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If there’s one thing you learn in astronomy that’s fundamental, it’s energy. We’re going to learn about energy and about orbits which are dependent on the energy of what they’re orbiting. When we talk about the science in science fiction, we’ll hearken back to this because energy explains a lot.
An example: on BSG we used bullets in our vipers instead of lasers. People thought it was low tech, but it’s harder to get a lot of energy in a laser than a big hunk of lead. With a laser, today, it’s almost impossible to get as much energy in target with a weaponry as we routinely get with our air-to-air guns since Vietnam. When you understand the concept of energy, you realize that wasn’t a bad choice.
What I said yesterday that a supernova outshines the rest of a galaxy, that’s a whoa, that’s the concept of energy.
First we start with mass. Mass it the amount of “stuff (neutrons and protons) that something has. It has been said that a physicist or physics student learns everything three times. This is true, and it’s true for a concept of force, which we’ll get to a second. First you start with f=ma. Then you realize more accurately, it’s expressed (a different equation), and even more accurately expressed as (yet another equation).
Mass is sometimes confused with weight. For instance, Cassini is six tons in earth’s gravity. That’s its weight, not its mass. So, mass is made of stuff. Electrons are trivial in mass compared to neutrons and protons.
Another concept that goes with mass is density. If I have a baseball sized piece of ice and a baseball sized piece of lead, which one weighs more? Lead. More stuff is crammed in the same size volume.
Another way you can look at it is that mass is an object’s resistance to motion. For instance, if you had a chair with casters on it, and pushed a small person along. Or pushed a larger person along. The object that has more mass is harder to push, because it’s more resistant to movement.
Thirdly, mass is the equivalent of energy (e=mc(2)). If you were to convert a person into energy, how much would it be? About 41x the total of the largest nuke ever detonated on the planet.
Neuton’s first law in the original language: every body continues in a state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. (Apparently, a piece of trivia: he spent the second half of his life looking for secret codes in the bible). By motion, Newton meant velocity. Instead of force, we could say push or pull. In (modern) English: every object remains at rest, or at a constant velocity, unless acted upon by a force.
Now, speed and velocity are synonymous colloquially, but not scientifically. Velocity is a speed and a direction.
In Michigan, in (city), there’s an area called black lake which is a big area of asphalt, and they have a skid pad. When you skid in a circle, you are constantly changing velocity (because you’re changing direction) and thus constantly accelerating.
Newton’s second law, original language: the change of motion is proportional to the force impressed, and it is made in the direction of the straight line in which the force acts. Modern: The acceleration is proportional to the force applied, and it is made in the direction of the straight line in which the force acts, or F=MA.
Newton’s law of universal gravitation, the way two bodies react to each other. Any two objects with mass trap each other gravitationally. We attract each other through gravity, though to a trivial amount.
His students constantly ask “how do people stand on the moon if there is no gravity?” but there is gravity on the moon. And not only on the moon, but also in space.
Equations: F=G(Mm/r(2)), a=GM/r(2), g=GM/r(2)
Yesterday we said Mercury and Titan are about the same size. Titan has an atmosphere; Mercury doesn’t; why? Well, Mercury’s hotter, so the molecules of the atmosphere move fast and escape.
Say you have a planet: Jupiter. (In Sf, we are constantly exposed to two models of gravity and don’t realize it. One is where gravity is a warp in space time, the other is where gravity is particles. These don’t entirely overlap. The graviton, or gravity particle, is less likely, but easier to explain.) So, if you have an object: Jupiter… (which right now has a second red spot, the Little Red or Not So Great Red Spot), so, yes. Gravity. Jupiter. You’ll notice that in the universal law of attraction, while it’s good for many things in physics, it’s not good for everything; there is a time dependence on gravity that Newton doesn’t consider. Say at the time 0, take a snapshot of all the gravitons leaving an object, radiating outward at the speed of light. In this spherical shell, you have N gravitons. You have N gravitons leaving the surface at a particular instant. The area of a sphere, or volume of an infinitessimally thin sphere, is 4(pi)(r2). So attraction is based on how many gravitons hit you at any given time? And the bigger you are, the more gravitons you get hit with?
Newton’s 3rd in original: to every action there is always an equal and opposite reaction; or the mutual actions of two bodies upon each other are always equal and act in opposite directions. For modern, read force instead of reaction, and equal in magnitude, opposite in direction. Say, we have a planet. (“We have a planet.”) And we have our astronaut. What gravitational force does the astronaut feel? there’s the distance between them, for one, getting us back to G=Mm/r(2). But by newton’s 3rd, the planet should also be experiencing a force G=Mm-R(2). That’s equal to the other force. But that’s not intuitive, it makes no sense.
Kevin is playing fast and loose between language and equations. This is all true, but f and m have different meanings in what he wrote.
Anything examined in detail becomes infinitely complex.
When you push off from a planet, you don’t push the planet away.
Work is the product of a force and the distance over which it acts.
Energy is the ability to do work, or the ability to move an object that has mass. There are two kinds of energy that can be interconverted. Kinetic (motion) energy and potential energy. Kinetic Energy = 1/2 mv^2. Gravitational potential energy is MGH, mass times gravitational acceleration times height of object. The generalized formula for potential energy is GPE = -GmM/r.
The navy is testing rail guns that will accelerate an eight pound slug to seven times the speed of sound.
Potential energy is the potential to have kinetic energy.
The total energy of an object moving within a gravitational field is the combination of its potential and kinetic energy.
A rollercoaster is a great demonstration of the combination of those two types of objects.
The energy of an object in the orbit dictates the size of the orbit.
Kepler’s first law: the orbits of all planets are ellipses with the sun at one focus. The longer bit of the ellipses is the major axis, the shorter bit is the minor axis. When we discuss the distance of an object from the sun, we’re talking about the major axis.
There are two main foci. One is where the sun is, and that’s the empty focus. The sun is not at the center of the ellipse. It’s off-center. This is important as we move to Kepler’s other laws.
For a lander to fly by, you just aim past and keep going. For an explorer to become captured, you have to slow down and go into negative acceleration. To be in situ, you have to dissipate all your speed in order to land without making a crater.
Mike cuts in: the sun’s massive, it has lots of gravity, but it’s still not easy to launch stuff into the sun. Most energy the spacecraft has if you want to go to the sun is not just orbit, because once you’ve reached orbit you’re out of most of earth’s gravity, but you have to kill all the velocity coming from earth in order to crash into the sun. That’s a big velocity to have to kill, so going to the sun is energy intensive. Kevin’s rephrase: the sun is the most difficult star to get to in the entire universe from an energy standpoint (from earth), if time is not a factor. Mike: It’s hard to get to the sun, so you can’t send your garbage there. Kevin: There are ways to do multiple flybys if you have several years and get it in, but if you just want to get it in, it’s hard.
A bound orbit is an ellipse; an unbound orbit is a hyperbola. Bound is a negative e; unbound is positive. Bound objects are hard to dislodge, whereas if you “look at a comet the wrong way, it’s out of there.”
So what if e=0? If you want to reach 0 energy in relation to earth, then you have to get to zero energy, which represents a transition between bound and unbound, staying put going round and round, or leaving hyperbolically.
The condition you can change most is the velocity, and to change the velocity to make e=0, you basically have to go at escape velocity. Which makes sense–that’s the difference between being bound in orbit, and being unbound. To move from the one to the other, you have to escape.
Eccentricity–the eccentricity of an orbit is a measure of how out-of-round it is and ranges between 0 and 1 (for a bound orbit). Earth’s is not actually circular, but is so close to circular that if you had a god’s eye view and watched for a year, you couldn’t tell. On the other hand, some comets are at .99.
Kepler’s second law–a line joining a planet and the sun sweeps out equal areas in equal intervals of time. There’s an implication with this second law that isn’t obvious from initial reading. If you draw a line from the sun to the planet at one moment, then wait X amount of time, then draw another line, that will give you area A. If you pick another time and draw a line from the sun to the planet, wait time X again, then even though the sun may be further from (or closer to) the planet during this time frame, then the area will still be A. That means that in an elliptical orbit, the planet does not move at a constant velocity. It goes faster and slower as the potential energy changes, maintaining a constant area, not a constant velocity. Things move slow when further from the sun, and more quickly when close in to it.
Kepler’s third law – the square of the period (T) of an orbit is proportional to the cube of the semi-major axis. All that means is that the further you go, the further out the planet is, the slower it moves, and this is not linear. Earth, at 1AU, takes one year to orbit the sun. Neptune is at 30 AU, but it doesn’t take 30 years to orbit the sun, even though it’s 30x bigger. In fact, it takes 165 years to orbit the sun, and next year will finish its first orbit since its official discovery (though Galileo may have discovered it before the person who got official credit).
Gravity assists: If you understand that energy can neither be created nor destroyed, only transformed from potential to kinetic, or from potential to another kind of potential, etc. Whereas mass can be created by E=mc^2. The sphere of influence dictates a region where you transition from heliocentric orbit, feeling the gravity from the planet, to planetocentric trajectory, feeling the sun secondarily. The closer you are to the planet, the less the sun’s gravity matters. When you’re moving within the sphere of influence (of the planet), it doesn’t really matter how the planet is moving through the solar system, because the whole system is moving at the same speed, but also because the gravity of the planet is the force that’s most majorly affecting you. The sun’s contribution becomes less and less important. For Jupiter, the radius of the sphere of influence is about 3AU, almost the orbit of Mercury.
To get a gravity assist you come in, you fly by, you keep on going. You have a velocity inbound and then you have an outbound arrow, the velocity outbound, which has a given speed and a given direction. Relative to Jupiter, the magnitude of the inbound velocity=the magnitude of the outbound velocity.
You can’t create more energy, so where’s the assist? Well, when you look relative to the sun, you take the inbound and outbound velocities and add them heliocentrically, so you see the heliocentric inbound and the heliocentric outbound velocities. Looking at it that way, you’ve changed direction and gained speed.
You pass behind a planet to gain speed, and in front of it to lose speed.
You can make these passes continually to gain and lose speed, and this is something they have done with the probes.
Jeremiah Tolbert wonders whether we could throw an object around planets over and over again and then crash it into something, producing a lot of energy which was gained from the energy of the solar system’s orbits, and then if we had sufficiently advanced technology, figure out a way to harness that energy to power a civilization.
A Russian astrologer sued NASA because we were taking energy from the solar system to power gravity assists, and thus changing everyone’s horoscopes.
Delta V means change of velocity, thus change of energy.
Mike’s simpler, less technically accurate version of gravity assist: Jupiter is moving around, you send a spacecraft, Jupiter starts moving it really fast. The craft loses speed as it moves away, but not as much speed as it gains from Jupiter. The craft spends more time behind Jupiter than in front of it. If instead you’re ahead of Jupiter, it slows you down.
Again, why does it take so much energy to get to the sun, asks Kelly Barnhill? OK, if you’re in one of those rides that spins really fast and slams you against the wall? If you threw a ball into the center of the room, you think it would go to the center, but it would actually deflect towards you. To get the ball into the center of the room, you have to knock more and more and more velocity off of the ball. There are ways to eventually get the sun into the center of the system, but it would take a long time.
What imparts the initial velocity to the solar system asks Jeremiah? The cloud that formed us was spinning very slowly, and as it condensed, went faster and faster, because of conservation of momentum.
At the subatomic level, we now believe and are starting to get the beginnings of experimental data to support that particles and anti-particles pop into existence and blink out. So to create this particle with mass, the universe literally goes into debt a small amount of energy to create the mass. Eventually they pair annihilate and pay back the debt. Particles and antiparticles are constantly going in and out of existence. Given that they all have mass, gravity, they all influence things to some degree, which is called quantum foam. This seems to explain the large scale structure of the universe, that the quantum fluctuations that occurred just before the universe began to explode afterward is mirrored in the way that the universe currently distributes mass. The universe is clumpy and has uneven distribution, and this may be because it was true before the mass spread vastly afterward, i.e. that the pattern of quantum foam pre-expansion is mirrored by the pattern of matter spread in our universe. Mike Brotherton recommends that we look at Alice in Quantumland: An Allegory of Quantum Physics by Robert Gilmore which explores these principles.
High speed pictures of explosions have the same clumpy effect as what we see when we look at the large-scale universe, says Bud Sparhawk.
Mike Brotherton asks how we use the slingshot effect to send a starship back in time?… Glazier says you couldn’t, but you might be able to slingshot around a star to get out of a galaxy. He adds that navigators hate the term slingshot. The analogy he likes is when you play racketball, your opponent will occasionally hit the ball against the back wall before it hits the ground and you have to catch it in the direction it’s already going to boost it before you can change its direction to where you need it to be.
We’re now realizing that our long-term ability to trakc the orbits of asteroids is complicated by the Yarakovsky effect… say an asteroid is spinning slowly, one side warms as it absorbs radiation, and as it rotates to face cool space, it expels that heat, and this alters its velocity, and complicates its long term orbit.
Jeremiah asks why that doesn’t affect planets. The issue is that the asteroid is much smaller so it can be affected.
The light comes out, radiates out radially, and the particle is in orbit and it’s like running in the rain. It looks like the rain is coming toward you and it looks like the photons are coming toward you and not radially. There’s a little component that means the light is slowing you down. The particles move in orbits quickly and this is a small effect, but for very small things, over the lifetime of the solar system, it can make a difference. (Not sure I got that at all right in transcription, just to warn you.) This is the Poynting-Robertson effect.