## What-If 0058: "Orbital Speed"

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Barstro
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### Re: What-If 0058: "Orbital Speed"

WIMP wrote:
segundus wrote:I don't understand this. Geostationary satellites orbit at the same speed the earth revolves. So if you launch one of them, why would you need to gain any speed in addition to the speed you already have from being on the surface of the earth?

The Earth spins at something like 1000 miles/hr at the equator. If you launch a satellite from the equator, it receives Earth's 1000 mph East velocity. Then you climb way, way up to geostationary orbit. Your orbit is now much larger than the Earth's ~24,000 mile circumference, and at 1000 mph, you cannot complete a full orbit in 24 hr. You need to add velocity, so you're covering your much larger orbit in the same amount of time as the slower-rotating Earth covers its smaller rotation.

Your basic premise (edit; segundus) is incorrect. The geostationary satellites orbit at the same rpm as the earth; not the same speed.

Consider a record player (remember those?). Put mark about an inch from the center of the turntable, and another mark four inches out. Both will revolve (revolution?) at the same rate, but the outer mark makes a larger circle, thus covers more distance in the same amount of time (travels faster).

In order to stay directly over a spot on earth that is traveling at 1000 mph, an object farther away from the earth's center would need to travel faster to maintain an rpm of one-per-twenty-four-hours.
Last edited by Barstro on Thu Aug 15, 2013 1:45 pm UTC, edited 1 time in total.

gmalivuk
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### Re: What-If 0058: "Orbital Speed"

Whose premise is incorrect? WIMP seems to have explained it accurately, correcting segundus's mistake.
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gmalivuk
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### Re: What-If 0058: "Orbital Speed"

marsilies wrote:Here's a question: If it takes such a high speed (and so much energy to reach that speed) to stay in low-earth orbit, why don't we simply go into a higher orbit?
Because you need even more energy do do that. The difference is that the energy of a high orbit is tipped more toward potential than the highly kinetic energy of a low orbit.

The vis-viva equation is useful to keep in mind here: http://en.wikipedia.org/wiki/Vis-viva_equation

As is the one for specific orbital energy: http://en.wikipedia.org/wiki/Specific_orbital_energy

Note in particular that a closed orbit with a larger semimajor axis always means more energy (with the usual convention of zero potential energy at infinity, and negative potential energy closer in).
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Chanfan
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### Re: What-If 0058: "Orbital Speed"

A friend was pointing out that Seattle sits on the Salish Sea (Puget Sound is part of it). So, to nitpick, I assume it was meant that "space is closer than the ocean".

ijuin
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### Re: What-If 0058: "Orbital Speed"

DanD wrote:
keithl wrote:Heat shields ablate. The temperature near the heat shield surface is far higher than any material can stand, so they evaporate, carry off some of the energy from the solid shield via heat of evaporation, and the ejected material keeps absorbing heat for a fraction of a millisecond while it is accelerated and blown away by the plasma stream. There might be a better way to do it, but many engineers and scientists spent many billions of dollars learning how to do heat shields, and how not to do heat shields. Gotta deliver those warheads, on time and intact, or it spoils the whole war.

Ablative heat shields ablate. Thermal soak heat shields don't.

On the other hand, ablative shields have less flight mass for any credible single-use reentry profile, and keeping the mass down is crucial when you need an entire oil tanker's worth of fuel just to get into orbit.

Barstro
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### Re: What-If 0058: "Orbital Speed"

gmalivuk wrote:Whose premise is incorrect? WIMP seems to have explained it accurately, correcting segundus's mistake.

You are correct. I mean to quote only segundus to demonstrate that he needed to only think of rpm instead of mph to find the logic.

Crossing out the extra quote, but leaving it in to show why you corrected me.

EDIT: well, I would cross it out if I knew how to do that on this forum. Still won't delete my error though, for continuity's sake.

brenok
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### Re: What-If 0058: "Orbital Speed"

Barstro wrote:EDIT: well, I would cross it out if I knew how to do that on this forum. Still won't delete my error though, for continuity's sake.

Use the [ s ] tags

lgw
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### Re: What-If 0058: "Orbital Speed"

keithl wrote:
rmsgrey wrote:
keithl wrote:But you must deal with vibrations and stored elastic energy in the tether. There's no natural damping in space like there is in an atmosphere, and damping with a mass at one end, shock absorbers, etc., is not very effective for something very long with a finite speed of sound. This is a big problem for hypothetical objects like space elevator cables. They are simple in concept, as static objects, but distributed nonuniform mass and tension and gravity and angular momentum makes them fiendish to model and implement and keep under control.

Though if you can get the maths right, you can, in principle, use the vibrations to dodge objects in intersecting orbits.

Sadly, there's a lot more to it than getting the maths right. There are many more degrees of freedom in the tether than there are in the attachment, so making it jiggle correctly to deal with the next half dozen collider candidates requires monumental calculations based on an incredible amount of precise measurement, both of the position and velocity of all the bits of tether and of all the potential colliders themselves. Complex series of perturbations must be launched days or weeks in advance. I presented some of this at the Space Elevator conference a couple of years ago. They were making calculations based on an average of two avoided colliders per day. But the rate is random, and the frequency distribution is a Poisson. Over 20 years, there would be six days when you would have to deal with as many as eight potential collisions.

A tapered space elevator cable is especially worrisome, because there is a big lump of fat cable through most of the middle, with relatively thin cable stretching down to the ground side attachment. There are also lump masses of climbers whose future movements and positions will also change predicted wave propagation. Move the ground attachment a kilometer sideways, and the lump in the middle will move - eventually. But it's like pulling on the Queen Mary with kite string; changes are slow.

Seemingly simple structures, like stretched strings, can do amazingly complex things. That's why some pianists and string musicians get big audiences.

This is, fundamentally, why space elevators are good SF but won't actually work: it's an engineering problem. To reach geosynchronous obit, about half the "non-wasted" energy is gravitational potential, and about half is lateral acceleration. In a Physics 101 world, a space elevator is great because it removes most of the "wasted" energy - atmospheric drag and gravitational "drag". The problem is the accumulation of energy of the counterweight "swinging about" its tether as angular momentum is conserved when loads are lifted. And there's basically no way to remove that energy from the system.

In a Physics 101 world, hey, no problem, we'll just send the second load up when the pendulum is "swinging the other way". But the real world problem is more like trying to stop a guitar swinging from a guitar string by playing a song on that string, except without the damping that makes a guitar string stop vibrating as it makes noise. Basically, everything you try is just going to add more energy to the system, in ever more complex modes of oscillation - BHG is going to be saying "but what if we add more energy" with every load lifted, and it won't end well.
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davidstarlingm
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### Re: What-If 0058: "Orbital Speed"

lgw wrote:This is, fundamentally, why space elevators are good SF but won't actually work: it's an engineering problem. To reach geosynchronous obit, about half the "non-wasted" energy is gravitational potential, and about half is lateral acceleration. In a Physics 101 world, a space elevator is great because it removes most of the "wasted" energy - atmospheric drag and gravitational "drag". The problem is the accumulation of energy of the counterweight "swinging about" its tether as angular momentum is conserved when loads are lifted. And there's basically no way to remove that energy from the system.

In a Physics 101 world, hey, no problem, we'll just send the second load up when the pendulum is "swinging the other way". But the real world problem is more like trying to stop a guitar swinging from a guitar string by playing a song on that string, except without the damping that makes a guitar string stop vibrating as it makes noise. Basically, everything you try is just going to add more energy to the system, in ever more complex modes of oscillation - BHG is going to be saying "but what if we add more energy" with every load lifted, and it won't end well.

Solar-powered compensating thrusters on the counterweight?

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### Re: What-If 0058: "Orbital Speed"

davidstarlingm wrote:Solar-powered compensating thrusters on the counterweight?

Using what for reaction mass?
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mjr0274
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### Re: What-If 0058: "Orbital Speed"

It would take you about two lines of the chorus (16 beats of the song) to cross the English Channel between London and France.

Sorry to be pedantic but the English Channel doesn't divide London and France. It divides England (or the UK, if you're being picky) and France. About 26 miles at its narrowest so a bit less than 16 beats.

mjr0274
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### Re: What-If 0058: "Orbital Speed"

segundus wrote:I don't understand this. Geostationary satellites orbit at the same speed the earth revolves. So if you launch one of them, why would you need to gain any speed in addition to the speed you already have from being on the surface of the earth?

Geostationary satellites orbit at the same angular speed as the Earth, not the same linear speed. In other words, they cover 360 degrees of an orbit in the same time that the Earth covers 360 degrees of its revolution. The higher up they are, the larger the radius of circle they have to travel, so the faster they have to be moving. If you think about sitting on a playground roundabout, the further out you are the faster you have to move. It's like that with a geostationary satellite, except without the dizziness.

lgw
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### Re: What-If 0058: "Orbital Speed"

Pfhorrest wrote:
davidstarlingm wrote:Solar-powered compensating thrusters on the counterweight?

Using what for reaction mass?

And helping how, exactly? This not being a freshman Physics pendulum, there's a significant amount of energy in the cable, and the counterweight moves as a complex hybrid of pendulum, orbiting satellite, and weight bouncing at the end of a spring.

For sure each load lifted would need to be mostly fuel (though still probably a higher percentage of payload than a chemical rocket that can reach GEO), plus you'd likely need to constantly paint the portion of the cable in the atmosphere with some sort of protective coating to prevent erosion. Still, I'm thinking it's the engineering difficulty in stabilizing a chaotic system that's the hard part.
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Red Hal
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### Re: What-If 0058: "Orbital Speed"

Longitudinal and transverse damping at each end. Edit: actually, that's a facetious statement on its own. Suitable damping should not be too hard to achieve, and the real risk will be from harmonics in the system rather than mere vibration of the ribbon.
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mathmannix
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### Re: What-If 0058: "Orbital Speed"

WIMP wrote:
segundus wrote:I don't understand this. Geostationary satellites orbit at the same speed the earth revolves. So if you launch one of them, why would you need to gain any speed in addition to the speed you already have from being on the surface of the earth?

The Earth spins at something like 1000 miles/hr at the equator. If you launch a satellite from the equator, it receives Earth's 1000 mph East velocity. Then you climb way, way up to geostationary orbit. Your orbit is now much larger than the Earth's ~24,000 mile circumference, and at 1000 mph, you cannot complete a full orbit in 24 hr. You need to add velocity, so you're covering your much larger orbit in the same amount of time as the slower-rotating Earth covers its smaller rotation.

OK, what if you built a really, really tall ladder (22,236 miles long!), carried a sattelite to the top, and let go? It would be in geosynchronous orbit, right?
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Red Hal
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### Re: What-If 0058: "Orbital Speed"

What if you held a really long stick horizontally and turned round? How fast would the end near you be moving? How fast would the other end be moving?
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brenok
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### Re: What-If 0058: "Orbital Speed"

mathmannix wrote:OK, what if you built a really, really tall ladder (22,236 miles long!), carried a sattelite to the top, and let go? It would be in geosynchronous orbit, right?

I believe that's the idea of the space elevator, mentioned on the discusson above.

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### Re: What-If 0058: "Orbital Speed"

mathmannix wrote:
WIMP wrote:
segundus wrote:I don't understand this. Geostationary satellites orbit at the same speed the earth revolves. So if you launch one of them, why would you need to gain any speed in addition to the speed you already have from being on the surface of the earth?

The Earth spins at something like 1000 miles/hr at the equator. If you launch a satellite from the equator, it receives Earth's 1000 mph East velocity. Then you climb way, way up to geostationary orbit. Your orbit is now much larger than the Earth's ~24,000 mile circumference, and at 1000 mph, you cannot complete a full orbit in 24 hr. You need to add velocity, so you're covering your much larger orbit in the same amount of time as the slower-rotating Earth covers its smaller rotation.

OK, what if you built a really, really tall ladder (22,236 miles long!), carried a sattelite to the top, and let go? It would be in geosynchronous orbit, right?

Yes, because the ladder will have imparted a great deal of tangential velocity on the way up.
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davidstarlingm
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### Re: What-If 0058: "Orbital Speed"

Pfhorrest wrote:
davidstarlingm wrote:Solar-powered compensating thrusters on the counterweight?

Using what for reaction mass?

Material mined from the counterweight. If we're capturing asteroids and attaching tethers to them, it's not terribly difficult to envision towing a smaller asteroid over now and then to keep the weight roughly constant.

lgw wrote:
davidstarlingm wrote:Solar-powered compensating thrusters on the counterweight?

And helping how, exactly? This not being a freshman Physics pendulum, there's a significant amount of energy in the cable, and the counterweight moves as a complex hybrid of pendulum, orbiting satellite, and weight bouncing at the end of a spring.

For sure each load lifted would need to be mostly fuel (though still probably a higher percentage of payload than a chemical rocket that can reach GEO), plus you'd likely need to constantly paint the portion of the cable in the atmosphere with some sort of protective coating to prevent erosion. Still, I'm thinking it's the engineering difficulty in stabilizing a chaotic system that's the hard part.

I'm just saying that thrusters on the counterweight would be a more manageable approach to compensating than trying to alternate angles when you're sending up payloads.

gmalivuk wrote:
mathmannix wrote:OK, what if you built a really, really tall ladder (22,236 miles long!), carried a sattelite to the top, and let go? It would be in geosynchronous orbit, right?

Yes, because the ladder will have imparted a great deal of tangential velocity on the way up.

The moon is so far away that it takes nearly a month to make a full revolution, but it's still moving more than twice as fast as the Earth's surface. Of course, if it weren't so heavy, it would move at around the same speed as the Earth's surface.

DanD
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### Re: What-If 0058: "Orbital Speed"

Dynamically damping a space elevator is far from unsolvable. Short sections of conductive tether acting as rotors in the earth's magnetic field. Servo driven hydraulic dampers built into the tether. Variable tension from linear motion of the counterweight along the tether outboard of geosynch. Those are just the ones I've come up with so far. We do complex vibration damping in all sorts of machinery right now, and the problem does not become infinitely difficult just because the structure is so big.

If nothing else, simple material strength make this still a science fiction concept instead of science, but I have yet to see something to convince me it is theoretically impossible.

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### Re: What-If 0058: "Orbital Speed"

Red Hal wrote:Longitudinal and transverse damping at each end. Edit: actually, that's a facetious statement on its own. Suitable damping should not be too hard to achieve, and the real risk will be from harmonics in the system rather than mere vibration of the ribbon.

It's just a Simple Matter of Engineering, if it still seems hard just wave your hands faster! You need some way to remove energy from the system - our intuitions are based on an environment where that's easy, but a space elevator is a particularly difficult environment. The one thing you have going for you for heat dissipation is a very high surface area (assuming some handwavium for damping in the first place).

davidstarlingm wrote:
Pfhorrest wrote:
davidstarlingm wrote:Solar-powered compensating thrusters on the counterweight?

Using what for reaction mass?

Material mined from the counterweight. If we're capturing asteroids and attaching tethers to them, it's not terribly difficult to envision towing a smaller asteroid over now and then to keep the weight roughly constant.
...
I'm just saying that thrusters on the counterweight would be a more manageable approach to compensating than trying to alternate angles when you're sending up payloads.

Well, you might not want to soil your own nest, but dragging a CHON asteroid into a higher orbit and mining it as needed would be a good source for fuel. That does illustrate the sort of engineering project we're talking about here, though - asteroid mining is just the start.

davidstarlingm wrote:
gmalivuk wrote:
mathmannix wrote:OK, what if you built a really, really tall ladder (22,236 miles long!), carried a sattelite to the top, and let go? It would be in geosynchronous orbit, right?

Yes, because the ladder will have imparted a great deal of tangential velocity on the way up.

The moon is so far away that it takes nearly a month to make a full revolution, but it's still moving more than twice as fast as the Earth's surface. Of course, if it weren't so heavy, it would move at around the same speed as the Earth's surface.

Wait, what? *boggle*

DanD wrote:Dynamically damping a space elevator is far from unsolvable. Short sections of conductive tether acting as rotors in the earth's magnetic field. Servo driven hydraulic dampers built into the tether. Variable tension from linear motion of the counterweight along the tether outboard of geosynch. Those are just the ones I've come up with so far. We do complex vibration damping in all sorts of machinery right now, and the problem does not become infinitely difficult just because the structure is so big.

If nothing else, simple material strength make this still a science fiction concept instead of science, but I have yet to see something to convince me it is theoretically impossible.

I'd never argue it's theoretically impossible, but the engineering is sufficiently difficult that the engineering for other approaches is easier. Really, if we can get the air-equivalent of a cavitation torpedo working, to allow low-drag hypersonic flight (which itself is no mean feat, but far easier than these problems and lots of research has been done), then LEO becomes a lot closer. And if we're talking about moving asteroids at all, having an asteroid's worth of fuel easily available in LEO makes chemical rockets vastly more practical for everything higher - heck, it even makes descending on a tail flame worth talking about.
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### Re: What-If 0058: "Orbital Speed"

segundus wrote:I don't understand this. Geostationary satellites orbit at the same speed the earth revolves. So if you launch one of them, why would you need to gain any speed in addition to the speed you already have from being on the surface of the earth?

Yes, but in this case, there is a substantial height: 35,786 kilometers above the earth's surface, or a circle nearly 4.5 times the size of the equator itself. The Equator moves about 1000 mph; the satellite moves about 4500 mph--so you don't gain anything.
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### Re: What-If 0058: "Orbital Speed"

lgw wrote:
davidstarlingm wrote:
Pfhorrest wrote:
davidstarlingm wrote:Solar-powered compensating thrusters on the counterweight?

Using what for reaction mass?

Material mined from the counterweight. If we're capturing asteroids and attaching tethers to them, it's not terribly difficult to envision towing a smaller asteroid over now and then to keep the weight roughly constant.
...
I'm just saying that thrusters on the counterweight would be a more manageable approach to compensating than trying to alternate angles when you're sending up payloads.

Well, you might not want to soil your own nest, but dragging a CHON asteroid into a higher orbit and mining it as needed would be a good source for fuel. That does illustrate the sort of engineering project we're talking about here, though - asteroid mining is just the start.

Yep. If we aren't up to asteroid-mining levels yet, we really shouldn't be attempting a space elevator.

davidstarlingm wrote:
gmalivuk wrote:
mathmannix wrote:OK, what if you built a really, really tall ladder (22,236 miles long!), carried a sattelite to the top, and let go? It would be in geosynchronous orbit, right?

Yes, because the ladder will have imparted a great deal of tangential velocity on the way up.

The moon is so far away that it takes nearly a month to make a full revolution, but it's still moving more than twice as fast as the Earth's surface. Of course, if it weren't so heavy, it would move at around the same speed as the Earth's surface.

Wait, what? *boggle*

The moon's roughly 400,000 km away. Quite coincidentally, this happens to be the distance at which the tangential orbital speed of a small satellite would be around 1000 mph, which happens to be the same as the equatorial rotation speed. Of course, there's no physical significance to this.

The moon moves a lot faster, though, because it's a lot heavier than a small satellite. Since its mass isn't negligible in comparison to Earth, the gravitational attraction is higher, necessitating a more rapid orbit. Bodies of significantly different mass have different orbital periods at the same axis....which COULD have exciting results if you didn't plan things well enough.

Really, if we can get the air-equivalent of a cavitation torpedo working, to allow low-drag hypersonic flight (which itself is no mean feat, but far easier than these problems and lots of research has been done), then LEO becomes a lot closer.

Come again?

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### Re: What-If 0058: "Orbital Speed"

davidstarlingm wrote:The moon's roughly 400,000 km away. Quite coincidentally, this happens to be the distance at which the tangential orbital speed of a small satellite would be around 1000 mph
Nope.

400,000km away is approximately the distance at which something should orbit at 1km/s. Coincidentally, that's about how fast the Moon orbits the Earth.

Did you see the speed in m/s and think it meant mph?

The moon moves a lot faster, though, because it's a lot heavier than a small satellite. Since its mass isn't negligible in comparison to Earth, the gravitational attraction is higher, necessitating a more rapid orbit.
This is true for a fairly restricted definition of "negligible". The Moon's mass is about 1.2% that of Earth. This increases its orbital speed (compared to something of truly negligible mass orbiting at the same distance) by 0.6% (since orbital speed is proportional to the square root of the total mass).

Sure, that's not negligible if you want to use simplified equations to predict its orbital period and schedule something for the first full Moon in 2050, but it's sure as hell more negligible than the factor of 2 that you're claiming.
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ijuin
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### Re: What-If 0058: "Orbital Speed"

It's a big enough difference that any small object sharing the Moon's orbit but outside of the Moon's gravitational influence (and not at the L3, L4, or L5 points) will eventually have the Moon overtake it, at which point it will either collide with the Moon, be catapulted into a different orbit, or (rarely) be pulled into lunar orbit. In other words, it is NOT a stable orbit for satellites, aside from the aforementioned L-points.

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### Re: What-If 0058: "Orbital Speed"

This is one of my favorite what-if's ever, but I feel like Mr. Munroe has missed or obscured an important point:

If I were at the International Space Station, orbiting at 350 km above the Earth's surface, and I was able -- using unobtanium fuel or some such -- to de-orbit a re-entry capsule by slowing it down until its orbital velocity was 0 m/s, it would begin to accelerate downward under the influence of Earth's gravity. Above 100 km, there is essentially no atmosphere, so the capsule would have about 200 km to accelerate, unimpeded by atmosphere.

The specific orbital energy of a capsule at 350 km of altitude above the Earth, with 0 Earth-relative velocity is simply the negative gravitational parameter of the Earth divided by the Earth's radius plus the altitude of the object:

e = -GM/(r+h)=-(398,600km^3/s^2)/(6371km+350km)= -59.3 kJ/kg

This quantity is conserved. At the top of the atmosphere, the specific orbital energy would include a velocity component:

e = 0.5*v^2-GM/(r+h), which we already know = -59.3 kJ/kg, so we can solve for v:

v= sqrt(2*(-59.4 kJ/kg+398,600km^3/s^2/(6371km+100km)) = 2.14 km/s

So you'd enter the atmosphere pointing straight down at Mach 6.3. While it's true that this is less than orbital velocities (~Mach 22), it's considerably faster than the highest speed reached by air breathing jets (~Mach 2.9), and I suspect you'd still require a heat shield to withstand the heat of re-entry -- assuming you can stop in the 30-60 seconds it would take you to hit the ground -- particularly since the atmospheric gradient would be far far steeper than any re-entry attempted by actual spacecraft.

TL;DR - If you wanted to slow down to have a gentle re-entry, you'd have to time it perfectly so that the atmosphere catches you before gravity gets hold.

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### Re: What-If 0058: "Orbital Speed"

segundus wrote:I don't understand this. Geostationary satellites orbit at the same speed the earth revolves. So if you launch one of them, why would you need to gain any speed in addition to the speed you already have from being on the surface of the earth?

Well. Basically, rotating the same number of rotations in a given time at a greater distance - such as in orbit, which we can all agree is farther from the center of the earth than the surface is from the center of the earth - requires more energy. This is because you're going faster and covering more distance.

A similiar example/experiment... do you have an office chair? Good. Clear some space. Now, start spinning, but keep your legs in. Once you're going as fast as you can, kick your legs out. You'll be going much slower... but if you pull your legs back in, you'll start going the same speed you were before you kicked them out, ignoring (ch)air resistance.

rmsgrey wrote:I think it's a Heinlein novel where a character observes that the idea of reaching escape velocity in order to get into deep space only applies if you're making essentially a ballistic launch (and then using your engines to compensate for atmospheric resistance) - if you can sustain the thrust, you could get into deep space at walking speed - it would just take longer and far more energy.

Actually, if you did it right, it wouldn't take any more energy. Get your periapsis sufficiently above the atmosphere, then burn prograde once in a while there. If you sent up an astronaut who could conjure up an infinite amount of food and water, you could just throw a loaf of bread backwards once in a while, singlehandedly propelling your spacecraft into the depths of space while dying of old age and bringing on Kessler syndrome years early.

The amount of energy to reach terminal velocity (and get past any further resistance you may face on the way out from atmosphere or solid objects) is the same amount of energy it would take to escape the sphere of influence and pass into the area where the sun's pull matters more than the earth's - though the earth's would still be exerting some force, it'd be negligible in comparison. And when you're on an escape trajectory, your speed at periapsis will, I believe, be escape velocity - though I could be wrong, it could just be your speed at periapsis if your periapsis were at the center of gravity of the body being escaped.

Regarding the what-if itself, he simply states it's impossible and doesn't discuss what would happen if it were possible, which is double irritating because it's theoretically possible. It's much more concievable than throwing a baseball at .9c - simply state that your fuel never runs out and detail the forces on the craft or any other problems it may run into from a light, 4m/s descent.
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### Re: What-If 0058: "Orbital Speed"

Ralith The Third wrote:And when you're on an escape trajectory, your speed at periapsis will, I believe, be escape velocity - though I could be wrong, it could just be your speed at periapsis if your periapsis were at the center of gravity of the body being escaped.

Escape velocity depends on altitude. (More specifically, it depends on the distance from the primary body's center-of-gravity.) So if you're on an escape trajectory, (i.e. parabolic or hyperbolic orbit) you're always travelling at escape velocity or greater.

escape_velocity = sqrt(2*G*M/r), where r is the radial distance from the primary body's center of gravity

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### Re: What-If 0058: "Orbital Speed"

... okay. Disregard what I said. I always took escape velocity as static for a given object, but measured at the center of mass. But I've got no formal orbital mechanics training, so definitely listen to the guy with the formulas that check out as far as I can tell.
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### Re: What-If 0058: "Orbital Speed"

This isn't in response to anything in particular, but it is also always worth remembering that while escape velocity is always (in a Newtonian approximation) sqrt(2) times the speed of a circular orbit at the same place, neither speed is directly related to the actual force of gravity at that point. The sun exerts far less force on us here than the Earth does, and yet its escape velocity is between 3 and 4 times as fast. At a distance where the sun accelerates things at 1g, about 1.2 million km from its center, escape velocity is about 470km/s.
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### Re: What-If 0058: "Orbital Speed"

Ralith The Third wrote:
rmsgrey wrote:I think it's a Heinlein novel where a character observes that the idea of reaching escape velocity in order to get into deep space only applies if you're making essentially a ballistic launch (and then using your engines to compensate for atmospheric resistance) - if you can sustain the thrust, you could get into deep space at walking speed - it would just take longer and far more energy.

Actually, if you did it right, it wouldn't take any more energy. Get your periapsis sufficiently above the atmosphere, then burn prograde once in a while there. If you sent up an astronaut who could conjure up an infinite amount of food and water, you could just throw a loaf of bread backwards once in a while, singlehandedly propelling your spacecraft into the depths of space while dying of old age and bringing on Kessler syndrome years early.

Once you get into an orbit, sure, you can enlarge your orbit to escape cheaply enough, but getting into an orbit (which doesn't intersect the ground) is more expensive the longer you take (and being in orbit hardly qualifies as "walking speed"...)

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### Re: What-If 0058: "Orbital Speed"

rmsgrey wrote:getting into an orbit (which doesn't intersect the ground) is more expensive the longer you take (and being in orbit hardly qualifies as "walking speed"...)

This isn't obvious. Once you're on a ballistic trajectory, you only have so much time to get to orbital velocity before you re-enter the atmosphere. The optimum ascent profile for getting into a ballistic trajectory in the first place depends on the characteristics of the rocket you're using. Sometimes it is more efficient to take longer. For instance, the Apollo missions took over 11 minutes to get to orbital velocity, while the Soyuz rockets take about 9 minutes.

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### Re: What-If 0058: "Orbital Speed"

Shifty wrote:
rmsgrey wrote:getting into an orbit (which doesn't intersect the ground) is more expensive the longer you take (and being in orbit hardly qualifies as "walking speed"...)

This isn't obvious. Once you're on a ballistic trajectory, you only have so much time to get to orbital velocity before you re-enter the atmosphere. The optimum ascent profile for getting into a ballistic trajectory in the first place depends on the characteristics of the rocket you're using. Sometimes it is more efficient to take longer. For instance, the Apollo missions took over 11 minutes to get to orbital velocity, while the Soyuz rockets take about 9 minutes.

The problem is gravity drag. The longer you spend accelerating to reach your ballistic trajectory, the more time you spend fighting gravity to no benefit. There are other trade-offs, such as wind resistance (the lower in atmosphere you reach a given speed, the more drag), and the ability of your vehicle and crew to stand up to higher accelerations, but RMSgrey is basically right. Longer acceleration time gives lower efficiency.

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### Re: What-If 0058: "Orbital Speed"

DanD wrote:The problem is gravity drag. The longer you spend accelerating to reach your ballistic trajectory, the more time you spend fighting gravity to no benefit.

I'm still not sure I understand this. Gravity is a conservative force, so you don't lose energy to heating or friction. Neglecting air resistance, specific orbital energy is fixed for a particular orbit; the rate at which you attain that specific energy is irrelevant. And sure, the longer you spend in atmosphere, the worse, typically, but even inside the atmosphere there are trade-offs. Travelling faster through atmosphere can have deleterious effects on your engine efficiency. Many first-stage engines, for instance, are designed for optimal operation at sub-sonic speeds.

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### Re: What-If 0058: "Orbital Speed"

Shifty wrote:
DanD wrote:The problem is gravity drag. The longer you spend accelerating to reach your ballistic trajectory, the more time you spend fighting gravity to no benefit.

I'm still not sure I understand this. Gravity is a conservative force, so you don't lose energy to heating or friction. Neglecting air resistance, specific orbital energy is fixed for a particular orbit; the rate at which you attain that specific energy is irrelevant. And sure, the longer you spend in atmosphere, the worse, typically, but even inside the atmosphere there are trade-offs. Travelling faster through atmosphere can have deleterious effects on your engine efficiency. Many first-stage engines, for instance, are designed for optimal operation at sub-sonic speeds.

Think about it this way. In order for a rocket to hover in place, it needs to provide a downward thrust sufficient to counteract gravity. If you instead provide thrust for 1.1g, you will accelerate upwards, but only at 0.1g, and you're spending ten times as much energy just to fight gravity than you are adding to your velocity. If you instead lift off at 3g, you're spending half as much to fight gravity as you are to accelerate. The higher your acceleration, the lower the fraction that goes towards simply keeping the ship from falling back down.

This largely goes away if you can accelerate perpendicularly to the gravitational field, such as can be done in moving between orbits, but you need to reach orbital velocity first for that to be relevant.

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### Re: What-If 0058: "Orbital Speed"

Yeah, even without actual friction drag from the atmospher, and even without having to increase your altitude at all, you lose energy to gravity as long as you're traveling below orbital speed at an altitude you don't want getting any lower (because, for example, you'll run into a planet if you go any lower).

If Earth had no air, then the best launch would be to accelerate horizontally instead of wasting extra energy climbing. If humans can withstand 3g acceleration for the duration of a launch, then you have to angle your 3g of thrust so that the vertical component is exactly 1g. This gives you sqrt(8), or about 2.8g of effective acceleration horizontally. This wastes less than 6% of your thrust fighting gravity, which is certainly better than wasting fully 1/3 of it in a vertical launch, but it is lost energy all the same. (And of course the vertical launch is far preferable if you have a whole lot of inconvenient atmosphere to get through on your way to space.)

And a walking pace rocket launch would require some fairly negligible amount of energy to get to walking speed in the first place, and then a whole lot of energy to maintain a constant 1g of thrust against gravity for the time it takes to get from the surface into space at that speed. The reason people talk about launch loops and space elevators is that they provide far more energy efficient ways to fight gravity than using rockets the whole way up, but they don't negate the fact that your large orbital speed still has to come from somewhere.
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### Re: What-If 0058: "Orbital Speed"

gmalivuk wrote:Yeah, even without actual friction drag from the atmospher, and even without having to increase your altitude at all, you lose energy to gravity as long as you're traveling below orbital speed at an altitude you don't want getting any lower <snip>

Ah, OK thanks. Your example makes sense. It's because you have to: 1)add velocity at a non-optimal angle, and 2) add velocity over time rather than instantaneously.

There was an interesting discussion on the Kerbal Space Program forums a few weeks ago about the optimum descent profile for a non-atmospheric body. Turns out that it's best to burn to lower your periapsis to near the ground, then when as close to ground as possible (while still maintaining enough height to avoid obstacles) burn at such an angle as to maintain your altitude while slowing your orbital speed. The efficiency of doing a constant altitude burn vice a full retrograde "suicide" burn was particularly noteworthy for low TWR vessels. This is basically the opposite (and therefore equivalent) of the 1g ascent you describe.

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### Re: What-If 0058: "Orbital Speed"

AvatarIII wrote:

uhuh, more like just about 1000 miles, or just about exactly 1142.328 miles

Alpha says 999.5 miles. Did you plug in "4 minutes" instead?

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### Re: What-If 0058: "Orbital Speed"

Let's forget satellites and orbiting for a moment.

What if we just want to leave Earth as quickly as possible and head out of the solar system?

Do you still want to orbit first, then achieve escape velocity before leaving earth?
Or would you do just as well to aim "straight up"?

Put another way:
In most sci-fi shows, space craft are seen leaving a plant by going "straight up",
and approaching a planet by going "straight down". What's wrong with this picture?

I think this question has been answered here as follows:

It's more efficient to first achieve orbit before heading out. Consider that you want
to be going fast anyway; what's the efficient way to do that? If you go "straight up",
then you are fighting against gravity the whole time that you are accelerating.
Once you achieve orbit, however, you aren't fighting gravity any more. Additional
speed puts you into higher orbit until you achieve escape velocity.

Essentially, you are following a spiral path. Now, the faster you can accelerate,
the more you can "unwind" this spiral trajectory into a straighter path.

So, I suppose, the real question is, how much acceleration do you need in order
to completely straighten out the spiral?

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### Re: What-If 0058: "Orbital Speed"

If you're sticking to optimal paths, a completely straight "spiral" only happens in the limit as acceleration approaches infinity. And since infinite acceleration is hardly optimal for any potential passengers, I'd say not even then.
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There's a reason people have said that once you're in orbit, you're halfway to anywhere. With gravity and atmospheric drag taken into account, it takes about 10km/s of delta-V to get to LEO. At that point, an additional 10km/s puts you well past Earth's escape velocity, with probably enough speed left over to be on a solar escape trajectory. (It would of course not be very efficient to bring up your own fuel for the additional bit, since this requires you to square your already significant mass ratio.)
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