neutron stars have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it. The three-dimensional angular momentum for

540-469: A particular axis. However, if the particle's trajectory lies in a single plane , it is sufficient to discard the vector nature of angular momentum, and treat it as a scalar (more precisely, a pseudoscalar ). Angular momentum can be considered a rotational analog of linear momentum. Thus, where linear momentum p is proportional to mass m and linear speed v , p = m v , {\displaystyle p=mv,} angular momentum L

600-793: A selection of discoveries and/or observations conducted with STIS: Other Hubble instruments : STS-82 STS-82 was the 22nd flight of the Space Shuttle Discovery and the 82nd mission of the Space Shuttle program . It was NASA's second mission to service the Hubble Space Telescope , during which Discovery's crew repaired and upgraded the telescope's scientific instruments, increasing its research capabilities. Discovery launched from Kennedy Space Center , Florida, on February 11, 1997, returning to Earth on February 21, 1997, at Kennedy Space Center. Discovery

660-466: A tradition of playing music to astronauts during the Gemini program , which was first used to wake up a flight crew during Apollo 15 . Each track is specially chosen, often by their families, and usually has a special meaning to an individual member of the crew, or is applicable to their daily activities. [REDACTED]  This article incorporates public domain material from websites or documents of

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720-400: A uniform rigid sphere rotating around its axis, instead, is given by L = 4 5 π M f r 2 {\displaystyle L={\frac {4}{5}}\pi Mfr^{2}} where M {\displaystyle M} is the sphere's mass, f {\displaystyle f} is the frequency of rotation and r {\displaystyle r}

780-659: Is always measured with respect to a fixed origin. Therefore, strictly speaking, L should be referred to as the angular momentum relative to that center . In the case of circular motion of a single particle, we can use I = r 2 m {\displaystyle I=r^{2}m} and ω = v / r {\displaystyle \omega ={v}/{r}} to expand angular momentum as L = r 2 m ⋅ v / r , {\displaystyle L=r^{2}m\cdot {v}/{r},} reducing to: L = r m v , {\displaystyle L=rmv,}

840-429: Is an extensive quantity ; that is, the total angular momentum of any composite system is the sum of the angular momenta of its constituent parts. For a continuous   rigid body or a fluid , the total angular momentum is the volume integral of angular momentum density (angular momentum per unit volume in the limit as volume shrinks to zero) over the entire body. Similar to conservation of linear momentum, where it

900-430: Is conserved if there is no external force, angular momentum is conserved if there is no external torque . Torque can be defined as the rate of change of angular momentum, analogous to force . The net external torque on any system is always equal to the total torque on the system; the sum of all internal torques of any system is always 0 (this is the rotational analogue of Newton's third law of motion ). Therefore, for

960-894: Is desired to know what effect the moving matter has on the point—can it exert energy upon it or perform work about it? Energy , the ability to do work , can be stored in matter by setting it in motion—a combination of its inertia and its displacement. Inertia is measured by its mass , and displacement by its velocity . Their product, ( amount of inertia ) × ( amount of displacement ) = amount of (inertia⋅displacement) mass × velocity = momentum m × v = p {\displaystyle {\begin{aligned}({\text{amount of inertia}})\times ({\text{amount of displacement}})&={\text{amount of (inertia⋅displacement)}}\\{\text{mass}}\times {\text{velocity}}&={\text{momentum}}\\m\times v&=p\\\end{aligned}}}

1020-450: Is directed perpendicular to the plane of angular displacement, as indicated by the right-hand rule – so that the angular velocity is seen as counter-clockwise from the head of the vector. Conversely, the L {\displaystyle \mathbf {L} } vector defines the plane in which r {\displaystyle \mathbf {r} } and p {\displaystyle \mathbf {p} } lie. By defining

1080-445: Is proportional to moment of inertia I and angular speed ω measured in radians per second. L = I ω . {\displaystyle L=I\omega .} Unlike mass, which depends only on amount of matter, moment of inertia depends also on the position of the axis of rotation and the distribution of the matter. Unlike linear velocity, which does not depend upon the choice of origin, orbital angular velocity

1140-401: Is related to the angular velocity of the rotation. Because moment of inertia is a crucial part of the spin angular momentum, the latter necessarily includes all of the complications of the former, which is calculated by multiplying elementary bits of the mass by the squares of their distances from the center of rotation. Therefore, the total moment of inertia, and the angular momentum, is

1200-402: Is required to know the rate at which the position vector sweeps out angle, the direction perpendicular to the instantaneous plane of angular displacement, and the mass involved, as well as how this mass is distributed in space. By retaining this vector nature of angular momentum, the general nature of the equations is also retained, and can describe any sort of three-dimensional motion about

1260-471: Is the angular momentum , sometimes called, as here, the moment of momentum of the particle versus that particular center point. The equation L = r m v {\displaystyle L=rmv} combines a moment (a mass m {\displaystyle m} turning moment arm r {\displaystyle r} ) with a linear (straight-line equivalent) speed v {\displaystyle v} . Linear speed referred to

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1320-510: Is the cross product of the position vector r {\displaystyle \mathbf {r} } and the linear momentum p = m v {\displaystyle \mathbf {p} =m\mathbf {v} } of the particle. By the definition of the cross product, the L {\displaystyle \mathbf {L} } vector is perpendicular to both r {\displaystyle \mathbf {r} } and p {\displaystyle \mathbf {p} } . It

1380-401: Is the radius of gyration , the distance from the axis at which the entire mass m {\displaystyle m} may be considered as concentrated. Similarly, for a point mass m {\displaystyle m} the moment of inertia is defined as, I = r 2 m {\displaystyle I=r^{2}m} where r {\displaystyle r}

1440-549: Is the disk's mass, f {\displaystyle f} is the frequency of rotation and r {\displaystyle r} is the disk's radius. If instead the disk rotates about its diameter (e.g. coin toss), its angular momentum L {\displaystyle L} is given by L = 1 2 π M f r 2 {\displaystyle L={\frac {1}{2}}\pi Mfr^{2}} Just as for angular velocity , there are two special types of angular momentum of an object:

1500-438: Is the length of the moment arm , a line dropped perpendicularly from the origin onto the path of the particle. It is this definition, (length of moment arm) × (linear momentum) , to which the term moment of momentum refers. Another approach is to define angular momentum as the conjugate momentum (also called canonical momentum ) of the angular coordinate ϕ {\displaystyle \phi } expressed in

1560-407: Is the matter's momentum . Referring this momentum to a central point introduces a complication: the momentum is not applied to the point directly. For instance, a particle of matter at the outer edge of a wheel is, in effect, at the end of a lever of the same length as the wheel's radius, its momentum turning the lever about the center point. This imaginary lever is known as the moment arm . It has

1620-1002: Is the perpendicular component of the motion, as above. The two-dimensional scalar equations of the previous section can thus be given direction: L = I ω = I ω u ^ = ( r 2 m ) ω u ^ = r m v ⊥ u ^ = r ⊥ m v u ^ , {\displaystyle {\begin{aligned}\mathbf {L} &=I{\boldsymbol {\omega }}\\&=I\omega \mathbf {\hat {u}} \\&=\left(r^{2}m\right)\omega \mathbf {\hat {u}} \\&=rmv_{\perp }\mathbf {\hat {u}} \\&=r_{\perp }mv\mathbf {\hat {u}} ,\end{aligned}}} and L = r m v u ^ {\displaystyle \mathbf {L} =rmv\mathbf {\hat {u}} } for circular motion, where all of

1680-636: Is the perpendicular component of the motion. Expanding, L = r m v sin ⁡ ( θ ) , {\displaystyle L=rmv\sin(\theta ),} rearranging, L = r sin ⁡ ( θ ) m v , {\displaystyle L=r\sin(\theta )mv,} and reducing, angular momentum can also be expressed, L = r ⊥ m v , {\displaystyle L=r_{\perp }mv,} where r ⊥ = r sin ⁡ ( θ ) {\displaystyle r_{\perp }=r\sin(\theta )}

1740-450: Is the sphere's density , f {\displaystyle f} is the frequency of rotation and r {\displaystyle r} is the sphere's radius. In the simplest case of a spinning disk, the angular momentum L {\displaystyle L} is given by L = π M f r 2 {\displaystyle L=\pi Mfr^{2}} where M {\displaystyle M}

1800-726: Is the sphere's radius. Thus, for example, the orbital angular momentum of the Earth with respect to the Sun is about 2.66 × 10 kg⋅m ⋅s , while its rotational angular momentum is about 7.05 × 10 kg⋅m ⋅s . In the case of a uniform rigid sphere rotating around its axis, if, instead of its mass, its density is known, the angular momentum L {\displaystyle L} is given by L = 16 15 π 2 ρ f r 5 {\displaystyle L={\frac {16}{15}}\pi ^{2}\rho fr^{5}} where ρ {\displaystyle \rho }

1860-681: The Goddard High Resolution Spectrograph and the Faint Object Spectrograph , exchanged for the Space Telescope Imaging Spectrograph (STIS) and the Near Infrared Camera and Multi-Object Spectrometer (NICMOS), respectively. In addition to installing the new instruments, astronauts replaced other existing hardware with upgrades and spares. Hubble received a refurbished Fine Guidance Sensor , an optical device used to provide pointing information for

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1920-659: The Lagrangian of the mechanical system. Consider a mechanical system with a mass m {\displaystyle m} constrained to move in a circle of radius r {\displaystyle r} in the absence of any external force field. The kinetic energy of the system is T = 1 2 m r 2 ω 2 = 1 2 m r 2 ϕ ˙ 2 . {\displaystyle T={\tfrac {1}{2}}mr^{2}\omega ^{2}={\tfrac {1}{2}}mr^{2}{\dot {\phi }}^{2}.} And

1980-473: The National Aeronautics and Space Administration . Angular momentum Angular momentum (sometimes called moment of momentum or rotational momentum ) is the rotational analog of linear momentum . It is an important physical quantity because it is a conserved quantity  – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and

2040-480: The spin angular momentum is the angular momentum about the object's centre of mass , while the orbital angular momentum is the angular momentum about a chosen center of rotation. The Earth has an orbital angular momentum by nature of revolving around the Sun , and a spin angular momentum by nature of its daily rotation around the polar axis. The total angular momentum is the sum of the spin and orbital angular momenta. In

2100-559: The Fine Guidance Sensor. During this EVA astronauts noted cracking and wear on thermal insulation on the side of HST facing sun and in the direction of travel. EVA 3 began at 9:53 pm, February 15, and lasted seven hours, 11 minutes. Lee and Smith removed and replaced a Data Interface Unit on Hubble, as well as a reel-to-reel Engineering and Science Tape Recorder with a new digital Solid State Recorder (SSR) that allowed simultaneous recording and playback of data. Also changed out

2160-751: The capability of the Space Shuttle to service orbiting spacecraft. Discovery's crew completed servicing and upgrading of the Hubble Space Telescope during four planned EVAs, later performing a fifth unscheduled space walk to repair insulation on the telescope. The Hubble Space Telescope was deployed in April 1990 during STS-31 . It was designed to undergo periodic servicing and upgrading over its projected 15-year lifespan, with first servicing performed during STS-61 in December 1993. Hawley, who originally deployed

2220-452: The case of the Earth the primary conserved quantity is the total angular momentum of the solar system because angular momentum is exchanged to a small but important extent among the planets and the Sun. The orbital angular momentum vector of a point particle is always parallel and directly proportional to its orbital angular velocity vector ω , where the constant of proportionality depends on both

2280-1031: The center of rotation – circular , linear , or otherwise. In vector notation , the orbital angular momentum of a point particle in motion about the origin can be expressed as: L = I ω , {\displaystyle \mathbf {L} =I{\boldsymbol {\omega }},} where This can be expanded, reduced, and by the rules of vector algebra , rearranged: L = ( r 2 m ) ( r × v r 2 ) = m ( r × v ) = r × m v = r × p , {\displaystyle {\begin{aligned}\mathbf {L} &=\left(r^{2}m\right)\left({\frac {\mathbf {r} \times \mathbf {v} }{r^{2}}}\right)\\&=m\left(\mathbf {r} \times \mathbf {v} \right)\\&=\mathbf {r} \times m\mathbf {v} \\&=\mathbf {r} \times \mathbf {p} ,\end{aligned}}} which

2340-568: The central point is simply the product of the distance r {\displaystyle r} and the angular speed ω {\displaystyle \omega } versus the point: v = r ω , {\displaystyle v=r\omega ,} another moment. Hence, angular momentum contains a double moment: L = r m r ω . {\displaystyle L=rmr\omega .} Simplifying slightly, L = r 2 m ω , {\displaystyle L=r^{2}m\omega ,}

2400-528: The coordinate ϕ {\displaystyle \phi } is defined by p ϕ = ∂ L ∂ ϕ ˙ = m r 2 ϕ ˙ = I ω = L . {\displaystyle p_{\phi }={\frac {\partial {\mathcal {L}}}{\partial {\dot {\phi }}}}=mr^{2}{\dot {\phi }}=I\omega =L.} To completely define orbital angular momentum in three dimensions , it

2460-888: The effect of multiplying the momentum's effort in proportion to its length, an effect known as a moment . Hence, the particle's momentum referred to a particular point, ( moment arm ) × ( amount of inertia ) × ( amount of displacement ) = moment of (inertia⋅displacement) length × mass × velocity = moment of momentum r × m × v = L {\displaystyle {\begin{aligned}({\text{moment arm}})\times ({\text{amount of inertia}})\times ({\text{amount of displacement}})&={\text{moment of (inertia⋅displacement)}}\\{\text{length}}\times {\text{mass}}\times {\text{velocity}}&={\text{moment of momentum}}\\r\times m\times v&=L\\\end{aligned}}}

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2520-413: The instrument was repaired by space shuttle astronauts during STS-125 , Servicing Mission 4, launched on May 11, 2009. The crew did a long (many hour) EVA to repair the instrument. Congratulations, you brought STIS back to life. STIS is both a spectrograph and an imaging camera, and is focused on ultraviolet light. The STIS has three 1024×1024 detector arrays. The first is a charge-coupled device with

2580-455: The mass of the particle and its distance from origin. The spin angular momentum vector of a rigid body is proportional but not always parallel to the spin angular velocity vector Ω , making the constant of proportionality a second-rank tensor rather than a scalar. Angular momentum is a vector quantity (more precisely, a pseudovector ) that represents the product of a body's rotational inertia and rotational velocity (in radians/sec) about

2640-556: The motion is perpendicular to the radius r {\displaystyle r} . In the spherical coordinate system the angular momentum vector expresses as Angular momentum can be described as the rotational analog of linear momentum . Like linear momentum it involves elements of mass and displacement . Unlike linear momentum it also involves elements of position and shape . Many problems in physics involve matter in motion about some certain point in space, be it in actual rotation about it, or simply moving past it, where it

2700-534: The positioning of Hubble's solar arrays. Also replaced covers over Hubble's magnetometers and placed thermal blankets of multi-layer material over two areas of degraded insulation around the light shield portion of the telescope just below the top of the observatory. Meanwhile, inside Discovery Horowitz and Lee worked on the middeck to fabricate new insulation blankets for HST. Final space walk, EVA 5, lasted five hours, 17 minutes. Lee and Smith attached several thermal insulation blankets to three equipment compartments at

2760-568: The potential energy is U = 0. {\displaystyle U=0.} Then the Lagrangian is L ( ϕ , ϕ ˙ ) = T − U = 1 2 m r 2 ϕ ˙ 2 . {\displaystyle {\mathcal {L}}\left(\phi ,{\dot {\phi }}\right)=T-U={\tfrac {1}{2}}mr^{2}{\dot {\phi }}^{2}.} The generalized momentum "canonically conjugate to"

2820-658: The product of the radius of rotation r and the linear momentum of the particle p = m v {\displaystyle p=mv} , where v = r ω {\displaystyle v=r\omega } is the linear (tangential) speed . This simple analysis can also apply to non-circular motion if one uses the component of the motion perpendicular to the radius vector : L = r m v ⊥ , {\displaystyle L=rmv_{\perp },} where v ⊥ = v sin ⁡ ( θ ) {\displaystyle v_{\perp }=v\sin(\theta )}

2880-439: The quantity r 2 m {\displaystyle r^{2}m} is the particle's moment of inertia , sometimes called the second moment of mass. It is a measure of rotational inertia. The above analogy of the translational momentum and rotational momentum can be expressed in vector form: The direction of momentum is related to the direction of the velocity for linear movement. The direction of angular momentum

2940-523: The same body, angular momentum may take a different value for every possible axis about which rotation may take place. It reaches a minimum when the axis passes through the center of mass. For a collection of objects revolving about a center, for instance all of the bodies of the Solar System , the orientations may be somewhat organized, as is the Solar System, with most of the bodies' axes lying close to

3000-558: The scientific capabilities of the HST and helped to keep the telescope functioning smoothly until the next scheduled servicing missions, which were STS-103 in 1999 and STS-109 in 2002. On the third day of the mission, Discovery's seven-member crew conducted the first of four spacewalks (also called Extra-vehicular Activities or "EVAs") to remove two older instruments and install two new astronomy instruments, as well as perform other servicing tasks. The two older instruments being replaced were

3060-515: The system's axis. Their orientations may also be completely random. In brief, the more mass and the farther it is from the center of rotation (the longer the moment arm ), the greater the moment of inertia, and therefore the greater the angular momentum for a given angular velocity . In many cases the moment of inertia , and hence the angular momentum, can be simplified by, I = k 2 m , {\displaystyle I=k^{2}m,} where k {\displaystyle k}

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3120-465: The telescope and as a scientific instrument for astrometric science . The Solid State Recorder (SSR) replaced one of HST's reel-to-reel tape recorders. The SSR provides much more flexibility than a reel-to-reel recorder and can store ten times more data. One of Hubble's four Reaction Wheel Assemblies (RWA) -- part of the telescope's Pointing Control Subsystem —was replaced with a refurbished spare. The RWAs use angular momentum to move and maintain

3180-422: The telescope in a desired position. The wheel axes are oriented so that the telescope can provide science with only three wheels operating, if required. Study of the returned mechanism provided a rare opportunity to study equipment that had undergone long-term service (7 years) in space, particularly for the effects of vacuum on lubricants which were found to be in 'excellent condition'. STS-82 demonstrated anew

3240-483: The telescope, operated the orbiter Remote Manipulator System arm on STS-82 to retrieve the telescope for second servicing at 3:34 am EST, Feb 13, and positioned it above Discovery's payload bay less than half an hour later. Relying on more than 150 tools and crew aids, Lee and Smith performed EVAs 1, 3 and 5, with Harbaugh and Tanner performing EVAs 2 and 4. EVA 1 began at 11:34 pm EST, February 13, and lasted six hours, 42 minutes. One of Hubble's solar arrays

3300-475: The top of the Support Systems Module section of the telescope which contain key data processing, electronics and scientific instrument telemetry packages. STS-82 EVA total of 33 hours, 11 minutes is about two hours shy of total EVA time recorded on first servicing mission. Discovery's maneuvering jets fired several times during the mission to reboost the telescope's orbit by eight nautical miles. Hubble

3360-500: The universe at near infrared wavelengths between 0.8 and 2.5 micrometers. EVA 2 began at 10:25 pm, February 14, and lasted seven hours, 27 minutes. Harbaugh and Tanner replaced a degraded Fine Guidance Sensor and a failed Engineering and Science Tape Recorder with new spares. Also installed was a new unit called the Optical Control Electronics Enhancement Kit , which further increased the capability of

3420-458: Was crewed by a seven person team for the STS-82 mission. The STS-82 mission was the second in a series of planned servicing missions to the orbiting Hubble Space Telescope ("HST"), which had been placed in orbit on April 24, 1990, by Discovery during STS-31 . The first servicing mission was done by Space Shuttle Endeavour on STS-61 . Work performed by Discovery's crew significantly upgraded

3480-399: Was one of four Reaction Wheel Assembly units that use spin momentum to move telescope toward a target and maintain it in a stable position. After this EVA, mission managers decided to add EVA 5 to repair the thermal insulation on HST. EVA 4 began at 10:45 pm, February 16, and lasted six hours, 34 minutes. Harbaugh and Tanner replaced a Solar Array Drive Electronics package which controls

3540-401: Was redeployed on February 19 at 1:41 am, into a 335-nautical-mile (620 km) by 321-nautical-mile (594 km) orbit. Initial checkout of new instruments and equipment during mission showed all were performing nominally. Calibration of the two new science instruments took place over a period of several weeks, with first images and data anticipated in about eight to ten weeks. NASA began

3600-585: Was unexpectedly disturbed by a gust of air from Discovery's airlock when it was depressurized, but was not damaged. Lee and Smith removed two scientific instruments from Hubble, the Goddard High Resolution Spectrograph (GHRS) and Faint Object Spectrograph (FOS), and replaced them with the Space Telescope Imaging Spectrograph (STIS) and Near Infrared Camera and Multi-Object Spectrometer (NICMOS), respectively. STIS expected to shed further light on supermassive black holes. NICMOS features more capable infrared detectors and gave astronomers their first clear view of

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