Janus

The aberration of light occurs between objects that have a relative velocity with respect to each other, it does not occur between objects that do not have a relative motion, such as in the example.

It is not only possible, it is most undoubtedly true. The only thing they have in common is the word "dark" in their names. The "dark" in dark matter stands for the fact that it does not emit or react with light. The "dark" in dark energy merely comes from the fact that we already had something called dark matter, so it seemed fitting to reuse the label "dark" for what ever was causing the accelerated expansion of the universe. As far as dark matter being repulsive to baryonic matter, this would be in direct contradiction to what dark matter is supposed to explain, which is why galaxies spin much faster and with different rotation curves then they would if just the gravity of baryonic matter holding them together. The reason there is little to no DM near the Earth is that even though the galaxy has much more DM than baryonic matter, DM is spread out over a much larger volume and thus has a lower overall density than the baryonic matter which is mostly constrained to the visible galactic disk. If you then add in the fact that the mass distribution of the solar system is in turn much much more dense than that of the visible disk overall, the amount of DM that you would expect to find in the whole of the Solar system works out to be the equivalent of a small moon. Since DM does not clump together the way that Baryonic matter does, this would be spread throughout the solar system. 3.

You're assuming something that Relativity denies, that there is such a thing as "absolute motion". Essentially you are saying that there would be a method of determining whether or not the objects are "moving" or not. Relativity states that no such test is possible. This is the same as the "light clock" example. Start off by bouncing a light back and forth between the objects. As seen from either object, the light passes directly between the two. Now accelerate the objects equally. repeat the experiment. The light will still bounce back and forth between the objects, and neither will see the light as coming "from behind" the other object. You can't tell any difference between before and after acceleration. The same would be true of gravity. Two objects "moving" behave the same as two "at rest". Mainly because "moving" and "at rest" are just arbitrary choices based on the frame of reference you decide to use.

The size/destructive ability of the explosion would depend on how much antimatter there was. (one of the inaccuracies of the story is the fact that there isn't enough antimatter on Earth to produce more than a modest bang.)

Well, it's a bit more complex than that. The only way to propel a craft through space is by the rocket principle. Rockets operate by the equation: [math]\Delta V =V_{ex} \ln (MR)[/math] Where [math]\Delta V[/math] is the change in velocity of the rocket Vex is the exhaust velocity of the rocket. and MR is the mass ratio or the mass of the fully fueled rocket divided by the mass of the rocket after the fuel is used. For example, a typical chemical rocket might have a exhaust velocity of 4500 m/s. Escape velocity from the surface of the earth is about 11000 m/s. Solving the above formula for MR for a rocket leaving Earth gives a value of ~11.5 , meaning your fuel must out-mass the the rocket by about 10.5 times. From this it is readily apparent that a chemical rocket has no chance of reaching 0.25c as it would need more fuel than there is in the observable universe. The limiting factor is the exhaust velocity, if we can increase the exhaust velocity, we can decrease the amount of fuel we need. Some ideas for fusion rockets boast possible exhaust velocities of up to 1000,000m/s. But even at this, it would take a mass equal to the Sun's worth of fuel just to get 100 kg up to 0.25c. So to get up to even to 25% of c practically would not only take huge amounts of energy but also a way to generate, contain and direct that energy in such a way as to produce much higher exhaust velocities.

Actually, that's not how gravitational time dialtion operates. It is related to the difference in gravitational potential not gravitational strength. To illustrate, consider a hypothetical "uniform" gravity field, or in other words, a gravityi field that does not decreae in strength with altitude. If you put two clocks in this field at different heights in the field, they will have a different potential (you would have had to expend energy to lift the lower clock to meet the upper clock.) In this example, the higher clock will run faster than the lower clock due to gravitational time dilation, even though both clocks experience exactly the same gravitational pull.

No, you don't. It just seems that way because the difference between your trajectory and the rotation of the Earth, while real, is very, very, very small.

The rocket will not stay over the same spot. As it rises, it will drift Westward with respect as seen by someone on the surface. Its trajectory will be determined by its initial "Eastward" velocity and its velocity upwards and will be independent of the Earth. This is something that became important to the big guns used as early as WWI. The long range of these guns meant that you had to correct for this effect. When fired, the path of the projectile would appear to curve with respect to the Surface of the Earth.

The difference is that water is more or less incompressible, while air is compressible. In other words, one cubic ft of water at the bottom of the abyss masses just about the same as 1 cubic ft at the surface. Air is different. Not only does its pressure go down with altitude but so does its density. 1 cubic ft of air weighs less at 100,000 m than it does at sea level. Since the buoyancy of our "balloon" depends on the balloon material weighing less than the volume of air it displaces, as you go to higher and higher altitudes, you have to lower the weight of the balloon to compensate. Thus the thickness( and strength) of the walls of your balloon must also get thinner meaning that they can withstand less and less pressure without collapsing.

That was because "negatron" was already an alternative name for the electron, and it would have been too easy to confuse negaton and negatron.

Free neutrons decay into a proton, electron and anti-neutrino in a half-life of ~15 min. Besides, a single free neutron actually masses more than a hydrogen atom, so hydrogen gas would be less dense and be more buoyant than a free neutron "gas", not to mention the problems of containing such a "gas".

Moontanman points out the main difficultly in this. When you use a gas, you are equalizing the pressure on the inside and outside, while still having the gas on the inside being of lower density than the outside air. Thus the material from which your container is made does not have to be rigid. If you try to contain a vacuum, you will have a pressure of ~14psi working to crush your container. So let's say that your "balloon" has a 1 foot radius. This gives a surface area of ~1810 in² for a total force of 25334 lbs. This also works out to a volume of 7238 in³. at 20°C, this much dry air weighs about 0.00004 lbs(0.02g). This is the maximum weight that the material of our "vacuum balloon" can have and have even neutral buoyancy. Diamond, for instance, has a density of 3.5g/cm³. A hunk of diamond with a mass of 0.02g would have a volume of 0.006cc. Spread into a shell with a surface area of 1810 in², you get a thickness of 5 nanometers,. This is about 1/40th the thickness of a typical sheet of aluminum foil. Since diamond is 3.6 times harder than aluminum, this hardly seems enough to withstand the 25334 lbs of crushing force exerted by the atmosphere on our balloon.

The gravitational attraction between the Sun and the Earth is proportional to the product of thoer masses (Msun x Mearth). If either gets larger the gravitational attraction becomes stronger. The amount of force that it takes to deflect a mass into a circular path (such as an orbit) agiant its natural tendency to travel in a straight line is proportional to the mass of the object. Thus, if you increase the mass of the Earth by half of the Moons mass (1/162 of the Earth's mass) thne you will increase the Sun's gravitational grip on it by 0.61%, but a the same time, you will be increasing the force needed to hold the earth in its orbit by the same amount. The two effects cancel out and you see no net effect in the Earth's orbit.

No, Gravity is infinite in range.

We can least estimate the maximum energy you dissipated. It takes about 0.06 A to be lethal. Since you weren't killed, we can assume that you passed less than this through your body. 400 V x 0.06 A = 24 W A Joule is a watt-second, so if you were being shocked for 5 sec, the maximum energy you dissipated was ~120 Joules. or about the energy it takes to lift a 1 kg weight 2.45 meters. Your body resistance would have had to be ~6667 ohms. If we instead, use the high end value of 100,000 ohms, then the current drops to 0.004 A and the Joules disapated to 8 Joules.

Yep, he even includes the original article as an afterward for the novel. Hal really took the concept of hard SF to heart. Mission of Gravity has an honored place on my bookshelf.

It depends on what you mean by "flood the World" . Yes, sea levels would rise by many meters, but not to the extent pictured in say, "Waterworld"

The shape of the Earth is due to its gravity and spin. It is a slightly oblate spheroid. Since the Earth's shape is shaped by these forces, are the oceans. the Oceans surface is is all at equal gravitational potential (not equal gravitational force). If the Earth spun faster, its shape would become more oblate and so would its oceans. An extreme example of this would be the world described in the article "Whirligig World" by Hal Clement, A world who's equatorial diameter is some 2.4 times its polar diameter.) Even with this world, the oceans follow the shape of the planet. The only way that would get an ocean that didn't follow the shape of the planet is if the planet was so small that its gravity is to small to have a dominant effect on the planet itself. In such a case, the oceans would still follow an equal potential surface, but necessarily the shape of the world. However, a body small enough to hold an irregular shape against the force of gravity would not have enough gravity to hold on to an "ocean" for very long.

While F=ma, E=Fd, where d is the distance over which the force is applied. Taking your 0-10 and 10-20 example, A car accelerating from 0-10mph covers less distance during accleration than a car starting at 10 mph and accelerating to 20 mph. Since energy is equal to the force applied times the distance, it takes more energy to go from 10-20 mph than it does to go from 0-10 mph.

Common confusion between the everyday usage of a word and the scientific meaning. In astronomy "Halo" refers to a spherical cloud or volume.

Dark matter does exist inside the galaxy. The way to look at it is that DM forms a large spherical "cloud" of nearly uniform density and the galaxy is "embedded" in this cloud.

1.8c is the "closing speed" between A and C in the rest FoR of B. It is the result of taking the starting distance between A and C according to someone at rest with respect to B and dividing it by the time it takes for A and C to meet according to the same FoR. There is nothing nonsensical about it. It is just as real physically as the fact that A measures its velocity with respect to C as being 0.994475c and measures the respective speed between B and C as 0.094475c ( or conversely that C measures the respective speed between A and B as being 0.094475c.) These are all perfectly valid and physically real measurements in each FoR.

Try looking at this animation I made. It goes back to your original scenario, with a rocket going out and then returning. the animation shows events according to the Earth (green dot) frame. The ship is emitting light (the expanding circles) as it travels. The red and blue indicate the red or blue shift seen by an observer at any given point. As the ship starts on its journey, light is emitted in all directions at c, as shown by the first expanding circle. Note that this circle always remains centered on the Earth. As the ship continues on, it continues to emit light as shown by the subsequent circles. Each circles center in turn remains at the pint where the light was emitted, making each circle offset from the last, causing the waves to be closer together on one side and further apart on the other.(essentially, this is the Doppler shift). After 25 days, the light emitted when the ship left Earth reaches the point where the ship will turn around (the first pause in the animation). This is when a person located there will first see the Ship leave Earth. At 50 days, the ship arrives at the turnaround point, 25 days after the person there saw them leave Earth. The animation pauses at 51 days to show the light emitted at the moment of turnaround(the circle that is blue on the left) heading back toward Earth. The return trip is the same as the outbound trip with left and right switched. At 75 days (third pause) the light from the turnaround reaches Earth, while the ship is some 12.5 light days form Earth. 25 days later, at 100 days the ship returns to Earth.

You're doing an improper frame switch. So far, this whole thread has been about the Earth frame. In fact, in your very first post you said: And in the Earth frame, the ship does chase after its own light. Besides, even if you switch to the traveler frame, you will find that the light from the u-turn will reach the Earth 25 yrs ahead of the traveler by the Earth's clock. You just have to take into effect that in the traveler FOR, the Earth is rushing to meet the light at 0.5c, that the earth clock runs slower and that the Earth clock reads later than 50 yrs right after the u-turn is made(Relativity of Simultaneity).

Neither does the Doppler effect for sound. If I'm standing next to the road and there is no wind, the speed of sound from the ambulance doesn't change, what changes is the distance between you and the ambulance, and the time it takes each successive "dee doo" to reach you. Example: The ambulance starts its siren when it is 340 m away, travels towards you at 34 m/s and emits a "dee doo" once a second. Sound travels at 340 m/s, so you hear the fisrst "dee doo" in one second. At this same time, the ambulance emits its second "dee doo" but since it has traveled 34 meters closer to you since it emitted it last "dee doo", the sound only takes 0.9sec to reach you. So, you hear the first "dee doo" at one sec, and 0.9 sec later at 1.9 sec you hear the second. One tenth of a sec later, the ambulance emits a third "dee doo", by which time it is another 34 meters closer so the sound onlt takes 0.8 sec to travel the distance and arrives at 2.8 sec or 0.9 sec after the second "dee doo" In other words you hear the "dee doo"s 0.9 sec apart even though they were emitted 1 sec apart. Not only that, since the distance between you and the ambulance changed over the course of the emission of the 'dee doo's, each part of each sound wave was emitted at different distances, and you will hear the pitch of the "dee doo's as being higher. All without any chnge in the speed of sound you here. Which just means that since the speed of light doesn't change for you, you can always treat it as if you are stationary and the other object is moving, unlike with sound, where you have to consider the speed of the receiver relative to the medium. This however does not change the fact that the distance between you is changing.