Centripetal Force and Gravity

[vivek]

Hello Learned Ones,

I was just wondering about some stuff.

1. Is there a relation between centripetal / centrifugal force and gravity ?
2. How does one simulate gravity in space ?

I am not looking for scientific / mathematical formulaes. Just simple explanation will be adequate.

Cheers

 

[PowerMacG5]

1. There does exist a direct relationship between centripetal force and gravity. As one increases the centripetal force, the gravity, or amount of g's/g-force, increases. The easiest way I can tell you an actual experiance that you may have encountered with centripetal force is on a roller coaster. As you go into the loop, centripetal force is increased, as well as you are pushed into the seat by the increase in g-force. The relationship also matters how far away from the center of gravity you are. If you are very close to the center of gravity, it will require high rpm's to experiance the same g-forces as if you were far away at lower rpm's.

2. The way one simulates gravity in sapce is by creating a centrifugal effect. The way they are doing this on the ISS (International SPace Station) is to have one area of the ISS with a centrifuge. This area will be the only one with simulated gravity because it is rotating. The crew members will actually walk on the walls rather than the floor because as the device rotates the g-forces go outward to the walls. You may have felt this effect on a carnival ride where it starts to spin at high speed and you are pushed into the wall. With long-term space flight it is not viable to have only one small area with simulated gravity. What they are planning to possibly do on the manned Mars mission is to have the crew cabin connected to a piece of, say one of the rocket stages, by a tether. They would then start to use thrusters to get the entire ship to rotate around a center of gravity at a determined speed for 1/3 gravity. They will use 1/3 gravity because that is what the gravity on Mars is.

Hope this helps

 

[joelnale]

Hey there,

Centripetal force and the gravitational force are actually two entirely different forces. The use of the term centripetal force is somewhat misleading. It is not a 'special' force like the force of gravity (one of the four fundamental forces of nature). The term centripetal force is a categorization of the unbalanced force acting on an object while it is in circular motion (Centripetal Force has its origin which means 'center-seeking' force). For example, think of these visual examples: (1) swinging a yo-yo over your head, (2) you in a gravitron ride at a theme park (the one that spins you around in a circle very fast. Also usu. the one where most people get sick!), (3) a fighter jet pulling a loop in the air. Let's take a look at all three cases here. Firstly, in order to understand centripetal force, you must understand that ALL objects have a natural tendency to EITHER be at rest or move in a STRAIGHT line at a constant rate. A property known as inertia (resistance to change). So to keep an object in circular motion one must apply a constant force always directed towards the center of the circle that the object is traveling around.

Now (1) the obect we were dealing with was the yo-yo. In this case, if we let go of the string, the yo-yo would have flew off in a straight line. However, it didn't! Why? Because the string was constantly pulling it at every moment. Thus the unbalanced force in this case, which we can categorize as the centripetal force, is the tension in the string. (2) The object in this case is you. In this case the walls are acting to keep you moving in a circle. If they weren't there, you would not continue moving in a circle. Thus the force that the wall exerts is considered the 'centripetal force'. (3) Fighter jet is the object. The force that the air pressure exerts on the jet is the unbalanced force keeping the jet in circular motion and thus the 'centripetal force'.

Now, why do we hear all the time esp. on TV terms like, g-force, etc? This is because we tend to use the acceleration due to gravity (9.8m/s^2) as a 'baseline' with which we can compare other things in nature that are accelerating. For example, a fighter jet pulling a loop experiences a tremendous acceleration while moving in this circular path. To compare this acceleration, we compare it with something we know. Namely, the acceleration due to gravity. So when we say a fighter pilot pulled 5g's he accelerated at a rate 5 times that of gravity on earth.

One can also 'simulate' gravity on Earth in a gravity free environment. The easiest way to do this is to have something accelerate you! Moving in a circular path is accelerated motion. Where the acceleration is directed always towards the center. Your 'feeling' of weight is a result of the ground pushing up on you on Earth. If the ground was not there to push up on (or the scale pushing up on you!) you would feel weightless. Imagine a car tire that had a diameter of a high rise building that is in empty space somewhere. If you could be placed inside this tire and the tire rotated at a high rate of speed, you would feel the walls of the tire always pushing on you directed towards the center (centripetal force in this case). Your body's inertia wants to keep you in a straight line, but the walls of the tire are preventing you from doing so. This effect, the constant pushing force of the walls of the tire countering your body's inertia, provides this 'feeling' of simulated gravity. One can simulate your weight if you knew the radius of the tire and had the ability to change the rotational speed of the tire.

Hope this helped. I am a physics teacher in New Jersey. Happened to stumble on this message. I had a link for you to check out, but it is dead at the moment. When it is up, I can send it to you.

 

[pm]

Nice post, JoelNale.

 

[rimshaker]

wow joelnale... that was an awesome first post

 

[Armitage]

Some other interesting stuff on simulating gravity with a centrifuge...
Unless it is really big (Ringworld ), you can have a substantial "gravity gradient". This means that the acceleration you feel at your feet will be higher then that at your head. In the extreme case consider a centrifuge with a radius slightly less then your height. Your feet could have gravity, while your head is still in freefall! Actually, here's a more extreme case! Consider a centrifuge with a diameter equal to your height. Your head & feet would have gravity, but your midsection would be in freefall ... makes me queasy just thinking about it! And if you spin it fast enough, it could pull you in half! (The plot of another Niven story )

Centripital "force" is also what keeps objects in orbit against the pull of gravity. Gravity basically acts as the Yo-Yo string in JoelNale's post.

Oops ... in re-reading this, I realized I made the exact same error I corrected KraziKid for below.
As below, gravity is the centripetal force.

Combining these two points ... the gravity gradient can be used to stabilize the orientation of an orbiting satellite. Basically, you put a long boom with a weight on the end on your satellite. You can work out the dynamics to show that, for a properly designed system, the gravity gradient will stabilize the satellite so that the end of the boom points at the earth. It's a cheap way to achieve low-precision pointing passively.

 

[PowerMacG5]

ergeorge, as joelnale said, gravity and centripetal force are two completely different forces. Gravity is a force of nature. In reality Gravity is not actually pulling on you. Gravity is the "well" that a planet, star, black hole, etc... creates in the fabric of space. Consider this analogy - If you were to have a trampoline with nothing on it, the fabric would be flat. Once you stand on it, it creates an indentation, and if you place something in the indentation it falls to the bottom. Gravity is actually the well. The deeper the well goes, the stronger the force of gravity will be. The reason the planets in our star system, Sol, stay in orbit around the sun is because the sun creates a giant well and the planets are sitting within the walls of the well. The way to escape gravity is to generate enough Isp (specific impulse) to climb the wall of the well. If you do not have a high enough Isp, you will just climb the wall but start to orbit higher up on the wall the you previousely were.

 

[Armitage]

Uhm KraziKid ... I know what gravity is .
Maybe my terminology was a little confusing ... I should have said, for example:
Your feet could have "gravity", while your head is still in freefall!
or better yet:
Your feet could have acceleration, while your head is still in freefall!

Sorry for the mis-statement.

Your understanding of Isp(specific impulse) is very confused though.
Isp is simply a measure of the efficiency of an engine, ussually a rocket or jet engine. It is the ratio of the thrust produced by a mass of fuel:

Isp = T/dW = Ve/g (T: Thrust, W: weight, Ve: exhaust velocity, g: gravitational acceleration)

It has nothing to do with climbing out of a gravity well. In fact, Ion propulsion engines have Isp orders of magnitude higher then chemical rockets, yet they can't even lift themselves off the ground. They have very high Isp, but very low thrust.

All you need to get out of the gravity well is enough thrust in the right direction
If you have a low Isp, it just means you need more gas

Now, if your Isp & thrust to mass ratio are to low, you can certainly show that your rocket cannot carry enough fuel to reach escape velocity, but I don't have time to get into that right now.

 

[PowerMacG5]

ergeorge, sorry for the mis-statement, I should have said thrust. But I do know what Isp is. A chemical rocket has extremely high thrust and acceleration but have a very low Isp. Ion engine have very high Isp, but very low acceleration and thrust. Here are a few example of rocket engines and their Isp's:

A Magnetized Target Fusion (MTF) Rocket has an Isp of 50,000 s - 100,000 s
Sperical Torus Nuclear Fusion system has an Isp of ~35,000 s
Magneta-plasmadynamic (MPD) Thruster has an Isp 2500 sec < Isp < 7000 sec
Pulsed Inductive Thruster has an Isp of 2500 sec < Isp < 7000 sec
Hall Effect Thruster (HET) has an Isp of 2500 sec < Isp < 7000 sec
Gridded Ion Engine has an Isp of < 6000 sec to >> 6000 sec

These measurements are from Nasa documents on possible missions to Callisto. They are not made up numbers. As you can see a NTR (Nuclear Thermal Rocket) is the most efficient rocket in the group. Although the Isp is higher than an ion engine, it has greater thrust. The way a NTR works is by having a nuclear reactor encased in a shell that will allow gas to flow around it. What you do is have a liquified gas and let it flow around the reactor. The heat from the reactor will then turn this gas into high temp. plasm. This plasma is then shot out of the back of the casing. The way we can currently do this is with a Fission reactor. In a MTF there will be a fusion reactor, which is much more efficient than a fission reactor and there is no radioactive waste.

 

[Chooco]

-centripital force when used perpendicular to the force of gravity is completely independant from the force of gravity, if you are swinging a bucket while spinning in a circle, the force of the bucket trying to release from you hand would be the same on earth as it would on the moon. if you were swinging it from up to down then gravity does make a difference as it is a force in 1 direction.
-centrifugal is not even a word
-gravity is simulated in space by the constant falling towards earth, the gravity on the space shuttle is actually like 5m/s but they are always falling towards earth. to keep at a constant distance from earth they have to make sure that the centripital force is equal to the gravitational force which is why they try to limit their speed, if the space shuttle went to slow it would crash to earth but if it went too fast it would shoot out of orbit.

 

[PowerMacG5]

- True, except the force pulling down on the object as you spin it in a circle is different on the Earth and Moon so that as the bucket is moving sideways it will fall to the ground faster on Earth than on the Moon.
- centrifugal is a word (look it up in the dictionary)
- Gravity is simulated in space by the use of centripetal force. Astronauts are constantly falling towards earth, but this does not create gravity. To simulate gravity in space you must either generate a gravity well (which we are not able to do), or start swinging the ship in a circular motion. Once going around in a circle, if you are in contact with the ship, you will feel the force of simulated gravity. To actually be walking in simulated gravity you must be in contact with the wall that is furthest away from the center of mass. The center of mass is the point in a system of bodies or an extended body at which the mass of the system may be considered to be concentrated and at which external forces may be considered to be applied. Center of gravity is a term that is used wrong nearly all of the time. When something is rotating around a point, the point is not the center of gravity, it is rather the center of mass. But the way we can currently simulate gravity is similar to the ride in the carnival "gravitron". If as this is spinning you stand on the wall, you will stay on the wall as long as the aparatus is spinning with a force going out at 1 g or more. The same is true in space, except it requires less force to be pushed outward because in space you are not have gravity pull down on you as on our planet. A comfortable simulated gravity level could be 1/3 the gravity of Earth as I explained in my previous post.

 

[Chooco]

i wonder if that's how the deep space nine starport works on star trek, you know how it has a spinning outer ring right? could it be that the peoples' feet are facing to space and the spinning of the thingy makes the gravity? ah who cares, new star trek sucks anyway

cen&Acirc;·trif&Acirc;·u&Acirc;·gal (sn-trfy-gl, -trf-)
adj.
1. Physiology. Transmitting nerve impulses away from the central nervous system; efferent.
2. Botany. Developing or progressing outward from a center or axis, as in a flower cluster in which the oldest flowers are in the center and the youngest flowers are near the edge.
3. Tending or directed away from centralization, as of authority: &acirc;??The division of Europe into two warring blocs, each ultimately dependent on a superpower patron, is subject to ever-increasing centrifugal stress&acirc;?? (Scott Sullivan).

 

[PowerMacG5]

Here is the definition from the American Heritage Dictionary of the English Language, Fourth Edition

cen·trif·u·gal Pronunciation Key (sn-trfy-gl, -trf-)
adj.
1. Moving or directed away from a center or axis.
2. Operated by means of centrifugal force.
3. Physiology. Transmitting nerve impulses away from the central nervous system; efferent.
4. Botany. Developing or progressing outward from a center or axis, as in a flower cluster in which the oldest flowers are in the center
and the youngest flowers are near the edge.
5. Tending or directed away from centralization, as of authority: ?The division of Europe into two warring blocs, each ultimately
dependent on a superpower patron, is subject to ever-increasing centrifugal stress? (Scott Sullivan).

 

[Armitage]

KraziKid,
Another thing you have to consider with ion & nuclear engines is the propellent mass fraction. Chemical rockets can have a propellent mass fraction as high as 94%!
If you need alot of shielding or heavy power generating equipment for your nuclear or electric engine, it will severely impact your propellent mass fraction which play directly into the maximum achievable velocity of the system.

dV = Ve ln(Mi/Mf) = Isp g ln(Mi/Mf)

Mi : initial mass
Mf : burnout mass (all fuel expended)

 

[PowerMacG5]

ergeorge, what I was trying to get at is that a NTR is the most efficient rocket ever considered. A NTR using fission based nuclear reaction is much more efficient than an ion engine, and any chemical engine. And an NTR using a fusion based nuclear reactor is much more efficient than an NTR using a fission based reactor. If you were to use a fusion based reactor you do not need radiation shielding because there is no radiation. In a common fusion reaction 1 deuterium atom and one tritium atom combine to form a helium atom plus a neutron. A fusion reaction once brought up to the correct temperature and pressure is extremely exothermic and self sustaining. Because it is self sustaining, as long as you keep the fuel supply, it should never stop. A fusion NTR, fully fueled, would weigh as much, if not less than a chemical engine. Also, a fusion NTR would last longer than a chemical reaction. An NTR could produce as much thrust as a chemical engine, but has an Isp of 50,000 s to 100,000 s. The thrust put out by a NTR has been estimated to be between 50,000 and 250,000 pounds. The way the NTR works is to pipe LH2 (Liquid Hydrogen) over the reactor core, which will in effect cool the core but also super heat the hydrogen to become plasm and is forced out of the back. This is an extremely efficient way to produce thrust because the same material is used to produce thrust and cool the reactor. The same principle is used in both fission an fusion NTR's. I am not saying that a NTR would replace the shuttle or a booster rocket to bring things into space, but what I am saying is that if we want a cheap power source for a long duration space flight, NTR would be a good choice because it also produces the electricity that the astronauts will need.

 

[Chooco]

what is NTR?

what about the anti-matter theory? would that work?

 

[PowerMacG5]

NTR stands for Nuclear Thermal Rocket. And The problem currently with anitmatter is that we cannot produce it in enough quantity to sustain a continuous non-stop reaction. Antimatter does produce more power than any known source of power. When matter meets its antimatter counterpart, they annihilate each other leaving residual radiation such as gamma rays, and extremely high amounts of heat. Currently we can produce decent amounts compared to other particles of antimatter are antiprotons, and positrons. They are currently produced in particle accelerators. A particle accelerator is a circlular aparatus that accelerates atoms, and sub-atomic partics to near light speed velocities. In the area of 99.99999% the speed of light. Within the accelerator there are giant electromagnets that are used to accelerate different particles depending on the charge. A use of a particle accelerator that is currently being used at FermiLab is to try and discover the Higg. The Higg is also known as the god particle. The way they do this is by accelerating a proton going, say, clockwise and an antiproton going counterclockwise. They then orchestrate the particles to collide within one of the 2 story tall sensors. Within these sensors they can detect different types of sub-atomic particle such as the different types of quarks, muons, electrons, etc... During each collision they are looking for a specific change withing each collision that would account for the presence of the Higg. The Higg is the particle believed to give every other sub-atomic particle mass, and the force of gravity. Currently, the cost of antimatter is $62.5 trillion dollars a gram, or $1.75 quadrillion an ounce. The production of any particle of anitmatter is only 50% effective because half of the substances produced is regular particles of matter. FermiLab is trying to increase the production of actual antimatter atoms from 1.5 nanograms a year to 15 nanograms a year. But to get back to antimatter, the reaction between .5 kilograms of antimatter with .5 kilograms of matter (making a total of 1 kilogram of substances) could produce 70,000 Terrawatts of energy. This is enough to power the average house for 540,000 years. The star trek idea of an antimatter engine is currently not possible. In Star Trek the create a "warp bubble" around the ship by using the matter/anitmatter reactor to produce the high energy radiation, and then transferring it to the "warp coils". In these warp coild the raditaion os converted into gravitons and exotic matter. The gravitons are directed towards the front of the warp bubble, and the exotic matter is directed towards the back. What this does is causes the front of the buble to contract and the rear of the bubble to expand. What is interesting about the warp theory created by Miguel Alcubierre is that if you have the warp bubble, you effectively will have 2 "spaces". You have the internal space of the bubble, and the space outside of the bubble. As most of you know Einstein's special theory of relativity states that an object can only move at speed less than light. With the warp theory the ship is in the inner space and is actually standing still while the bubble is moving. Their exists no limit on how fast space can move within space. Actual Matter/Antimatter engines that we could create would probably operate similar to an NTR. But as our science and technology increases, we will be able to find new ways of harnessing the energy from the reaction and turning it into thrust and power.


If you want to know more about matter/antimatter in detail please let me know. I have studied all of the theories and documentation I could find behind it and a lot of information about the creation of anti-matter, and the uses.

 

[Imancer]

I'm surprised no one mentioned this, considering the title of the thread.

Consider the case of a satellite (natural or man-made) moving in a circular orbit. (yes, I know orbits are virtually always actually elliptical ). A centripetal force is required to keep the the satellite moving in a circle. And what supplies this force? Gravity of course.

"Centrifugal" (outward) is used to describe an apparent force that is observed when your frame of reference is moving in a circle. For example, from your point of view on the Gravitron (sp?) ride, there seems to be a force pushing you outward against the wall. But since you're being accelerated (towards the center of the circle), your frame of reference is non-inertial (Newton's first law does not apply), and the analysis of the situation if very much complicated.

It's much easier to analyze from an inertial reference frame outside of the ride. From there, it's apparent that it is simply interia (your tendancy to move in a straight line) that "pushes" you against the wall, and the wall provides the cetripetal force that keeps you moving in a circle. That's why people say "there's no such thing as centrifugal force."

Here's link on inertial reference frames:
http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Inertial/Inertial.html

Einstein provided the final (so far) word on accelerated reference frames in his General Theory of Relativity.

 

[PowerMacG5]

Imancer, one thing you have to understand is that gravity and centripetal force are two different forces. Gravity is a force of nature. When a satellite orbits a planet, centripetal force does not keep it in orbit, gravity does. Centripetal force has nothing to do with keeping moving in an elliptical orbit. If you were to measure centripetal force, it is the force be applied outward, while gravity is a force that is applied inward. When you are in the gravitron, the outward centripetal force is keeping you pinned up against the wall, not gravity. If I were to follow you exactly and say that a satellite stays in orbit due to centripetal force, the satellite would keep moving outward and fly into deep space. Gravity is an inward moving force because as something orbits Earth, they are constantly being pulled to Earth, not repelled. When you orbit any planet you must keep an orbit of geosynchronous speed or greater becauseif you do not, the force of gravity will pull your ship inward and you will not have enough momentum, or speed to keep it from pulling you into the atmosphere. When the space shuttle is ready to return from its space flight, it actually turns around and fires the OMS engines and reduces its orbiting velocity. When the velocity is decreased the force of gravity is stronger, so in turn the ship is pulled towards the source of the gravitational field. When you look at a centripetal force, as the speed of the ship is decreased withing a device generating the centripetal force, it is pulled outward towards the wall of the device.

 

[Belegost]

Ummm, Krazikid, you're a bit mistaken. Imancer was very correct in his post.

In the case of an orbiting satellite, gravity IS the centripetal force. A centripetal force is defined as a force which holds a moving object to a curved path. It is a resultant force, meaning it only exists as the net of other forces. In the example of a satellite the centripetal force is gravity, if we were to consider a swinging bucket the centripetal force would be the tension in the string. In the case of the gravitron at the carnival the centripetal force is provided by the walls which push against the rider keeping them from flying off tangentially.

The outwards "force" you describe is commonly known as the "centrifugal force", however it is not a true force at all, merely the effect of the change in inertia, the resistance provided by the natural tendency for the body to move in a straight line with constant velocity. As Imancer said, from the accelerated reference frame of the rotating body, the situation is rather complicated, but fairly simple from an inertial reference frame observing.

As for the space shuttle slowing to return to earth. You must think about what is occuring as an object orbits the planet. The object is constantly being pulled towards the center of the earth, however its velocity causes it to always miss, so the object continues to orbit. If however the velocity is reduced (as in the case of the space shuttle) the object no longer has enough velocity to miss the planet and collides with it. The force of gravity is only dependent on the masses of the objects and the distance apart, and is not affected by the velocity. (unless there are some relativistic effects at near light speeds that I'm unaware of, but the space shuttle doesn't get anywhere near light speed.)

 

[Armitage]

Yea Kid, Belegost & Imancer are right, and you are confused



<< one thing you have to understand is that gravity and centripetal force are two different forces. >>


Here is a pretty good link on centripetal force & circular motion.
Here's another link


<< Gravity is a force of nature. When a satellite orbits a planet, centripetal force does not keep it in orbit, gravity does. >>


Gravityis the centripetal force in this case.


<< Centripetal force has nothing to do with keeping moving in an elliptical orbit. If you were to measure centripetal force, it is the force be applied outward, while gravity is a force that is applied inward. >>


Nope


<< When you orbit any planet you must keep an orbit of geosynchronous speed or greater becauseif you do not, the force of gravity will pull your ship inward and you will not have enough momentum, or speed to keep it from pulling you into the atmosphere. >>


Uhm, you can easily have an orbital speed of less then "geosynchronous speed" If it's a circular orbit, it would be termed a "super-sync" orbit. The simple example here is the moon, which is certainly far slower then "geosynchronous speed" .


<< When the velocity is decreased the force of gravity is stronger >>


This is a very serious misunderstanding. As Belegost said, gravitational attraction is not a function of velocity. At least not for the Newtonian physics we are discussing here.
Gravitational attraction is only a function of mass & distance.

 

[Sahakiel]

Have fun with this one:
Gravity is a bend in spacetime; much like putting a bowling ball on a bedsheet, only in four dimensions.

 

[PowerMacG5]

Sahakiel, that is exactly what I was trying to get at with my previous posts. In my second post in this thread, I said <<Gravity is the "well" that a planet, star, black hole, etc... creates in the fabric of space.>>

 

[Armitage]

<< Sahakiel, that is exactly what I was trying to get at with my previous posts. In my second post in this thread, I said <<Gravity is the "well" that a planet, star, black hole, etc... creates in the fabric of space.>> >>



Yea, but I'm still not sure what your point is.
It's a pretty picture and maybe a useful mental model.
But it doesn't contradict or really add anything to what else has been said here.

 

[Agent004]

<< Have fun with this one:
Gravity is a bend in spacetime; much like putting a bowling ball on a bedsheet, only in four dimensions. >>



So can we bend gravity?




<< This is a very serious misunderstanding. As Belegost said, gravitational attraction is not a function of velocity. At least not for the Newtonian physics we are discussing here. >>



Yes. Actually for satellites in orbit, it's the other way around, velocity is a function of gravity