Ask me about Science! (Theoretical, Factual, or otherwise)

[Hainted]

Ok little research yielded some more insight. Planets would be tidally locked with the same hemisphere facing each other. Due to gravity massive oceans would be on the hemispheres facing each other, depending on mass, and the distance between them they may be distorted and egg shaped. They would orbit on a horizontal plane, and more than likely this orbit around a central point would replace the rotation of the planets to induce a day/night cycle. I'm still not sure how a moon(s) would work in this arrangement though?

 

[Penpilot]

Coincidentally, I came across this article on cracked of all places, and it explains why a counter-earth would be easily detectable to us. Obviously take the resource with a grain of salt. It is cracked after all. 5 Awesome Planets We Used to Think Were in Our Solar System | Cracked.com

In the article it states that counter-earth could be indirectly detected because if it would have measurable gravitational affects on the other bodies in the solar system, like Venus and Mars.


As for an arrow fired that has it's mass increased, you can see what happens by using the following formulas. F=MA and A=V/T. If you combine them you get V= (FT)/M. With initial F not changing, the increase in M will decrease V.

 

[BWFoster78]

Ankari and psychotick,

Here's my understanding of physics (granted it's been a while since sophomore year of college):

If I drop two objects the same size and shape but different density, the two objects will hit the ground at the same time. The mass of the objects have no impact on the rate of fall.

Is my recollection, wrong?

If not, how does it change the matter if it's an arrow flying up instead of an object being dropped?

Penpilot,

I'm not sure your equations are applicable. Since I'm using magic to increase mass, there's no reason to say that I'm not also increasing it's force.

 

[Ankari]

Because that rule only applies to the gravitational pull on an object. That is one type of force. Your arrow example has a secondary source of force: the bow that shot the arrow (and, by extension, the person who weilded the bow). You have to now consider the conservation of energy. Since the initial force applied to the ar

I'm typing from a phone. If you need further clarification, I'll be on the laptop later tonight.

 

[buyjupiter]

BW Foster: in a perfect universe with no other forces besides gravity acting upon the objects, yes they fall at the exact same rate. However, a bowling ball would appear to fall faster than a feather because of air resistance, or drag.

If you're shooting an object "up", you have to overcome the effects of gravity (and air resistance) long enough for the object to hit its target. It's why there's a max distance on how far a cannonball will go or why you can't shoot an arrow all that far away from your initial position. It's also why you see an increase in pull (force) being put into bows/crossbows as time progressed. Everyone wanted to increase that range.

I wish I could draw you a diagram, but imagine a gentle hill (or parabola shape if that's easier). There's a max point at which the object can go no higher and that's when gravity starts to take over. I think it's a transfer from the kinetic energies (from the person who shot the object) to the gravitational energy as it plummets to the target/ground. But it's been a few year since physics. So I could be wrong there.

Even in the simplest of acts, there are a bunch of forces acting upon the objects in question, and systems get really messy really quickly.

 

[Penpilot]

If I drop two objects the same size and shape but different density, the two objects will hit the ground at the same time. The mass of the objects have no impact on the rate of fall.

Is my recollection, wrong?

To my recollection, this applies only to a vacuum. Air resistance changes things. Each object will have a terminal velocity, a top speed where wind resistance (drag force) equals the force of gravity accelerating the object. Parachutes work on this principle. They decrease a skydiver's terminal velocity to a survivable level. If they didn't, then parachutes wouldn't work.

Penpilot,

I'm not sure your equations are applicable. Since I'm using magic to increase mass, there's no reason to say that I'm not also increasing it's force.

If magic is increasing the force on the object, acting like thrust, then the object can speed up or slow down as you please. In this instance you're changing two variables instead of one, Force and Mass.

 

[psychotick]

Hi BWF,

No.If you drop two objects of the size and shape but different densities, the denser one will hit the ground further. Try dropping a cricket ball and a tennis ball out a two story window, or a ballon and a beach ball and you'll see.

The reality is that we live in an atmosphere, and air provides friction which resists movement. And the faster you go the bigger the resisance. If there was no air all four would hit the ground at the same time. With air the densist object wins because it has the greatest force acting on it - since gravity acts on mass - while all four experience the same resistance. The more force you apply the greater the resistance you can overcome.

And equally the terminal velocity of the densist object is fastest too. This is because as you travel faster through the air the resistance increases, and at some point the force that you put into pushing (or in this case pulling down) an object balances out against the resistance. Again you can see this in your daily life. Get in your car and to go faster you have to push the throttle harder. If resistance was always constant you would simply push the throttle to whatever amount you like and the car would accelerate at a constant rate for potentially forever.

Cheers, Greg.

 

[Super Fun Pop]

I was actually asking about a planet on the opposite side of the sun, but this answer is much better. It does lead to more questions about the nature of the worlds, and how they function though.

1. Would the planets orbit each other on a horizontal plane or vertical?
2.Would they be "locked" so that with a similar mass, rotation,size,etc the same hemispheres face each other always?
3. Would their orbit be longer than their rotation, and what would the difference be?
4. HOW would a moon orbit these two worlds? elliptically or a figure 8 motion...?
5. If they orbit each other on a horizontal axis(and the Goldilocks zone is big enough) wouldn't this have a huge impact on the seasons?
6.The idea of an object, earth sized, as a twin has huge implications in society, but wouldn't it lead to more eclipses, or a funny day/night cycle as each world passed into the other's shadow, or would light reflected from each other's atmosphere make up for it?

I know it's a lot, but you've set my wheels to spinning, and my strength lies in more social aspects of society. I'm not interested in how the tides work(though they would be crazy it seems) just enough to make it plausible that these places exist, so someone doesn't pull the whole thing down by pointing out a fatal flaw.

Ok little research yielded some more insight. Planets would be tidally locked with the same hemisphere facing each other. Due to gravity massive oceans would be on the hemispheres facing each other, depending on mass, and the distance between them they may be distorted and egg shaped. They would orbit on a horizontal plane, and more than likely this orbit around a central point would replace the rotation of the planets to induce a day/night cycle. I'm still not sure how a moon(s) would work in this arrangement though?

Technically there is no direction in space; no up or down. So it wouldn't really be horizontal or vertical and as space doesn't have the same friction laws as we do, it could rest easy at any plane. We have not found an ACTUAL example of this to my knowledge, so it's mostly, if not completely hypothetical. Because it is hypothetical, there are quite a few variables that aren't very well perceived, but it's possible for a array of distinct qualities, binary system to binary system, and differences between the planets.

Now to answer your questions.

Question 1, 2, & 3:
This all depends on the formation timeline of both planets, the solar system, and any interactive gravitational forces.
- If planet A is the same size as planet B; it's likely the two planets formed separately, or at least, grew a large amount of mass before their gravitation towards each other. They would most likely pass, shift, and spin around one other, orbiting the sun, slowly latching on to each other until they form a infinite loop, creating one orbiting path. (which, I'm guessing 99,999,999 times out of 100,000,000 they would collide instead)
- If planet A is relatively larger in size compared to planet B; I could see a likely possible formations. Planet B, was at one time as large or larger than planet A, but sometime during the early period of both A & B's formation, B was struck by another planet, C, or a large mass comparable to a planet. This both tore a considerable chunk from planet B and changed its orbiting path. Some or most of B's broken debris and planet B itself was set on a similar and extremely close orbiting path towards A, B's broken debris collided with A, changing A's path slightly as well. Both A & B pass, shift, and spin around the other until their orbiting paths align. (which, again, I'm guessing 99,999,999 times out of 100,000,000 they would collide instead)

Both these scenarios could explain its formation and a wide verity of different outcomes as far as rotation, speed, orbit... meaning, if these two outcomes are indeed possible, just about any variation is possible.

4) I did say moon, but now I'm thinking its far more likely that they'd have some form of debris field, as if there was indeed a moon at one point or multiple moons, it would, in all likelihood have at some point crashed into one of the two planets, or collided with another. OR they may have no debris or moon at all.

This asteroid protection could also come from other places in the Universe or by cosmic luck, not many pass through this particular solar system, or miss our binary planet system completely.

5) Seasons are affected, mostly, by the distance the planet is from its sun. The further out; the cooler the season is, the closer; the hotter. Weather on the other hand would indeed be affected by this other planet, actually both planets should be, theoretically, equally affected.. Meaning, depending on their distance from each other, they will most likely have similar weather conditions. This effect happens indirectly though; as the orbiting planet would affect the ocean, tides, currents, where these oceans, tides, and currents would change and alter weather conditions. This is equally affected by the Geography of the planet, so there will be variations, as the two planets would have radically different Geography.

6) There would definitely be a big, even strange, difference. Your guess on the matter is as good as mine; it all depends on the formation of the planets and exactly how they rotate and orbit one another and the sun.

 

[Super Fun Pop]

I fire an arrow straight up and then use magic to increase its mass. What happens to the velocity of the arrow?

I see a few others have helped answer this, but I have a slightly different understanding of your question.

Like a few others have mentioned, there are quite a few different laws and forces affecting this arrow, but you are asking if, using magic, you could alter how the arrow is affected & how it reacts to these forces; specifically, how would a change in mass affect velocity, even more specifically, what is its affect on terminal velocity.

Terminal Velocity is, in a simple explanation, the velocity of an object when all these forces have balanced out and the object has a steady & non-changing velocity; meaning it will, from this point, with no new outside forces, travel at the exact same rate until impact. Velocity, in itself, is the measurement of movement overtime.

Velocity = Displacement / Time Velocity = Change in Position / Time.

A change in mass can be described in two ways, as Mass = Density x Volume.
- A positive change in Volume will have a negative effect on Velocity.
- A positive or negative change in Density will have almost no effect (fractional change ~[.0001]) on Velocity.

What you're really asking what effect would a change in mass have on the arrow's impact with its target.

The arrow's impact is only marginally affected by velocity; it is, more heavily, if not fully affected by the arrow's momentum (which is in part calculated by velocity), and momentum is equally affect by the objects mass.

Momentum = Mass x Velocity.

The more momentum, the larger the impact.
The more Mass, the larger the momentum.
The more Velocity, the larger the momentum.

At the moment you have no magic spell to change velocity, but if you did, the momentum could be greatly increased.

Speed (Acceleration), is the rate of change in velocity. If you have a magic spell to increase the speed, it would increase velocity.

Therefore:
-if you increase the density of an object through magic, you can affect the momentum and the impact of that object.
-if you increase the speed of an object through magic, you can affect the moment and the impact of that object.
-if you increase the speed & density of an object through magic, you can GREATLY affect the momentum and impact of that object.

This way you not only have the greatest impact, but you also have ~125% magic efficiency, as every fraction of power used has a direct affect on the impact with zero waste. This is also the easiest and most efficient explanation as it only has two variables which can both be altered without side effects (Density & Speed).

Others have mentioned force, but this is a non-efficient method as Force x Time = Momentum. Overtime, as the arrow travels through the air, it would loose momentum, as it looses acceleration. Force would come from from the bow or any magic altering the bow or archer. Magic energy would still be wasted as the direct change in force would not have an equal change in the impact, as overtime momentum would decrease.

By directly affecting the momentum through magic, you'll have ~125% efficiency while also having 100% control over the impact of the arrow with no outside forces acting or changing the results you've manufactured.

More importantly, a change in density and speed would in no way affect trajectory. Meaning an arrow fired, will hit the target in the same spot, with or without these magical changes. As gravity on the arrow is not affected by the arrow's density, but the density of the planet. A change in density or speed would not alter course.

Equation for efficiency:

Magic Energy Expelled = Magic Spent on Density + Magic Spent on Speed
Momentum = Mass (volume x density) + velocity
Velocity = rate of change in position = speed

MEE = MSD + MSS
Momentum = Mass (VO x (MSD + D)) + VE
Velocity = Speed + MSS

2 = 1 + 1
Momentum = Mass (1 x (1+1)) + VE
Velocity = 1 + 1

2 = 1 + 1
Momentum = 1 x 2 + 2
Momentum = 5

Without MEE, MSD, and MSS
Momentum would equal = 2

So the magic energy expelled in this instance has 125% efficiency, base value. For every one part of magic energy expelled 1.25 is invested into momentum. This may change when volume is not equal to density, or when mass is not equal to velocity, but for this equation, everything was given the value of 1. This is a theoretical equation, magic will not always have an exact 125% efficiency, but it is still impressive.

A value in this equation has to be greater than 0, for it to be largely efficient. At no point would efficiency go bellow 100%, no matter the value, as long as its over 0.

 

[Malik]

Super Fun Pop,

Do you have any links for celestial mechanics modeling, either online or free to download? Specifically, my WIP takes place on an Earth-sized moon orbiting a giant planet and I'm trying to work out the transit time -- days when the giant would eclipse the sun and their world would be in total darkness -- and how often that happened in a given "year" -- a year being the giant planet's orbit around the sun.

I've played around with Kerbel but it's not quite what I'm looking for. I modeled this on my desk with rubber balls and a flashlight and I think I got it fairly close, but I'd love to have better modeling behind it.

 

[Super Fun Pop]

Super Fun Pop,

Do you have any links for celestial mechanics modeling, either online or free to download? Specifically, my WIP takes place on an Earth-sized moon orbiting a giant planet and I'm trying to work out the transit time -- days when the giant would eclipse the sun and their world would be in total darkness -- and how often that happened in a given "year" -- a year being the giant planet's orbit around the sun.

I've played around with Kerbel but it's not quite what I'm looking for. I modeled this on my desk with rubber balls and a flashlight and I think I got it fairly close, but I'd love to have better modeling behind it.

It isn't free, but there is a trial period for it. You could also download it by other means, I'm sure.

Universe Sandbox

It may take a little work from your end to figure out how to get it to do what you want, but it simulates a lot of the spacial & gravitational forces found in outerspace. If you can get it to work, you can make a model of your moon and planet, their solar system, and see exactly what you're looking for.

 

[BWFoster78]

Super Fun Pop,

You said:

What you're really asking what effect would a change in mass have on the arrow's impact with its target.

Actually, I think I've got that. I describe the character as having the ability to throw some pebbles in the air and have them crash down with the weight of boulders, with the force of boulders.

The issue is this:

My mage is flying above the enemy army. Archers fire arrows at him. If he makes all the arrows tremendously heavy, will they reverse slow faster than they would have otherwise?

My initial thought was that my mage's solution was good. Then, I had a beta reader tell me I was wrong. I've done further research, and I'm positive the statement below is correct:

Two objects of the same size and shape but different densities dropped from the same height will hit the ground at the same time.

Even if one is 100lbs and one is 1000lbs, they'll hit the ground at the same time!

How is my situation different?

If a 5lb arrow and a 50lb arrow are dropped, they'll hit at the same time. One does not travel faster than the other assuming they're the same size and shape (so that air acts on them the same).

Now, what happens if I fire the 5lb arrow straight up and magically make it 50lbs? Is there some difference that stems from the fact that it's going upward, or does the same principle of the dropping apply?

 

[Super Fun Pop]

Now, what happens if I fire the 5lb arrow straight up and magically make it 50lbs? Is there some difference that stems from the fact that it's going upward, or does the same principle of the dropping apply?

Dropping is gravity based, only the density of the planet is taken into factor there, the lesser dense arrow 5lbs or 50lbs will fall towards the earth at the planets gravitational pull.

That said, force is used to propel an arrow, in which is turned to momentum overtime.

If the bow releases 50lbs of force on a 5lbs arrow, that's about 10 times the force of the weight. As the force is converted to momentum overtime, it degrades; 40lbs of force, 30lbs of force, 20, 10, 5, until there is no force left on the arrow to push it up. At which point gravity takes over. This force is also added to the pressure in the exact opposite direction of gravity and resistant forces.

If you, lets say, switch that, and exert 5lbs worth of force on a 50lbs arrow, we know it won't go anywhere.

The question is, would multiplying the mass of the object using magic also multiply the force? If not, more mass will radically tip the scale, make the 50lbs worth of force inert, meaning it no longer has an effect on the arrow, causing gravity to take over quicker.

I would say you're correct in that assumption. The denser you are able to make it, the faster the change will happen. Now, though all mater falls at relatively the same speed, the impact will greatly depend on its mass at impact. So those archers are in for a world of hurt.

 

[Hainted]

Ha Ha, finally got the Binary Worlds math worked out(Thanks to the astrophysics people on Reddit) the planets orbit at a mean distance of 702,904.823 Km from each other and 167,323,260 Km from their parent star. And they would have a full eclipse every month, and a full "moon" would be 8 times brighter than a full moon on our world.