Special: Pioneer Effect and Energy Conservation

[kmarinas86]

Correct:<br />GPE+KE=constant<br />-GMm/r+m*pioneeracceleration*r+.5mV²=C=0<br />-GM+pioneeracceleration*r²+.5V²r=0<br />.5V²=.5*(Escape Velocity)²=(Orbital Velocity)²=v²<br />-GM+pioneeracceleration*r²+v²r=0<br />r=(sqrt(v^4+4*pioneeracceleration*GM)-v²)/(2*pioneeracceleration)<br /><i>Energy is conserved</i><br /><i>Real Distances</i><br /><i>units (m/s)^4 are positive</i><br /><i>units (m/s)² are either negative or postive</i><br /><i>kinetic and potential energy</i><br /><br />Incorrect (Suggests an acceleration of kuiper belt objects that is not observed):<br />Acceleration=GM/r²+pioneeracceleration<br />Acceleration=v²/r<br />If M=0, Acceleration=pioneeracceleration : Acceleration towards sun (contradicts the idea of using the pioneer anomaly for cosmological purposes)<br />v²/r=GM/r²+pioneeracceleration<br />-pioneeracceleration*r²+v²r-GM=0<br />r=(sqrt(v^4-4*pioneeracceleration*GM)-v²)/(2*-1*pioneeracceleration)<br /><i>Energy is not conserved</i><br /><i>Complex Distance</i><br /><i>units (m/s)^4 are "negative"</i><br /><i>units (m/s)² are imaginary</i><br /><i>imaginary energy</i><br /><br />Correct (Suggests that using GM/r² leads to an understimation of the solarsystem's mass):<br />Acceleration=GM/r²-pioneeracceleration<br />If M=0, Acceleration=-pioneeracceleration : Acceleration away from sun (i.e. the Hubble Acceleration which = c*HubbleConstant)<br />Acceleration=v²/r<br />v²/r=GM/r²-pioneeracceleration<br />pioneeracceleration*r²+v²r-GM=0<br />r=(sqrt(v^4+4*pioneeracceleration*GM)-v²)/(2*pioneeracceleration)<br /><i>Energy is conserved</i><br /><i>Real Distances</i><br /><i>units (m/s)^4 are positive</i><br /><i>units (m/s)² are either negative or postive</i><br /><i>kinetic and potential energy</i><br /><br />Conclusions:<br />Pioneer acceleration is due to a change in Gravitational Potential Energy formula.<br />Pioneer acceleration <i>decreases</i> orbital velocity.<br />Pioneer acceleration leads to <i>energy loss</i>, not <i>energy gain</i>.<br />The only way there would be a relative

 

[Saiph]

I'd love to reply...but I can't follow your work as there is no real explaination to why you chose those forms of the equations. Present it like a textbook. We know this, and can do this operation because.....and that gives us this. etc.<br /><br />Otherwise I give you a...wha...huh?<br /><br /> <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

 

[kmarinas86]

Taking into consideration Gravitational and Kinetic Energies, while disregarding Chemical and Nuclear Energies, etc.:<br /><br />GPE+KE=constant<br /><br />Where Graviational Potential Energy is directly converted to Kinetic Energy.<br /><br />We know that originally, we have:<br />GPE=-GMm/r<br />This found in many textbooks where:<br />G is the Gravitational Constant<br />M is the Mass of the Massive object<br />m is the mass of the smaller object<br />r is the distance between the center of masses M and m<br /><br />Force*Distance=Work=Mass*Acceleration*Change in Height<br /><br />m*GM/r²*r=GMm/r<br /><br />Therefore, for the pioneer effect:<br /><br />m*pioneeracceleration*r<br /><br />We know that with increasing r, -GMm/r increases, because it is negative. It tends to 0 at infinite distances. However, the new idea is that the pioneer effect modifies this. So with increasing r, m*pioneeracceleration*r increases.<br /><br />Therefore:<br /><br />GPE_new= -GMm/r + m*pioneeracceleration*r <br /><br />Ignoring friction and other forces, the sum of Gravitational and Kinetic Energies is constant.<br /><br />GPE_new + KE = constant<br /><br />KE=.5mV²<br />Where V = Escape Velocity<br /><br />Escape Velocity is the velocity needed to overcome the gravitational potential.<br /><br />Substitute:<br />-GMm/r + m*pioneeracceleration*r + .5mV² = constant<br /><br />Reorder:<br />m*pioneeracceleration*r + .5mV² - constant - GMm/r = 0<br /><br />Divide by m:<br />pioneeracceleration*r + .5V² - constant - GM/r = 0<br /><br />With the pioneer effect, we no longer take the following relationship as precise:<br /><s>.5V²</s> = <s>GM/r</s><br /><br />So instead we will solve the equation using the quadratic formula, but first we have to convert the equation to quadratic form:<br /><br />Mutiply by r:<br />pioneeracceleration*r² + (.5V²-constant)*r - GM = 0<br /><br />a=pioneeracceleration<br />b=(.5V²-constant)<br />c=-GM<br />r=[-b+sq

 

[alkalin]

I appreciate your ability in the math area, but should there be other considerations due to the extremely small effect we are seeing?<br /><br />Is it possible this may be happening? When we are in the vicinity of the sun and earth we have a large gravity influence from these bodies. For practical purposes we might ignore other nearby gravity sources such as the other planets because their effect would be pretty much in the noise. Also very much in the noise would be the Kuiper belt objects. But nonetheless there could be a slight tug from them that would cause an almost unnoticeable acceleration toward them, yet for our practical gravity and acceleration measure, we attribute all gravity to the earth or sun. One result is we might be calculating our suns mass slightly under actual. There might also be a slight under calculation because of photon pressure coming from the sun. I suspect these issues might have already been considered. But over a great distance from the sun, the Kuiper belt gravity may become above the noise level.<br /><br />So when a pioneer has arrived in the Kuiper belt vicinity, the belt’s gravity influence becomes one of deceleration. Since regional densities of the Kuiper belt could vary, both pioneers might be affected gravitationally a little different. Gravity influence from earth and other planets is now pretty much in the noise, but the sun still does have a small tug. <br /><br />This might also imply there are a large number of bodies in the kuiper belt that we do not yet know about, and have greatly underestimated so far. I think some studies on these objects seem to suggest this possibility.<br />

 

[Saiph]

that could happen only if there is an assymetrical distrubtion of material out there. Otherwise the gravity will cancel out.<br /><br />Sounds plausible right?<br /><br />But there are two pioneer probes heading in pretty different directions, both experiencing the same thing. <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>