I have heard that the Voyager spacecrafts received gravitational boosts from some of the planets before they left the solar system.  How is this achieved?  Since we have to conserve energy it seems that whatever speed is gained due to gravity would then be lost as the object flys away from the planet.   Specifically I want to know how we can willingly slow the planets orbit to steal some of its energy.  How do we know that the fly by is going to take energy from the planet rather than lose energy to the planet?
57534
I read in  in this site that the KE a free-falling ball acquires is not originated by the attracting body but that energy was actually stored in the ball when it had been lifted to the height it dropped from.  In this way, it was said, gravity is subject to the conservation of energy principle and cannot change the total energy of an object.  Consider now the maneuver known as a  (also gravity assist) used by space probes such as the . A space probe approaches a planet with velocity $v$, slingshots around, and ends up with velocity $v+2U$, where $U$ is the velocity of the planet.  Consider the energy of the probe. Before, it was $E_i=\frac{1}{2} mv^2$ and after it is $E_f=\frac{1}{2} m(v+2U)^2$. It looks like $E_f$ is much bigger than $E_i$ - but where did the additional energy come from?   Is this not a violation of the conservation of energy principle?
2471
So I asked my science teacher how wind could feel colder than normal air when the particles would be moving faster than normal air particles, meaning that they would have more kinetic energy and a higher temperature. My teacher told me that the faster rate of particles hitting your body would mean that the heat would leave faster than in normal air, but I was confused as to why they would take energy.   Eventually, I figured out that the air particles have kinetic energy separate from their velocity and my teacher confirmed this. He also confirmed that the particles would vibrate in place while they are moving.  How is this possible, and how does the vibration dictate the heat transferred, and not the velocity?
53761
I understand that energy conservation is not a rule in general relativity, but I'd like to know under what circumstances it can still be possible. In other words, when is it possible to associate a potential energy to the gravitational field, so that the energy is constant in the evolution of the system?  Here are some examples, is there a convenient way to define energy in these scenarios?   Just a system of gravitational waves. A point mass moving in a static (but otherwise arbitrary) space-time. Equivalent (if I'm not mistaken) to a test mass moving in the field of a second much larger mass, the larger mass wouldn't move. Two rotating bodies of similar mass.   Overall, I'm trying to understand what keeps us from associating a potential energy to the metric. When we break the time translation symmetry of a system by introducing an electromagnetic field, we can still conserve energy by defining an electromagnetic potential energy. Why can't we do the same when we break TT symmetry by making space-time curved?
122051
I've seen them maneuver. They definitely can go backwards. How fast can they go in reverse? Is warp speed possible, or is reverse limited to impulse power? If it is limited to impulse power, can they travel backwards under impulse power as fast as they travel forwards under impulse power?
26676
When a spaceship is experiencing a constant acceleration of $10m/s^2$, the astronauts will be moving at nearly the speed of light after about a year in the earth's reference frame. This means the spaceship's energy will start to diverge as a function of the speed $v$ so there will be a huge amount of energy necessary to increase the speed of the ship any further. This way, the speed of light can never be crossed.  All of this is clear to me, but all of this is also formulated in earth's reference frame. But from the astronaut's reference frame: the spaceship is simply accelerating at $10m/s^2$ and so the force on the spaceship is constant. Then why would we need huge amounts of energy to accelerate the spaceship?  For example, I read somewhere that the amount of energy that would be needed to accelerate a large spaceship to half the speed of light is more than 2000 times the current world annual energy consumption. How does this make sense in the astronaut's (non-inertial) frame?
24711
When we push the wall, no work is being done. But we feel tired after some time. Since energy cannot be destroyed , the question is where does all the energy get transferred in this scenario. Note : It cannot be all heat as we feel more tired than standing still and if it is being transferred in heat then why it is faster than standing still if no work is being done?
11750
What exactly is ? My book confuses me:     a force can lift an object to a height h, or it can accelerate an object through gravity. In all these cases, a force displaces an object and change the object's total energy.   The examples it gives confuse me. On one hand, there is lifting and on, accelerating through gravity.   I can imagine how lifting will change total energy (kinetic + potential). It essentially gives it more potential energy, and does not take from it any kinetic energy. But just dropping an object and let gravity do the work does not seem to me to increase total energy. Because the total amounts of kinetic and potential energy should be equal.  If just let drop, the object will gain kinetic and lose some potential. Not really anything added to the total energy.
78725
Kind of an odd, random question that popped into my head. Tidal energy - earth's ocean movement, volcanism on some of Jupiter's moons, etc. - obviously comes from the gravitational interaction between large bodies. On earth the interactions with the moon are pulling water around the surface, creating some amount of heat due to friction, etc.   My question is, where does that energy come from exactly? More specifically, what potential energy source is getting depleted to do that work? Is the earth minutely slowing down in its spin - or are the orbits of earth and the moon subtly altered over time by the counteractive movement and friction of liquids and gasses?
122361
I'm watching the first two seasons of Voyager and various episodes have commentary on having energy limitations -- but we constantly see crew using extremely complicated holodeck simulations. Why would they allow use of the holodeck if they need to conserve energy?
67437
Will a machine or a technique ever be possible that allows  in interplanetary space?  And I ask out of pure curiosity. I know there is the "Vomit Comet" that allows for a non-gravity 'simulation' (for lack of a better word) on Earth, and I was thinking about if there would be a way to reverse that and rather have gravity in space.    edit: Say I was building a space shuttle because I'm dying to go to the moon (true story). Unlimited budget, the smartest people you can fathom helping me build my space shuttle.  I get motion sickness and the whole "anti-gravity" thing wouldn't really work for me.  Would there be a way to have gravity on my space shuttle? Perhaps by using a type of machine or magnets or something of the like?
100151
Hypothetically, if you were to travel say, 6 months into the past with no spatial displacement, you would end up floating in space because the Earth would be on the opposite side of the sun.  I know when it comes to sci-fi, they can't account for everything and I don't expect them to. So I'm not nit-picking or anything, I'm just wondering if this is something that has been addressed to any detail, as it seems like it would have to be a major component of any time travel.
41632
I'm trying to make a simple game where a spaceship is launched and then its path is effected by the gravity of planets.  Similar to this game:   I wish to know how to replicate the effect the planets have on the spaceship in this game so a spaceship can 'loop' around a planet to change direction.  I have managed to achieve some bogus results where the spaceship loops in a huge ellipse around the planet or is only slightly affected by the gravity of a planet using Vectors.  Thanks in advance.  p.s I have plenty of coding experience just none to do with game dev.
15849
This is a problem that has bothered me for a couple of weeks now, and I can't seem to wrap my head around it and understand it.  Let's say we have a planet with a mass of m. We also have an object of relatively small mass (so small that its gravitational field would not affect the planet), and we know that at time 0 it is at position h.  If we know the acceleration due to gravity (g), we can calculate the position y  at time t:  $y = h - { g \; t^2 \over 2 } $  And we know that the acceleration due to gravity could be calculated:  $g = G { m \over y^2 }$  But since the acceleration depends on the position of the object relative to the planet, and the position of the object is dependent on the acceleration, this would obviously mean that the first formula won't work when we are working with displacement so large that it would change the acceleration significantly.  So, in essence, my question is, what formula can we use to calculate the position of an object, taking into consideration the change in acceleration due to gravity?
36228
I know that I cannot do this because of conservation of energy, so I am looking for an answer as to why this will not work.  So by my understanding of Einstein's whole famous $E=mc^2$ thing it is possible to turn matter into energy, and energy into matter. So what if you were to create a space station way up high and run a wire down to Earth, then pump some energy up it.  The space station would then turn that energy into matter and let it drop down to Earth. People down at Earth would harvest the kinetic energy somehow, then turn the matter back into energy, pump it back up, then repeat the process. The result would be the energy they started with plus the kinetic energy. Where is the flaw in this reasoning?  (I'm guessing it might take energy for the electrons to fight gravity up to the space station).
119846
Consider a photon is an energetic particle and therefore has a gravitational field. When a photon passes a molecule or particle of dust in space it will pull the dust towards it and deform the dust. This will lose energy in the normal Newtonian way, and the energy is supplied by the photon.   Assuming that the speed of light is constant this implies that the photon will become less energetic and therefore red-shift over its travels, simply as a consequence of interactions with near objects. Is the effect real and/or measurable?
40808
Following the measurement of gravitational waves, many sources described them and explained they carry energy away. What I don't get is how this energy will get transfered back to anything else.  If the fabric of space-time itself is vibrating, it would seem to be in impossible for any physical object to gain this energy.    What am I missing?  How would one hypothetically get energy out of gravitational waves?  If impossible, does the universe end up with nothing but GW?
106655
My understanding of orbital mechanics is very limited, but as I understand geostationary satellite, they stay in place by having an orbital speed corresponding to the spot they're orbiting over.  So my basic intuition tells me that it's not possible to have a geostationary satellite over the poles, since they're effectively standing still, and to my knowledge, a satellite must keep a certain velocity to keep from getting pulled down by gravity.  Am I missing something?