This may be such a basic question that I might be missing the obvious answer.
I got to thinking today about the sheer amount of power needed to escape the pull of the Earth’s gravity. We used massive rockets to get our spacecraft up into orbit.
Now, this is what puzzles me. Wouldn’t the pull of gravity decrease the further away one got from the surface? Shouldn’t it require less energy as a ship gets higher and higher?
It just seems to go against common sense.
It’s because on Earth you’re at the bottom of a gravitational well. Look at it this way. Suppose you dug a hole one mile deep. Raising a weight from the bottom of that hole to the surface would require a lot of work, roughly 5,280 foot-pounds per pound, in fact. I discount the fact that the force of gravity is slightly higher one mile below the surface because the difference is piss all.
Now, starting with the same weight on the surface lift it one mile. It’s the same amount of work, just slightly less. You’d have to lift it hundreds of miles to get any appreciable decrease in the force of gravity. It will decrease with the square of the difference in the distance, but you’re starting damn near 4000 miles away, so moving 100 miles high only decreases the force of gravity by about 5% or so.
“Aha!” you say, “I have seen the space shuttle in low Earth orbit and it doesn’t fall. What about that? It doesn’t look like there’s any gravity there”
The shuttle is not in zero gravity, it is in free fall. It falls towards the center of the earth just like any other object, but its forward velocity carries it towards the horizon at the right speed so that the falling shuttle never intersects the Earth, because of the Earth’s curvature.
Picture yourself climbing a hill that’s curved on the top. As you get closer and closer to the top, the slope gets shallower and shallower, but that doesn’t mean you don’t have to do a lot of climbing first to get there.
Part of the reason they’re so massive is that they have to launch not only the payload, but the fuel, which creates a vicious cycle: Payload, fuel to lift payload, fuel to lift payload and fuel, lather, rinse, repeat.
The rockets aren’t all that massive once you appreciate how gi-friggin-gantic the Earth is. They’re really quite tiny in that regard.
I’m trying to wrap my head around this.
Let’s say I’m in a helicopter or a plane. I can fly it to an alititude of 1000 feet. To fly from 1000 feet to 2000 feet, it seems as though it would take less energy, and because I went from 0 to 1000 with no trouble, surely it would be easier to go the extra 1000 feet. And the 1000 feet after that.
I realize that there are considerations such as atmosphere that would prevent one from literally using a helicopter in this way.
IIRC it doesnt really take that much energy to GO UP a hundred miles give or take (and then you fall right back down like a rock). IIRC it takes about 10 times that amount energy to get up to a speed of 20,000 miles per hour to have the SPEED required to ORBIT the earth.
This would be where you went completely off track. It takes a LOT of trouble to do this. And you have to do it 20 times to just get out of the first layer of atmosphere (troposphere).
Correct - but only in the sense that buying a second lottery ticket doubles your chances of winning millions of dollars (i.e. so unbelievable negligible and incremental that it’s a completely meaningless distinction).
As has already been posted the difference between 0-1000 and 1000-2000 would be utterly negligible because what matters is the distance from the centre of the earth. In addition, yes you can go up slowly and you can go as far away as you want without needing escape velocity, but escape velocity is what is needed to be able to turn off your engines and not fall back to earth.
The difference between the amount of gravity you’d feel at 1000 feet and 2000 feet is very tiny. From Wikipedia:
Aside from needing to get a spacecraft to to an altitude that it can orbit at (for an example, the International Space Station orbits at an average of 230 miles above the Earth’s surface), they need to get up to a very high speed (ISS orbits at nearly 18,000 miles per hour). This takes quite a bit of fuel.
It does take less energy to go from 1000 feet to 2000 feet. The problem is that sea level starts at 20,925,525 feet above the Earth’s center of gravity.
When you go up 1000 feet you end up at 20,926,525 feet. You see the difference between 1000 feet and 2000 feet as twice as far. It’s really only 0.005% further away. You have to measure the distance from the center.
Without orbital velocity you could lift something to the moon and it would still fall towards the Earth. The moon itself is constantly falling towards the Earth.
It takes more fuel to go from 1000-2000 than it does to go from 0-1000?
No. But it takes about an eyedrop less amount of fuel, not the gallons you seem to think.
Wasn’t that a plot point for some Andy Griffith movie?
People have already said it plainly but you are suffering under a very common misconception so I will say it even more plainly. Astronauts aren’t weightless in space because there is no gravity in space. There is plenty of gravity in earth orbit, almost as much as there is on the ground. The earth and moon are tied together by gravity as well.
The reason that things are weightless in orbit (a different thing) is that that ship and everything in it are falling at the same speed around the earth. You don’t have to go into space to get the same effect. Roller coasters can do it briefly as well as training aircraft that flew in carefully calculated arcs that let people in the passenger area float around for 30 seconds at a time or so. The decrease in gravity as you move away from the center of the earth has little to do with this.
Imagine descending in an elevator from a very tall building. The elevator descends so fast that you float in the air inside it. What is happening is that you are falling at the same rate that the elevator is descending. You still have weight… you are falling.
What’s happening in the space station or shuttle is that aside from when its being launched, the spacecraft is actually falling towards the earth, but is moving so fast forwards that it keeps missing. So the astronauts and cosmonauts may seem to be weightless, but that is not the case.
The big rockets are fighting against this weight all the time that they are being launched. As all the fuel in the lower engines gets burned out, it is not necessary to carry that engine anymore because it becomes useless weight. So it gets dropped away and the next engine up fires up, not as powerful but carrying much less weight.
Well, for a helicopter, the reduced energy (minuscule) is probably outweighed by the decreased efficiency due to the lower density of the air – that is quite important to a helicopter. That probably isn’t major either, at 2,000 feet. But it becomes important as they go higher than that.
That’s why, until recently, you weren’t able to simply take a helicopter to the top of Mt. Everest. The low density of the air (plus some pretty fierce cross winds) made it impossible to land or even hover there.
True, but again, consider that rounded hill. The higher you go, the easier each step gets, but that doesn’t mean that you’re not tired when you get to the top.
Also, most of the energy goes to a sideways motion, so that as you fall back to Earth you are moving fast enough to clear the horizon every time.
Ignoring air resistance and obstacles, you could be in free-fall one foot above sea level, if you were moving sideways fast enough to miss the ground as you fell that foot.
IIRC the multiplcation factor for the Apollo lunar landing program was something like 25. That is, for every pound of payload you wanted to send all the way to the moon, you needed to add an additional 25 pounds (of fuel and structure) to the rest of the rocket in order to get it there.
Since kinetic energy is proportional to the square of speed, it takes a humungous amount of energy to reach orbital velocity (shuttle orbits at around 17,400 MPH). To lob a 1-pound mass up to an altitude of 100 miles (with a final velocity of zero)takes about 528,000 pound-feet of energy. To accelerate a 1-pound mass up to 17.4k mph requires a staggering 10.1 million pound-feet of energy, a factor of 20 higher.
If you add up the gravitational potential energy that an object has when moved infinitely far from the earth and convert it to kinetic energy, you find that you can fire an object straight up from the earth’s surface at about 25,000 MPH, and expect it to never return to the earth (this neglects atmospheric drag for the first part of the object’s journey). This is called escape velocity,, and it’s about twice the energy required for the 17.4k mph mentioned in the previous paragraph.
Contrast all of this with a 747 cruising 600 mph at 35,000 feet. On a per-pound basis, this vehicle has only 35,000 pound feet of gravitational potential energy, and about 12,000 pound-feet of kinetic energy. That’s 47,000 pound-feet of total energy per pound of mass about a half a percent of the 10.7 million pound-feet for the space shuttle. Whereas all of the space shuttle’s fuel is used to achieve altitude and (orbital) speed, only a tiny portion of the 747’s fuel load is required to achieve its cruising altitude and speed; the rest of the fuel it carries is to fight aerodynamic drag over the remainder of its flight.
This is correct. The pull of gravity does decrease as you move away from earth, and smaller amounts of energy are required for each additional increment of altitude as you move further and further away. Going from 1000 feet to 2000 feet of altitude takes less energy than going from zero to 1000, but only very slightly. We typically reference altitudes to sea level, but as Bill Door has said, the equation for calculating gravitational force measures distance to the center of the earth, which is some 4000 miles below the surface. So your “zero” (sea level) is really 4000 miles in this equation, and your “1000 feet” is actually 4000.19 miles in this equation. Moreover, gravitational force is inversely proportional to the square of this distance. So going from 1000 to 2000 feet actually takes about 99.991% as much energy as it takes to go from zero to 1000 feet.
So you’re right, it gets easier as you go up - but it happens with agonizing slowness.