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Why cancel the angular momentum when we can utilize it?
i may be mistaken but I don’t think it can be utilized to descend toward the sun
It’s the foundational principle of “Launch Windows.” Because the earth rotates the sun and also spins on an axis, we can launch at a time of day that gives us time to accelerate and then leave earth orbit in the direction of earth’s orbit around the sun with minimum amount of energy required. The majority of energy used is simply to escape Earth orbit. Once orbiting the sun, comparatively very little energy would be required to approach it utilizing it’s own gravity.
During Perihelion the sun is 147100632 KM away, as the distance from the sun is not constant for earth’s orbit.
It requires energy to shrink an orbit just as it does to grow it. Since we’re launching from Earth, we start with Earth’s orbit around the sun, and we have to burn enough to bring the perihelion of our launched child’s solar orbit to within the sun itself. We could use Venus or Mercury for gravity assists but the angular speed of the orbit does have to be mostly cancelled to hit the sun
It’s still a lot cheaper than instantaneously cancelling angular velocity.
well the other stipulation was that it has to happen from a single kick
Yes the source of thrust is still cheaper using a launch window. Basically, you don’t need to kick directly to the sun you just need the child to land somewhere below a maintainable orbit given their velocity. The closer they get the more gravity will effect them and do more work that we don’t have to do.
Okay the math is obviously wrong, and it’s not even answering the question.
The question was, how much force. If punting the kid involves a kick, let’s say the foot makes contact with the kid for about 25 cm. Then the force required over this distance is on average 45 GN.
This is equivalent to the child experiencing roughly 180,000,000 G
“Then you’ll be fired.”
“Fine!”
“Out of a canon into the sun.”
Or just get another child. I know they don’t grow on trees but I’m sure they grow somewhere
Cut the extra inch off the long side to get a 4" square, then cut the remaining 1" x 4" piece into 4 1" squares. The boy never said the squares had to be the same size.
If the triangles have already been cut, it’s a peanut butter sandwich: use peanut butter on the edges to glue it back together and cut the squares. The child gave you a challenge, think outside the box!
Parent’s already thinking outside the biosphere.
If your leg has a mass of 2kg, 1.1×10^10 J of kinetic energy would require your leg to be moving at about
150100 km/second not faster than the speed of light.TLDR: Their math is shit.
It’s your own damn fault for not asking first what they wanted. Now if they DID contradict themselves I can see why that would feel that way.
Thats inefficient, you dont need to cancel the angular momentum as there was no time limit on how long it takes rhe child to enter the sun and there also was not a specified required trajectory. The child can just spiral into the sun
There are no spiral orbits. Canceling the forward motion is exactly what you need to do, to bring down the next periapsis to 0. Now, you can go with a periapsis of about half a million km, because the sun is pretty big, but that is not a significant difference. Getting anywhere near the sun, is the hard part.
It’s much more efficient in this case to do a bi-elliptic transfer: raise apoapsis very far out, then lower your periapsis once you are at apoapsis. Wikipedia says you could do it with about 8.8 km/s delta v. Versus 24 or so for a basic Hohman transfer (still a bit better than 30)
Sadly the bi-elliptic transfer requires two burns so you can’t do it with a kick.
Right, and what force is acting on the child to make it deviate from a circular orbit into a spiral one?
Right, I wanted to ask: is that actually the minimum energy to make the child reach the sun? What’s the minimum energy to launch something so it reaches the sun?
The minimum would be something like punting your kid to the orbit of Venus for a gravity assist that takes it to one of the outer planets where another gravity assist can push it to the edge of the solar system.
Out there, the angular momentum of the orbiting child will be very low and can be canceled out by a small thrust.
The child will then fall back into the sun. But this requires remote controlled thrusters strapped to the child. And a life support system if you want your child to actually die by burning in the sun. And then, the child will be well into their teens by the time they reach it.Give them time to think about what they did, maybe learn from it
The speed will be related to escape speed of sun. Based on https://en.m.wikipedia.org/wiki/Escape_velocity It will be Vte which is 16.6 km/s (or Ve 42.1). So when object at earth orbit and has lower speed than 16.6 it can’t keep the orbit and will slowly fall into sun.
