How much did Earth's gravity alter the course of 2005 YU55?

[2milehi]

Just like the title says - with the meteor passing close by the Earth, gravity should alter the meteor's course. So how much was it?

 

[DaveC426913]

Earth: 5x10^24kg
Aircraft carrier: 7x10^7kg
Separation:300,000,000m

http://www.wsanford.com/~wsanford/calculators/gravity-calculator.html

 

[2milehi]

Earth: 5x10^24kg
Aircraft carrier: 7x10^7kg
Separation:300,000,000m

http://www.wsanford.com/~wsanford/calculators/gravity-calculator.html

That wasn't my question. As the meteor passed by Earth there was a varible force that acted on the meteor. This force would alter the trajectory of the meteor. Was it a degree, an arcminute, an arcsecond?

 

[berkeman]

That wasn't my question. As the meteor passed by Earth there was a varible force that acted on the meteor. This force would alter the trajectory of the meteor. Was it a degree, an arcminute, an arcsecond?

Dave was giving you a way to calculate the sideways force on the object. Do you know how long the object was within the orbit of the moon? You could get a pretty good approximation for how much the trajectory was altered by applying the average gravitational attraction of the Earth on the object in a perpendicular direction for the duration of the time inside the Moon's orbit.

 

[tony873004]

Earth boosted 2005YU55's semimajor axis by about 2 million km. It reduced its inclination from about a half a degree to about a third of a degree.

In this image, the green orbit is 2005 YU55. The interior one is before, the exterior one is after.

 

[2milehi]

Thank you for answering my question. :-)

 

[Grizzled]

Actually, the question is quite a bit misguided.

The trajectory remain the same as it ever was - all gravitational perturbations included.

Look at it as an object traveling in a perfectly straight line tnrough some very uneven surface (gravity wells of Earth, Sun, Moon...). The object still rolls/flies in a straght line... But the line is warped.

 

[Grizzled]

To continue: Even if you fall back on the classical/Newtonian physics the question still doesn't make sense. "changed" compared to what? To what it would be in the Earth's absence? But... hold on a sec, in Earth's absence that asteroid wouldn't even arrive here in the first place - Earth's gravitational pull is part of the reason that asteroid got where it was anyway.

 

[2milehi]

Tony understood my question. Griz you are not adding anything to my question. I will expand to clear any confusion - what was the change in the orbital characteristics of 2005 YU55 when it recently passed by Earth.

This gif makes a lot more sense when comparing it to
Tony's pic
[PLAIN]http://upload.wikimedia.org/wikipedia/en/c/c5/2005_YU55_approach_8-9_November_2011.gif [Broken]

 

[Grizzled]

Well, perhaps I misunderstood your question. (I'm actually inclined to think so).

But the basic fact remains that the question "how much did the Earth gravity changed the course of that asteroid" is pretty much meaningless. It didn't. In any shape, size or form UNLESS you mean how it shaped the course from the start, to begin with. But then... the question about "change" is once again a bit odd.

 

[2milehi]

Well, perhaps I misunderstood your question. (I'm actually inclined to think so).

But the basic fact remains that the question "how much did the Earth gravity changed the course of that asteroid" is pretty much meaningless. It didn't. In any shape, size or form UNLESS you mean how it shaped the course from the start, to begin with. But then... the question about "change" is once again a bit odd.

Change - like before and after. Tell me that you don't see it with the following image.

The meteor was "sling-shot" when passing by Earth. Space probes use Jupiter to "sling-shot" to add speed and change direction.

 

[Grizzled]

What -I- don't see is how this pretty picture indicates a changed orbit.

What -you- don't see is the fact that orbits are never the same perfect ellipses. Doesn't happen.

So, what your picture shows is just a normsl, pretty ordinary orbit.

Perhaps you should make distinction between the words course/trajectory/orbit?

 

[2milehi]

Earth boosted 2005YU55's semimajor axis by about 2 million km. It reduced its inclination from about a half a degree to about a third of a degree.

In this image, the green orbit is 2005 YU55. The interior one is before, the exterior one is after.

Griz maybe you missed this post. The inside green circle represents the orbital characteristics of the meteor before it was "sling-shot" by Earth. The outer green circle represents the new orbital characteristics of the meteor. The Earth change the direction and the speed of the meteor via gravitational attraction.

It seems you are going out of your way NOT to understand what I am asking/saying.

 

[Drakkith]

Grizzled, I'm sure your technically correct, but I think you're simply confusing some people. Suffice it to say I think the OP's question was answered by the picture.

 

[Grizzled]

Drakkith,

I can't help it if some people are so easily confused. Perhaps they should study a bit?

I also can't help it if all they want are some pretty pictures which they (for some mysterious reason) insist on posting over and over again.

At least you agree that I am "technically" correct.

Thanks.

 

[Drakkith]

Drakkith,

I can't help it if some people are so easily confused. Perhaps they should study a bit?

Why do you think they are here at PF if not to study and learn? EVERYONE is easily confused when they know very little about something. Just because you know more about the subject does not give you a reason to be rude. Instead it might help if you explained what the different terms mean for this particular scenario.

I also can't help it if all they want are some pretty pictures which they (for some mysterious reason) insist on posting over and over again.

There is nothing wrong with pictures and diagrams. They help people to visualize a concept, which is very important for most people when attempting to learn something new.

 

[DaveC426913]

Drakkith,

I can't help it if some people are so easily confused.

You can. You can address the question asked.

I also can't help it if all they want are some pretty pictures which they (for some mysterious reason) insist on posting over and over again.

If pretty pictures answer the question asked then pretty pictures are the thing.

At least you agree that I am "technically" correct.

I am "technically" correct when I mention that Mercury precesses. The issue, of course, is whether that answers the question being asked.


The OP's is a legitimate question. He wants to know how much YU 55 was deflected by Earth's passage. consider: if you were stationary wrt the asteroid and looked in the direction of its travel, you'd see a point it's heading toward. If Earth had not crossed its path that point would move steadily as the asteroid proceeded in its orbit. After Earth fly-by the point would be completely different.

Does that make it clearer to you what the OP is asking?

 

[2milehi]

Perhaps you should make distinction between the words course/trajectory/orbit?

First I never said orbit. I used the words course and trajectory.

course n. - The route or path taken by something, such as a stream, that moves.

trajectory n. - The path of a projectile or other moving body through space.

I used orbital characteristics to clear any confusion that you had.

orbital characteristics n. - a table of values that gives the positions of astronomical objects in the sky at a given time (see ephemeris).

synonym n. -
1. A word having the same or nearly the same meaning as another word or other words in a language.
2. A word or an expression that serves as a figurative or symbolic substitute for another.

Griz if you can't see how course/trajectory relates to my question, you are thick. Everyone else seems to understand me.

What -you- don't see is the fact that orbits are never the same perfect ellipses. Doesn't happen.

I never said that orbits are consistent perfect ellipses.

Drakkith,

I can't help it if some people are so easily confused. Perhaps they should study a bit?

I also can't help it if all they want are some pretty pictures which they (for some mysterious reason) insist on posting over and over again.

At least you agree that I am "technically" correct.

Thanks.

Now you are acting arrogant and being sarcastic (humor for the small mind). Please quit posting, you are removing value from this topic.

 

[DaveC426913]

Or to put it another way...

Look at it as an object traveling in a perfectly straight line tnrough some very uneven surface (gravity wells of Earth, Sun, Moon...). The object still rolls/flies in a straght line... But the line is warped.

Fine. How much did Earth warp the straight line?

 

[WhittyMike]

Perhaps I'm reading too much into the (nicely done) diagram showing the before-and-after orbits of 2005 YU55, but: does it look like the shifted orbit will now make a collision with Mars more likely?

 

[DaveC426913]

Perhaps I'm reading too much into the (nicely done) diagram showing the before-and-after orbits of 2005 YU55, but: does it look like the shifted orbit will now make a collision with Mars more likely?

You're definitely reading too much into it.

The very fact that the orbit as shown is smooth and curvilinear is a strong indication that YU55 is pretty much never near Mars in its orbit. Space is very big and orbiting bodies very small.

Furthermore, as it stands, YU55 is no more in Mars' gravity well than it was before.

 

[2milehi]

With the "before" orbit of YU55, there would be zero chance of the asteroid colliding with Mars since it never crosses Mars' orbit. With the "after" orbit of YU55, there are two times that the asteroid crosses Mars' orbit. This has to increase the chance of a collision between the two bodies with all things remaining the same. I assume that YU55 and Mars are on the same orbital plane.

 

[DaveC426913]

With the "before" orbit of YU55, there would be zero chance of the asteroid colliding with Mars since it never crosses Mars' orbit. With the "after" orbit of YU55, there are two times that the asteroid crosses Mars' orbit. This has to increase the chance of a collision between the two bodies with all things remaining the same. I assume that YU55 and Mars are on the same orbital plane.

But Mars is not a billiard ball floating in space. It is a gravity well, much larger than its physical size. Before Earth fly-by, if Mars had been in just the right spot in its orbit, YU55 would have passed through its gravity well. After Earth fly-by, if Mars were in just the right spot, YU55 would pass through it gravity well.

i.e. Not a lot has changed.

And since its interacting with the gravity well, not the body, it would not collide with Mars, it would have a close encounter, altering its orbit, just as with Earth, sending it off on a another trajectory, perhaps never to bother Mars again.

 

[Janus]

To continue: Even if you fall back on the classical/Newtonian physics the question still doesn't make sense. "changed" compared to what? To what it would be in the Earth's absence? But... hold on a sec, in Earth's absence that asteroid wouldn't even arrive here in the first place - Earth's gravitational pull is part of the reason that asteroid got where it was anyway.

Generally speaking, such a question does make sense. Outside of a certain distance from the Earth, the Sun's gravity dominates the object's trajectory and the Earth's effect can pretty much be ignored for all practical purposes.

This radius defines what is called the "gravitational sphere of influence" of the Earth. It was calculated by Laplace to be:

$$rp = \sqrt[5] {\frac{M_p}{M_s}}^2$$

And for the Earth, works out to being about 927,000 km.

So when we talk about how much the Earth deflects something like 2005 YU55, we are talking about how much its path changes from the time it enters the sphere of influence until it leaves.

You can find the angle of deflection (relative to the Earth) with the formula:

$$b = \frac{GM_e}{v^2} \cot q$$

Here b is the impact parameter, or the closest approach to the Earth the object would have had if it had traveled on a straight line through the sphere of influence.
v is the relative velocity between Earth and object.
and
q is the deflection angle.

Thus
The process would go something like this:

From the Earth's and object's motions relative to the Sun, transform to the object's motion relative to the Earth.

Use the formula above to determine the deflection angle and new trajectory relative to the Earth.

Using the new Earth relative motion, transform back to a Sun relative frame, giving you the new trajectory of the object relative to the Sun.

 

[tony873004]

I assume that YU55 and Mars are on the same orbital plane.

They're close, but not exact, and that translates into lots of km of separation along the z-axis. Although the Earth passage raised YU55's SMA by about 2 million km, it also reduced its inclination. At the point where Mars and YU55's orbits appear to intersect, Mars' orbit is 7.7 million km above the ecliptic. Before the Earth passage, YU55 was about 2.2 million km above the ecliptic at that point. Afterwards, it is about 1.5 million km above the ecliptic, distancing itself from Mars along the z-axis.

In either case, their orbits don't actually intersect. As time goes on, the longitude of perihelion precesses for both objects. Such change is usually measured in arcseconds per century. So from time to time, their orbits can intersect in the very distant future. Since Mars is near aphelion at appearant point of intersection in the image, even without an Earth encounter a change in their longitude of perihelions could still cause their orbits to intersect.

Even if they did line up such that their orbits perfectly intersected, chance of a collision is very low. Mars is very small compared to the size of its orbit. Each time YU55 perfectly crossed Mars' orbit, it would stand about a 1 in 150,000 chance that Mars would be there at that moment.