Acceleration..

[Mohit Pandey]

Tormod-A geostationary satellite, for example, appears to be completely still when seen from the ground of the Earth, but it moves around it at the speed of one orbit per Earth rotation, which is pretty fast, or 11000 km/h.

Sorry, but what is 11000 km/h? speed of rotation of earth or its revolution? Please tell me both speed.

Sanctus-Mohit, it is right in the given reference frame (which may be the sun with some given axis, not earth because there you don't move).

 

Pyrotex-If you consider only the speed of the Earth's surface spinning about its center, then your speed (at the equator) is about 1000 mph or about 1700 kph

Can you explain it so that I can understand in a better way. :-)

One more thing, there is a conflict between Pyrotex and Sanctus. Please tell me the correct through explanation.

[modest]

Mohit,

Anything in earth’s rotating reference frame makes one revolution around earth’s axis of rotation per day. As such, it has a speed of (2 π r) / day where r is the distance to earth’s axis of rotation. Speed increases with r.

 

A person on the equator moves about 40,000 km / day while a geosynchronous satellite moves about 265,000 km / day. They both are in earth’s rotating reference frame and the earth appears relatively unmoving and unrotating to them.

[Pyrotex]

...A spaceship with constant force and mass will have constant acceleration. ...

You have to explain HOW a constant mass spaceship can have a constant force. It takes energy to produce an accellerating force. Energy must come from somewhere, ultimately from mass. Either that, or the force must come from expelling mass.

 

Modest, your understanding of physics seems a bit shaky. At best. :)

[Tormod]

Sorry, but what is 11000 km/h? speed of rotation of earth or its revolution? Please tell me both speed.

 

A person on the equator moves about 40,000 km / day while a geosynchronous satellite moves about 265,000 km / day. They both are in earth’s rotating reference frame and the earth appears relatively unmoving and unrotating to them.

 

Modest replied for me. :)

[Pyrotex]

...One more thing, there is a conflict between Pyrotex and Sanctus. Please tell me the correct through explanation.

Assume the Earth is rotating about its axis, the line connecting the north pole to the south pole. Ignore the Sun. Ignore the Earth's rotation around the Sun. Just focus on the spinning Earth. Like a soccer ball spinning on the tip of your finger.

 

The Earth spins once each day. The circumference of the Earth at the Equator is 25,000 miles.

 

So, if you stood on the Equator, you would spin around with the Earth, 25,000 miles in 24 hours. This calculates to a speed of 1,042 mph -- or 1667 km/hr.

[CraigD]

You have to explain HOW a constant mass spaceship can have a constant force.

There are several approaches to propulsion that permit a spaceship to have a (nearly) constant mass and thrust, notwithstanding that nearly no spacecraft using such propulsion system has yet been built and flown.

 

Solar sail propulsion is one of the best known examples. Although it’s of no obvious advantage to do so, a solar sail craft could vary the sail area it presents to the light that drives it in inverse proportion to the light flux (eg: increase its area by a factor of four when doubling its distance from the sun). Such a craft would have a constant mass, and a constant force and acceleration.

 

A variation on the simple solar sail is to propel it not with naturally occurring sunlight, but with a laser beam. Because a laser beam can be made to diminish in flux (attenuate) at much less than the [math]f \approx r^{-2}[/math] of a normal light source, such a craft can have a constant mass and fairly constant thrust without changing the area of its sail. It can also have a much greater thrust over a much greater range than one that relies on natural sunlight.

 

Other “non-rocket” propulsion systems include a “fountain”, in which a precisely aimed stream of projectiles is expelled to strike the spacecraft, thrusting it.

 

In addition to the practical space-engineering challenges of constructing powerful lasers or projectile throwers, the latter two of these approaches present tremendous aiming challenges, as none of them will work if the laser beam or projectiles miss the ship. Nonetheless, they are the subject of serious, if currently somewhat far-term, research.

It takes energy to produce an accellerating force. Energy must come from somewhere, ultimately from mass. Either that, or the force must come from expelling mass.

In all present-day, rocket-propelled spacecraft, the mass equivalent of the energy required to accelerate the craft and its reaction mass is so tiny compared to its reaction mass that it can be ignored.

 

For example, assuming the example in post #6 is in units of kg, meters, and seconds, the mass equivalent of the energy required to accelerate it to a realistic delta-V of 2310 m/s (a bit less than the 3200 of the third stage of a manned Apollo moon mission used insert it into a trans-lunar trajectory) its energy mass equivalent is about [math]\frac{45202021 \,\mbox{J}}{c^2} \cdot= 5 \times 10^{-10} \,\mbox{kg}[/math], while it expells 89.06 kg of its 100 kg total mass as reaction mass.

 

Although increasing the exhaust velocity of the rocket can reduce the disparity between energy mass equivalent and reaction mass, it must be increased to relativistically large values before the ratio approaches or exceeds 1:1. The energy density requirements of such a rocket are tremendous, almost certainly requiring larger masses of antimatter than have ever been manufactured – in short such rockets are, at present, as or more far-fetched as the non-rocket propulsion schemes described earlier.

 

Modest, your understanding of physics seems a bit shaky. At best.

I humbly suggest, Pyro, that you reassess. Modest’s post history suggest to me a strong grasp of basic mechanics (and a helpful, pleasant disposition :)). I believe he used the example of a constant mass, constant force spacecraft in an effort to explain a point of basic mechanics as simply as possible, not as a realistic suggestion.

[modest]

Acceleration is force / mass. A spaceship with constant force and mass will have constant acceleration. Your solar-sail spaceship will have constant mass until its total change in velocity becomes relativistic. However, solar sails do not give constant force. As the distance from the sun increases, the force propelling your spaceship would decrease by the inverse square law. This would be the limiting factor on this type of spaceship design.

 

You have to explain HOW a constant mass spaceship can have a constant force. It takes energy to produce an accellerating force. Energy must come from somewhere, ultimately from mass. Either that, or the force must come from expelling mass.

 

I do.

 

Your solar-sail spaceship will have constant mass until its total change in velocity becomes relativistic.

 

I assume a solar-sail because rudeonline does

 

I was thinking about a spaceship, using solar energy to accelerate.

 

I explain diminishing force is the problem with solar-sails

However, solar sails do not give constant force. As the distance from the sun increases, the force propelling your spaceship would decrease by the inverse square law. This would be the limiting factor on this type of spaceship design.

 

and so constant acceleration is not possible using solar energy as rudeonline hopes

 

-modest

[Qfwfq]

Although increasing the exhaust velocity of the rocket can reduce the disparity between energy mass equivalent and reaction mass, it must be increased to relativistically large values before the ratio approaches or exceeds 1:1.

You certainly couldn't exceed this ratio. To attain it, one may simply use a well-focussed laser beam as a rocket engine; the more perfect the laser's conversion efficiency, the more exactly you would have the ratio.

 

It is however true that most of the energy is going into the beam and little of it into increasing the vehicle's kinetic energy, which I believe was the real point of the original question. The total amount of energy expended depends on so many things that I really don't think it was the intent of the OP, whether one discusses the method of propulsion or issues such as friction. :shade:

[Pyrotex]

...I humbly suggest, Pyro, that you reassess. Modest’s post history suggest to me a strong grasp of basic mechanics (and a helpful, pleasant disposition....

I have reassessed. :doh:

 

I did not pick up on the posibility of using external sources of energy/momentum to propel the craft. In spite of having read many of Robert Forward's science fiction novels. :hihi:

[Little Bang]

This is off topic but Boerseun brings up a rather interesting point in post #4. If a particle is moving at near C with respect to us it's mass would appear to be approaching infinity. Doesn't far off galaxies that are speeding away from us at near C fit this scenario?

[CraigD]

This is off topic but Boerseun brings up a rather interesting point in post #4. If a particle is moving at near C with respect to us it's mass would appear to be approaching infinity. Doesn't far off galaxies that are speeding away from us at near C fit this scenario?

Indeed, an interesting question.

 

As best I’m able to figure out, no major issues arise from it, as while the relativistic mass of distant, co-receding objects approaches infinity as the distance between them approaches infinity, their gravitational attraction approaches zero as the square of the distance approaches infinity, preventing the appearance of “infinity absurdities”.

 

The physics here is a bit over my head and beyond my comfort zone, but here’re a few data and derivations:

The radius of the observable, causally-connected universe is thought to be about 14400 Mpc. (from wikipedia article “observable universe”)

The Hubble constant, [math]H_0[/math], is about 75000 m/s/Mpc

So, according to Hubble’s law, the most distant objects in the universe appear to one another to be receeding at about [math]75000 \cdot 28800 \dot= 2.16 \times 10^9 \,\mbox{m/s} \dot= 7.2 \,\mbox{c}[/math]

 

Now, the iffy part. Treating this speed [math]v_r[/math] as due to relativistic dilation,

[math]v_r = \frac{v}{\sqrt{1-\left( \frac{v}{c} \right)^2}}[/math]

, we get

[math]v = \frac{v_r}{\sqrt{1+\left( \frac{v_r}{c} \right)^2}}[/math]

Giving a relative speed of about .99049227 c for the most objects in the universe.

The mass dilation for this, [math]\frac{1}{\sqrt{1-\left( \frac{v}{c} \right)^2}}[/math], is about 7.27.

 

Combining Hubble’s law, Relativity, and Newton’s universal gravitation, we get

[math]K\frac{\sqrt{\left(\frac{H_0}{c}x \right)^2 +1}}{x^2}[/math], where K is a constant.

 

Where [math]\frac{H_0}{c}x[/math] is much less than 1, this gives the same result as universal gravitation, [math]\frac{K}{x^2}[/math]. As it nears and exceeds 1, at around [math]x = 4000 \,\mbox{Mpc}[/math], it approaches [math]\frac{K}{x}[/math].

 

Assuming I’ve not made some conceptual blunder, this derivation seems so obvious that I’m sure professional and well-trained amateur cosmologists concerned with large-scale gravity know it well. It adds a bit of additional complexity to the subject, but doesn’t appear to have a dramatic impact on anything – no “infinity absurdities” emerge from it.

[Little Bang]

Your logic appears to be valid and brings another question to mind. Is the mass gain apparent or real? If real what about the galaxies just outside of the visible universe, they will be even closer to C with infinite mass and infinite gravity. Would explain the accelerated expansion of the observable universe?

[Pyrotex]

Okay, time to give the

 

:cup: :applause: STANDARD INTERPRETATION OF RELATIVITY. :santa3: :cup:

 

...hey! knock it off with the drums!... [ahem]

 

In both Special and General Relativity, Einstein made it clear that we could never see any part of the Universe as if we had "God's Eyes". All that we can do is observe with our own eyes (telescopes, instruments, etc.). The equations of Relativity tell us what WE will observe from our own 'backyard' Frame of Reference (FOR).

 

Experiments with subatomic particles and atomic clocks seem to say that these observations are more than just illusions, they are "real" (in some sense). Q can prolly explain better than I.

 

But it is important to ask questions that permit of US making an observation from our own FOR.

[Little Bang]

So your saying that we can ignore the effects of mass outside the visible universe?

I'm off topic because the original question has been answered.

[Pyrotex]

So your saying that we can ignore the effects of mass outside the visible universe?...

Yes, I think that is correct.

 

Remember, the "visible" universe is not just "what we can see" like it was some arbitrary or accidental limit. What we can see is bounded by the age of the universe and the speed of light. Anything farther away than the visible universe cannot have affected us in any way. (Assuming that gravity and all other forces are also bound by the speed of light.)

 

A huge "wave" of gravitational force or cosmic radiation or whatever may have set out in our direction from "beyond the visible universe" at some point after the Big Bang, but the "wave" will never reach us. Only events that originated within our "universe" ever have a chance of reaching us. An event that occurred exactly ON the EDGE of our visible universe would take a near infinite amount of time to reach us.

 

(I think)

[freeztar]

Hopefully I'm not putting words in Pyro's mouth (unlike nothing [inside joke]) when I say:.

Every "event" conceivable is bound by the Light Cone.

 

If we can't see it, it didn't happen. :)

[Qfwfq]

And when your world line finally intersects that event's light cone, all of a sudden it did happen. Even if it happened two billion years before.