If I have a rocket that theoretically has enough fuel to keep my speed constant, why can't I just point it at the sky and GTFO? I assume that by the time I'm 100,000,000 miles away I'll have "escaped."
If I have a rocket that theoretically has enough fuel to keep my speed constant, why can't I just point it at the sky and GTFO? I assume that by the time I'm 100,000,000 miles away I'll have "escaped."
Who says it can't?
Just depends on the weight of the rocket.
If it weighed in the region of 1 microgram would probably be fine.
Weird question wrote:Just depends on the weight of the rocket.
No, escape velocity is independent of the mass of the rocket.
It could. An object moving at escape velocity doesn't need additional force to "escape", though. Would take a lot of fuel to escape as you describe.
you can, however; it would take a large amount of "delta v" - or change in velocity. Far more that our technology can do. So to simplify things we say you can't and only consider trajectories that are as efficient with delta v as possible.
When my son asks if he can go to the moon I say he can't, even though it is possible.
Because the definition of escape velocity is that there is no forces except gravity. Certainly you could leave earth's gravity well by maintaining a constant velocity of 1mph, but that requires you to apply a force, so it isn't escape velocity.
Why can't a baseball moving 1 mph eventually make it across home plate?
serious question: wrote:
Why can't a baseball moving 1 mph eventually make it across home plate?
If a rocket is heading to the moon, and each second it halves the distance to the moon, will it ever make it to the surface?
Yes, escape velocity depends on the gravitational field strength of the planet, the mass of the planet and also, most importantly, the DISTANCE from the center of gravity that the object in question is trying to escape.
At the surface of the earth escape velocity is 11.5km/s or something. If you reach that velocity on earth's surface then gravity no longer has a hold over you, so to speak.
However if you are generating enough propulsion to constantly move your object away from earth's center at 1mph then eventually you will be far enough away from earth to reach a point where escape velocity is 1mph. It's easy to calculate but would probably be in the region of tens of thousands of AUs.
OP, If you are mistaking escape velocity to mean something to do with the atmosphere, then you misunderstand and of course you can leave the earth's atmosphere at a constant 1mph. Just takes a lot of fuel.
Yes. This is Zeno's Paradox. (if memory serves)
The argument is defeated in that with each segment the time needed is also cut in half.
Even though there are theoretically infinitely many half-segments, the time for each segment approaches zero.
Oh Please wrote:
serious question: wrote:
Why can't a baseball moving 1 mph eventually make it across home plate?
If a rocket is heading to the moon, and each second it halves the distance to the moon, will it ever make it to the surface?
Yes, at roughly 62 seconds you will be an atoms length away from the moon and you're not going to be getting any closer than that.
Orbital mechanics is hard.
Gravity is everywhere. It is a wave that permeates the universe. Right now you are being affected by the gravity of Jupiter. And Saturn and Pluto and the Andromeda Galaxy. It is so tiny you just can't feel it, and we likely don't have equipment to measure it But it is there and it can be calculated.
The astronauts in the space station are weightless not because there is no gravity there, but because in the one second that they have fallen 9.8 meters towards the earth, their 17,000 forward velocity has moved them forward far enough so that the earth's surface has curved away from them by 9.8 meters and they are still at the same height.
They don't detect this, and from their perspective appear to be floating weightless because the space station is moving exactly along with them.
If you were to build a tower 210 miles high so that you could see the space station zoom by at the same height, a 200 lb man standing on the tower would weigh about 180 pounds.
Fun fact, if you could stand on the cloud tops of Saturn and Jupiter would would weigh very nearly earth normal. They have much more mass and much more gravitational pull than the earth, but you are 5 to 10 times further away from the center of mass, and gravity falls off by the inverse square law. (twice the distance means 1/4 the pull, three times the distance means 1/9 the pull)
You could achieve orbit by building a spaceship that moves upwards at 1 mph. In 200 hours you would get to the height of the space station. But that is orbital height, not orbital velocity. Remember the earth's gravity is pulling you back at about 90% of what you feel on the ground. You need to turn you spaceship sideways and start building up forward velocity. In 17,000 hours you would achieve the velocity necessary to fall around the earth. But the amount of fuel you would burn in those 17,200 hours of constant rocket burn is ginormous.
The faster you get up, the shorter time your rocket burns and the less fuel you need. But beyond a certain acceleration the human body gets crushed.
A minute after lift off you still need to burn fuel to climb., but you had to burn fuel to lift that fuel you will burn at the 1 minute mark.
Two minutes after lift off you still need to burn fuel to climb, but you had to burn fuel to lift the fuel that you burned in the first minute to lift your other fuel you will burn at the 2 minute mark.
Three minutes after lift off you still need to burn fuel to climb, but you had to burn fuel to lift the fuel that you burned in the first minute to lift the fuel that you burned in the second minute to lift the fuel you will burn at the 3 minute mark.
Four minutes after lift off you still need to burn fuel to climb, but you had to burn fuel to lift the fuel that you burned in the first minute to lift the fuel that you burned in the second minute to lift the fuel that you burned in the third minute to lift the fuel you will burn at the 4 minute mark.
And so on.
So you get to orbit in 200 minutes.
If you want 100 pounds of fuel to burn in orbit, you had to burn about 2,000 more lbs of fuel during the launch, and you need more pounds of fuel to lift those pounds of fuel. If you want 1 million pounds of fuel in orbit, you need to start with 20 million more on the ground, and then you need more fuel to lift that fuel.
Ginormous isn't a big enough descriptor for how much fuel would be needed.
Gravity is a wave? Gravitational wave? What about quantum gravity?
Yabadaba wrote:
Yes, escape velocity depends on the gravitational field strength of the planet, the mass of the planet and also, most importantly, the DISTANCE from the center of gravity that the object in question is trying to escape.
At the surface of the earth escape velocity is 11.5km/s or something. If you reach that velocity on earth's surface then gravity no longer has a hold over you, so to speak.
However if you are generating enough propulsion to constantly move your object away from earth's center at 1mph then eventually you will be far enough away from earth to reach a point where escape velocity is 1mph. It's easy to calculate but would probably be in the region of tens of thousands of AUs.
OP, If you are mistaking escape velocity to mean something to do with the atmosphere, then you misunderstand and of course you can leave the earth's atmosphere at a constant 1mph. Just takes a lot of fuel.
This is the most succinct correct explanation. If you want to move at a constant 1 mph from the surface of the earth upwards into space, it will take a lot of fuel to maintain that pace while dealing with the downward force of gravity.
stateroftheoblivious wrote:
Yes. This is Zeno's Paradox. (if memory serves)
The argument is defeated in that with each segment the time needed is also cut in half.
Even though there are theoretically infinitely many half-segments, the time for each segment approaches zero.
No it isn't Zeno's Paradox. The time segment is always one second in his scenario
I think that escape velocity means that when an object reaches that speed it no longer needs a force to propel it out of the gravitational pull of the Earth. For example, a space probe NOT traveling at escape velocity and has no more thrust will be caught in an orbit around the Earth.
yyy wrote:
Gravity is a wave? Gravitational wave? What about quantum gravity?
Do you have a decent quantum gravity theory in mind?
Voyager 1 wrote:
I think that escape velocity means that when an object reaches that speed it no longer needs a force to propel it out of the gravitational pull of the Earth. For example, a space probe NOT traveling at escape velocity and has no more thrust will be caught in an orbit around the Earth.
No no no.
Bodies orbiting the earth (like satellites or space stations) are most certainly under the gravitational pull of the Earth. Orbit is actually a state of free-fall.
Escape velocity just refers to the velocity such that the kinetic energy and gravitational potential is equalized. With lower velocity (kinetic energy) than the escape threshold the object eventually gets dragged back by gravity.
stateroftheoblivious wrote:
Orbital mechanics is hard.
Ginormous isn't a big enough descriptor for how much fuel would be needed.
Thanks.
I find astronomy and propulsion engineering fascinating even though I don't have the brain power to understand most of it.
Thank you very much!
observer_of_things wrote:
Voyager 1 wrote:
I think that escape velocity means that when an object reaches that speed it no longer needs a force to propel it out of the gravitational pull of the Earth. For example, a space probe NOT traveling at escape velocity and has no more thrust will be caught in an orbit around the Earth.
No no no.
Bodies orbiting the earth (like satellites or space stations) are most certainly under the gravitational pull of the Earth. Orbit is actually a state of free-fall.
Escape velocity just refers to the velocity such that the kinetic energy and gravitational potential is equalized. With lower velocity (kinetic energy) than the escape threshold the object eventually gets dragged back by gravity.
Right, I understand orbits are "falling" toward the Earth. That's what I mean by "escaping" the gravitational pull of Earth, beyond orbit, beyond the influence of Earth's gravity.