Factually. I mean, as far as I know, if you’re on an asteroid that’s in orbit in the belt, if you threw a rock, it would end up merely in a slightly different orbit around the sun. So, to rephrase the title, if you were on an asteroid in the asteroid belt, could you actually launch a missile and hit the sun? How many ‘g’ for how long would you have to fire your rocket ?
I’d just like to know because “The Expanse” is a show I really like, but they keep saying “Hey! Let’s fire blank into the sun!” and it just makes me pop a vessel. Thanks.
If your aim is reasonably close, then a rocket launched from an asteroid toward the sun should be a hit … I’m looking at what it would take to get a rocket past the sun and that would be an exceptional high speed … comet C/2011 W3 (Lovejoy) was clocked at 536 km/s … I think your g-force could be quite small, just applied for a long time like a year … depends on long you want to wait until it crashes into the Sun …
Post the video after, I’m curious how it works out …
:dubious: But you can’t just point a rocket at the sun and send it on its way. It will have a tremendous amount of angular momentum, so you will need to counteract its orbital velocity in order to get it to fall closer to the sun. It had better be a pretty big rocket.
And that’s where my knowledge of such things ends.
Come to think of it, perhaps the trick would be to keep slowly raising the apogee and dropping the perigee until the orbit intersects…is that what you were getting at?
The orbital speed of Ceres is about 18 km/s, one g of acceleration is about 10 m/s[sup]2[/sup]. If you want to do a single burn to get to the sun, you would just point your rocket in the opposite direction from your orbital velocity and decelerate to zero, at which point you’d fall into the sun. At one g you would need to decelerate for 18,000/10 seconds, or about 30 minutes. If your rocket and payload could withstand 10 g’s, it would take 3 minutes. Obviously, no one can throw a rock at 18 km/s.
This calculation ignores the gravity of Ceres, which should be an excellent approximation, since escape velocity of Ceres will be much smaller than 18 km/s.
You would need too cancel the orbital velocity of Ceres, which is almost 40,000 mph, or 11 miles per second. So, you would have to accelerate at 1G for about 30 minutes.
The average speed of Ceres in orbit 18 km/s. So if you fired a rocket at that speed directly back along the path of the orbit, it would in theory then drop straight into the sun assuming Mars, Earth, Venus and Mercury, didn’t get in the way. So that’s the maximum speed you’d need.
I suspect, if you could get the rocket above Ceres’ escape velocity by a bit and enough to get it close to Earth, you could use the Earth-Moon system in an inverse gravity boost way to perhaps slow it down to make the sun as well.
Then of course, you needn’t have it hit the Sun dead center, if you could get it close enough to the Sun, friction with the photosphere, would do the rest of the job.
The rocket would have the same velocity vector as Ceres … as we get closer to the Sun, orbital velocity increases … thus if we magically place Ceres in Earth’s orbit, at it’s current velocity, Ceres would spiral into the Sun … same with our rocket …
However, if we wanted our rocket to fly in a straight line to the Sun … then yeah, we’ll need a big rocket …
Just for comparison - the New Horizons probe weighed 478 kg, and launched on top of an Atlas V 551, which is normally used to launch payloads 40 times heavier than that (it can launch 18,814 kg into low earth orbit). Thanks to all this excess power, the probe left earth at a speed of about 16 km/s.
Of course, most of the rocket’s fuel is spent fighting the earth’s atmospheric drag and the earth’s gravity. Launching something from Ceres and accelerating it to the ~18 km/s (needed to drop it into the sun) would be a whole lot easier.
Lots of partial ninja-ing, but the answer is yes if I did my math correctly:
At aphelion, Ceres is only moving at 16.59 km/s at a distance of 445.41 million km. NASA launched the New Horizons probe at an Earth-relative speed of 16.26 km/s. Therefore, if we launched New Horizons 2 at Ceres’ aphelion in the direction opposite its motion, we would have a Sun-relative speed of only 330 m/s. It would orbit around the Sun with a semimajor axis of 222.75 million km. This means that its aphelion would only be at 90,000 km – well inside the Sun’s radius of 695,700 km.
(Main formula used: v^2 = GM(2/r - 1/a), where v is the velocity of the object in orbit, G is the universal gravitational constant, M is the mass of the sun, r is the distance from the object to the sun, and a is the semimajor axis of the orbit.)
Nothing can spiral into the sun. It is physically impossible. If you had an object with the orbital velocity of Ceres and magically placed it in Earth’s orbit it would have an elliptical orbit around the sun, not a spiral orbit, because spiral orbits are not a thing.
As for a rocket thrusting at 10 g’s for 3 minutes, ask yourself this: how much rocket propellant does this rocket need to accelerate at this rate?
This is something science fiction writers can’t wrap their heads around, even if they get how really really really big space is, and the speeds involved, and the time it would take to accelerate to various velocities at various accelerations. A rocket works by taking matter and shoving it out the back of the rocket really fast. And you’ve only got so much of this stuff, and the amount you can change the velocity of your rocket by is fixed by the amount of rocket fuel you have. Adding more rocket fuel doesn’t help that much because the more fuel you have the more fuel you need to expend just to move the fuel.
To cut down on the delta-v you could use a series of flybys to change the orbit of your Ceres-Sun mission. There are four planets between Ceres and the Sun, and you could fly past each one more than once; this would reduce the amount of acceleration you would need significantly. The Messenger probe to Mercury, for instance, flew past Earth, Venus (twice) and Mercury(thrice) before finally arriving; they didn’t do this for fun, but it took seven years to get there. Getting to the Sun using flybys could take even longer.
Note as well you don’t actually have to hit the centre of the Sun, so you don’t need to kill all of your orbital speed; the Sun is more than half a million km in radius, and it has a fairly significant atmosphere which could allow a certain amount of atmospheric braking. Your missile would arrive as a shower of metal vapour, but it would (mostly) get there.
The Sun is just about the most difficult place to get to in the Solar System, but if you really wanted to, it could be done- but it certainly isn’t the default destination for any unwanted junk or discarded spacecraft.
I don’t know from orbital mechanics but even I can tell you are completely out of your depth on this subject. This is GQ dude. I know I’m junior modding but maybe you just sit this one out and just spectate and learn.
The piece in the puzzle you are missing, by the way, is that if you put Ceres - at its current velocity- in the location of Earth orbit it would as you say be going too slowly to maintain Earth orbit BUT you are assuming a constant speed. Actually, it would gather speed as it’s trajectory was affected by the Sun’s gravity. It would trade gravitational potential for speed. The extra speed would result in it achieving orbit; just not the same orbit as Earth.
As the last episode made clear, they also have the Epstein Drive to play with, so they’re not limited to what can be done with present day engines. They have 200 years of progress and a magical handwave engine.
Agree with your overall points, but I’ll throw a nit out there for the benefit of the rest of the audience.
Thrust happens from “reaction mass” exiting the vehicle. “Fuel” is a source of energy. Those are different ideas.
In a chemical rocket, the fuel (plus oxidizer) *is *the reaction mass and the reaction mass *is *the fuel (plus oxidizer). So no real harm comes from conflating the two ideas.
But there is no inherent reason the fuel and reaction mass have to be the same stuff. We now have ion engines where the “fuel” is electricity derived from solar panels or radioactive decay heat. In these engines the reaction mass is a chemically inert gas.
Presumably the magic drives of SF and the more efficient / effective drives of our real future will by and large not be the chemical rockets that have gotten us this far but cannot possibly take us much farther.
So going forward it becomes increasingly important to maintain the distinction between fuel = the power source and reaction mass = thrust medium.
Unfortunately for space travel, the Tsiolkovsky rocket equation - Wikipedia rules the physics. Which, as you rightly say, implies a vast amount of reaction mass is needed to achieve either high G, long duration, or worse yet, both.
It’s easy enough for an SF writer to invent an energy source = fuel (matter + antimatter from dilithium crystals, etc.). It’s too hard, as you say, for them to invent a reaction mass that evades Tsiolkovsky.
Can the payload tolerate high g forces? A rail gum might be used to leave the fuel on Ceres. At 100 g you could accelerate to 18000 m/s relative to Ceres in only 18 seconds, if I haven’t screwed up the math. Of course, that’s a hellish long rail gun, somewhere over 165 kilometers long, around 1/6 of the diameter of Ceres, but it would be reusable, so there’s that. You got anything else to throw into the sun?
Essentially, yes. Well, the dropping the perigee* part. To hit the sun there’s no reason to raise the apogee. Everyone who wants a better feel for what’s going on in the TV The Expanse should go out and play the game Kerbal Space Program. You simply can’t get ahead in KSP without understanding orbital maneuvering, and how it’s affected by things like your maximum thrust and Delta-V.
The one hand-wavium thing about The Expanse is they’ve created a Space Drive that largely eliminates limits on your delta-V. It’s also typically capable of 15G acceleration, but that is limited by the endurance of the crew. The backstory of this drive was a sub-plot in this week’s episode, and last week, they also made the point that the ship could continue driving long after the crew had all died due to the effects of prolonged high-G acceleration.
Aside from the magic space drive, they are trying to stick close to real physics.
*Yes, okay, that’s not the technically correct term.
Circular orbits are essentially an object “falling” around the center. An object describes a circle if it experiences a constant acceleration toward the center of that circle (I.e. perpendicular to its - tangential - velocity) and that velocity exactly matches the acceleration.
If the velocity is too low or too high - too low, the object starts to fall inward as it goes around, until the velocity reaches a high enough value that it starts to fly away again… elliptical orbit. (The logical minimal condition - too little tangential velocity, the elliptical orbit intersects the central attracting body) Too fast, it flies outward as it goes around; if the velocity is less than escape velocity of the central attractor, again, it’s an elliptical orbit. If the velocity exceeds escape velocity - it describes the remainder of a hyperbolic orbit until it flies away from the system. Simplistic rule of thumb - the object will return to the same point with the same velocity as it started, unless it exceeds escape velocity.
The problem with earth orbits - within low orbit, there is still a residual atmosphere providing a tiny amount of drag. This causes most objects to “spiral in” over the course of decades, as wind resistance slows down their tangential velocity. It is most pronounced in objects like SkyLab where you have a huge cross-section relative to weight, like a big sail or solar panels. But again, this took 10 years and was aggravated by an active sun heating the top of the atmosphere to make the density of the extreme upper atmosphere a little bit more.
I always wonder why Star Trek was so stupid they kept putting the Enterprise in orbits where the decay could be measured in days.
To “spiral in” from deep space, the spiral would be the result of a constant acceleration (er, deceleration); the satellite would have say, an ion engine producing 1/100g constantly firing against the direction of the orbit. As the tangential velocity decreases, the object moves closer and closer to the gravitational source. 18,000m/s with a deceleration of 0.098m/s - 184,000 seconds, or 51 hours.
Yeah the Epstein drive in the show isn’t FTL, but it might as well be a warp drive.
From what I’ve read (and my very limited understanding) the only things that might make the types of acceleration possible in the show have a lot of real world issues that might make them unworkable.
An engine using a fuel like a lattice of metallic atomic Hydrogen could work, except, we don’t know if such a thing could be stable or even possible, and it sure as well would be incredibly dangerous. The heat given off by such an engine, capable of the necessary delta-v would wreck any known substance, destroying the engines.
Some sort of atomic reaction/fusion engine might be possible, but again, we run into the issue of both heat, and now incredible amounts of radiation when reaching the required delta-v, which would destroy the ship and kill the crew.
This is a function of those Magic Space Drives again.
All of this discussion of orbits relates to ballistic orbits. That is, the object, except for brief times of acceleration to change the orbit, is “on the float”, moving solely under the influence of gravity. At that point, the orbit is determined by the velocity of the object, and all the issues of stable orbits vs. decaying orbits vs. escape trajectories applies.
But if we had a Magic Space Drive that allowed us to ignore limits on delta-V, we could use powered orbits. That is, we use thrust from the engine to maintain our desired position relative to the central object, rather than just relying on the balance of gravity and velocity.
Consider a geostationary orbit. Currently, there’s essentially only one way to do that: use an orbit high enough that the orbital velocity allows you to make exactly one orbit in one day. If we tried that in a lower orbit, we’d be going too slow to maintain orbit, and would fall out of orbit.
But if we had unlimited delta-V, we could just burn continuously, essentially “hovering” in space, allowing us to maintain a geostationary position at any desired altitude. Of course, if the drive dies, we’re then falling to our deaths, which is what happens to the Enterprise. It’s like taking a corner in your car, and too late finding out that the road is icy - what would normally be a safe maneuver becomes a car accident.