What makes some forces unnoticeable?

[great_scott]

Hello people,
this is my first time on here so i hope I am posting this in the correct category. if not I am sorry.
Im a phd student in high energy physics and am to be a doctor by this summer. but i do have some basic questions i can't answer and that make me hate myself. i need to know what i misunderstand from Newtonian physics. i know that's indeed embarrasing for a phd student to say. but i ask those questions to the prof.s i work with and they couldn't give any satisfactory answers either. in my first question i will take the Earth as an example, i can actually pick any other objects as an example to make the question easy to understand.

okay when an asteroid hits the earth, there is a force acting on Earth in some direction but there is no opposite force to cancel it. so due to the change in accelleration from zero to something very tiny, the Earth gains an initial velocity thorugh the direction of the force created by the astreoid. we all know the Earth is not moving off its orbit or anything liek that because with a relatively small asteroid as in our example its hard to make the Earth reach the escape velocity or changing the angular momentum vector or magnetic field from the sun ... etc. I am not into this kind of analysis. i just need an analysis of the system (earth and asteroid) in terms of forces, only forces. basically there is a force pushing the Earth but there is no opposite force to cancel it so why does the Earth not move? like i said above i do know why it doesn't move but i cannot show or prove it by just using the forces. please help me understand the picture in term of forces. or do i miss something? do i misunderstand the concept of force? thanks

 

[nDever]

According to Newton's description of force, acceleration is directly proportional to the force and inversely proportional to the mass. If your asteroid has a relatively small mass compared to the earth, then the asteroid's acceleration due to the gravitational force of Earth is going to be faster than the acceleration of the Earth due to the force of the asteroid. They both accelerate, but the Earth's acceleration is so small that it can't be noticed.

 

[great_scott]

It should be noticeable in years. Because there is no deacceleration, and also because of Newton's first law of motion the Earth will keep moving in the same direction as the acceleration is, even if the acceleration is canceled and gone by chance for instance another impacting asteroid creating an acceleration of the same magnitude in the opposite direction.
All i need is a free body diagram where i can realize how and by what the force on Earth due to the asteroid is being canceled. if it doesn't get canceled, why does it not become noticeable in say millions of years.

 

[nDever]

Are you asking why the Earth doesn't move because of the impact of the asteroid? The momentum of the Earth and the asteroid during their gravitational attraction are equal, so upon impact, the Earth stops the asteroid (and most likely breaking it apart) and the asteroid stops earth. Remember too, that everything with mass attracts everything else with mass. The sun is responsible for holding all of the planets in their respective orbits. Above all, the Earth is still under the influence of the gravitation due to the sun.

 

[Michael C]

The Earth's velocity will change. We just need to know the mass and the impact speed of the meteorite to work out the change in momentum of the Earth. What size of meteorite are you thinking of?

 

[great_scott]

thank you for your responses. i always have some language barriers when it comes to talk to native english speakers about science or philosophy. i think that's why you guys thought i was talking about momentum. I am really sorry about that.
i know we all can easily prove why the Earth has to stay in its orbit by using the concepts, formulas and ideas of energy, momentum, gravitational field etc...
what i am exactly asking for is a free-body diagram in sense of forces when an asteroid impacts the Earth to see what force kills the force exerting on Earth by the asteroid so the Earth does not move. there doesn't have to be an impact. I am just making example of it to make my question obvious. ok I am going to try to make it more clear;
lets assume i get to one of those artificial satellites orbiting around the world and push it as hard as i can with my hand. we all would agree that the satellite will not move off its orbit. we can easily show that by using some formulation regarding energy, momentum... what i am asking is that when we try to analyze this system with the principles of and according to the dynamics but only dynamics, can you please tell me what opposite force cancels the force that i am exerting on the satelitte with my hand so it keeps orbitting in the same trajectory and not moving off at all? the answer and the explanation should contain only forces and should be regardless of energy or momentum or anything else. sorry for the language barrier but i think i can't make the question easier. thank you for your understanding

 

[great_scott]

Are you asking why the Earth doesn't move because of the impact of the asteroid? The momentum of the Earth and the asteroid during their gravitational attraction are equal, so upon impact, the Earth stops the asteroid (and most likely breaking it apart) and the asteroid stops earth. Remember too, that everything with mass attracts everything else with mass. The sun is responsible for holding all of the planets in their respective orbits. Above all, the Earth is still under the influence of the gravitation due to the sun.

lets say the asteroid had been pushed toward the Earth before it started moving toward the Earth so the Earth's gravitational force is not the only reason why the asteroid is about to hit the earth. i know your explanation with momenta will still aplly. but there will be a force on the Earth that will not be called forever unless another asteroid of the same size and speed hits the Earth through the opposite direction of the first asteroid. i just need to analyze using a free-body diagram I am repeating myself sorry

 

[Acid92]

Im not sure what youre asking for here but I used to find this sort of physical interaction somewhat counterintuitive because I used to take Newtons laws too abstractly instead of just visualizing and having a "feel" for it intuitively, and in the case of the third law, was mislead by how it was described.

When the asteroid collides with the Earth (action), the Earth will push simultaneously against the asteroid (reaction) as the asteroid pushes against the Earth but the Earths "reaction", i.e. its push, isn't independent of the asteroids push on the Earth, the actual interaction here (collision) is basically the two objects sort of "pushing against each other" but really fast and hard, this is Newtons third law. If the asteroids mass is much smaller than the Earths, its deceleration (caused by the Earths push on it) is much greater than the Earths acceleration (Newtons second law). If the Earths motion is not disturbed, its simply because the force exerted on it is too small compared to the mass of the Earth to have any directly notable effect, you could perhaps say that the Earths inertia here is relatively too large (Newtons first law).

I think you are thinking of forces too abstractly here, the force in your example is the two masses colliding against each other, if the asteroid decelerates to a velocity of 0 it is not pushing against the Earth anymore so why would it continue exerting a force (ignoring gravity here)? The asteroid or Earth can exert forces on each other only as long as theyre pushing against each other (again ignoring gravity).

I imagine an analogy of swinging a rope with a mass attached to it and somehow say a fly or something like that collides with it, the mass will exert a force on the fly and because of its very small mass, it will decelerate very quickly however the same but opposite force exerted on the mass here is relatively too small to have a notable effect on its motion.

 

[great_scott]

Im not sure what youre asking for here but I used to find this sort of physical interaction somewhat counterintuitive because I used to take Newtons laws too abstractly instead of just visualizing and having a "feel" for it intuitively, and in the case of the third law, was mislead by how it was described.

When the asteroid collides with the Earth (action), the Earth will push simultaneously against the asteroid (reaction) as the asteroid pushes against the Earth but the Earths "reaction", i.e. its push, isn't independent of the asteroids push on the Earth, the actual interaction here (collision) is basically the two objects sort of "pushing against each other" but really fast and hard, this is Newtons third law. If the asteroids mass is much smaller than the Earths, its deceleration (caused by the Earths push on it) is much greater than the Earths acceleration (Newtons second law). If the Earths motion is not disturbed, its simply because the force exerted on it is too small compared to the mass of the Earth to have any directly notable effect, you could perhaps say that the Earths inertia here is relatively too large (Newtons first law).

I think you are thinking of forces too abstractly here, the force in your example is the two masses colliding against each other, if the asteroid decelerates to a velocity of 0 it is not pushing against the Earth anymore so why would it continue exerting a force (ignoring gravity here)? The asteroid or Earth can exert forces on each other only as long as theyre pushing against each other (again ignoring gravity).

I imagine an analogy of swinging a rope with a mass attached to it and somehow say a fly or something like that collides with it, the mass will exert a force on the fly and because of its very small mass, it will decelerate very quickly however the same but opposite force exerted on the mass here is relatively too small to have a notable effect on its motion.

can you please tell me what is the minimum force to move the Earth off its orbit, doesn't matter what direction? there is no collision, no impacting, no touching but just a force acting on the Earth to move it off its orbit. I am sure you can easily calculate how much force is needed to do that. Let's name it F. now what happens when a force of (F-1) or (F/2) or anything smaller than F exerts on the earth? where is the opposite force to keep the equilibrium of forces. what force cancels the force F ? what creates an opposite force to kill F to keep the Earth in its orbit?

 

[Q_Goest]

can you please tell me what is the minimum force to move the Earth off its orbit,

Hi great_scott. Welcome to the board. What everyone is trying to say is that there is no minimum force. If a particle of dust impacts the earth, then to some excruciatingly small degree, the Earth's orbit will have changed. Every impact will change the Earth's orbit, no matter how large or small. For tiny specs of dust, we can't measure nor notice in billions of years any noticeable change simply because the change is so small. But there will be a change!

 

[Michael C]

Let's try an example. There's a tiny chance that asteroid 2006 JY26 could hit the Earth. What would be the change in velocity of the Earth if this happens?

According to this page, 2006 JY26 has a mass of about 5.2 x 10$^{5}$kg and could hit the atmosphere with a velocity of about 1.153 x 10$^{4}$m/s. That's 500 tonnes of stuff moving at about 34 times the speed of sound: for a mere human a huge and terrifying thing, but peanuts for the Earth:

The momentum of the asteroid would be 5.2 x 10$^{5}$ x 1.153 x 10$^{4}$ kg·m/s. That's about 6.0 x 10$^{9}$ kg·m/s.
The mass of the Earth is 5.97 x 10$^{24}$ kg, so if all that momentum gets transferred to the Earth the change in velocity of the Earth will be 6.0 x 10$^{9}$/(5.97 x 10$^{24}$) m/s. That's about 1.0 x 10$^{-15}$m/s.
If we move at 10$^{-15}$m/s, how far do we move in a year? There are 31 556 926 seconds in a year, so we'd move about 3 x 10$^{-8}$m in a year. In a million years, we'd move about 3 x 10$^{-2}$m.

So if I've got all my powers of 10 right, the impact of that asteroid would make a difference to the motion of the Earth of 3 centimetres in a million years.

 

[great_scott]

thank you all. it's so clear and satisfactory.