> explain WHY you want to know this.
Because I want to know if it can be done apart from vectors.
> Why, exactly, do you think you need to know the "speed through space" (whatever that means)
A plane moving through a crosswind has a forward velocity and a "true" (through space) velocity when the crosswind is taken into account.
> And why did you pick those numbers?
Because 3 and 5 are less likely to be miscalculated. 300 and 500 were more realistic.
> then a delay of a week do the work asked of you.
Do the W O R K ? ? ? W. T. F.
There's no work for you to do ! ! ! !
Just tell me the method or equation.
By the way, does the moon move in a helix or does it move with the earth's orbit and then against the earth's orbit ?
Permit me to make something clear RIGHT FROM THE START.
If it doesn't apply to you, all the better.
Over the years, innumerable people have asked questions of me in a completely disingenuous manner -- they pretend to want to know something, when all they just really want is a lead-in to an argument with me. If this is the game you're trying to play, I DON'T WANT TO JOIN. If you plan to reply to my answer with anything along the lines of, "That's not correct" -- in other words, if you already have an opinion on this question and are just searching for my opinion -- my immediate response will be to click on the button stating, "This is one follow-up too many."
I hope this makes myself clear.
> There's no work for you to do !
> Just tell me the method or equation.
There ISN'T a simple equation or method. There's a lot of work for me to do to explain the situation -- which I'm perfectly willing to do, even if it's a lot of work on my part.
> A plane moving through a crosswind has a forward velocity
> and a "true" (through space) velocity
First thing to know about velocities: there is NEVER such a thing as a "true" velocity. There are only velocities relative to another frame. If you drop an object while flying in a plane with a constant air speed of 250 meters per second, the object goes straight downward with an acceleration of about 9.8 m/sec^2 RELATIVE TO THE PLANE. It also move horizontally at 250 meters per second RELATIVE TO the surface of our Earth. The object also has a velocity as our Earth revolves on its axis, as our Earth goes around our Sun, as our Sun goes around the center of the Milky Way Galaxy, as that galaxy moves towards the Andromeda Galaxy within our Local Cluster, and as our Local Cluster moves towards the Great Attractor. So, unless one defines a certain frame as the "true" one, there is no "true velocity."
From your question, however, I think I can safely conclude you're interested in the speed of our Moon relative to the frame of our Sun. If that is indeed the case, we can look at our Moon's speed as a constant (our Earth's speed, relative to our Sun) plus an harmonic motion (the speed added to, or subtracted from, our Earth's speed) of our Moon as it goes around our Earth. We will ignore the fact that neither speed is a constant, as both orbits are elliptical. Just so you know, the speed of our Earth (relative to our Sun) is about 30 km/sec, and the Moon speed (relative to our Earth) is about 1 km/sec.
For starters, imagine a plane going a constant 30 meters per second RELATIVE TO the surface of our Earth, and inside is someone spinning a ball around his head,
with an orbital speed of 1 meter per second, RELATIVE TO THAT PERSON.
I hope you agree that, on each revolution of the ball around the person, the ball is sometimes moving in the SAME direction as the plane, sometimes in the OPPOSITE direction to the motion of the plane, and sometimes at right angles to the motion of the plane (in all cases, this motion is considered to be relative to surface of our Earth). If you can't see this, then this is as far as I can take you.
When the ball is moving in the same direction as the plane's motion, its speed RELATIVE TO THE SURFACE OF OUR EARTH is 31 meters per second (ie, 30 m/sec for the plane motion, plus 1 m/sec for the ball's motion relative to the plane). In the same way, when the ball is moving in the direction OPPOSITE to the motion of the plane, its speed relative to the surface of our Earth is 29 meters per second. Again, if you can't see this, I can't help you any further.
One last thing: when the ball's motion is at right angles to the motion of the plane, its speed relative to the plane is neither added nor subtracted to its speed relative to our Earth's surface. At that instant, its speed is identical to that of the plane.
Now, instead of a ball moving at 1 m/sec within a plane going 30 m/sec relative to the surface of our Earth, let's look at our Moon, moving around us with an orbital velocity of 1 km/sec, while our Earth goes around our Sun with an orbital velocity of 30 km/sec. Again, once a lunar month (ie, once a "Moon"), our Moon is moving in the same direction as that of our Earth; once a lunar month, it's moving in the opposite direction. Once a lunar month, it's in front of the motion of our Earth; once a lunar month, it's behind that motion. In both of the latter cases, our Moon's motion is at right angles to the motion of our Earth. And thus, just like the case of the ball going around a person inside a plane moving at 30 meters per second, the speed of our Moon (relative to our Sun) is the same as the speed of our Earth.
It's possible to get a mathematical formula for the speed of our Moon relative to our Sun. If we define Ɵ as the directional angle of our Moon as it moves around our Earth, as viewed by someone looking down from a pole
and the zero point for Ɵ as being the direction of our Earth's movement (in this diagram, the point of Ɵ=0 is at the point of the first quarter), then the speed of our Moon RELATIVE TO OUR SUN is given by
30 km/sec + (1 km/sec)(sin[Ɵ])
Once a lunar month, the speed will be 31 km/sec (full moon); once a lunar month, 29 km/sec (new moon); and twice a lunar month (when Ɵ=0 and when Ɵ=180) it will be 30_km/sec.
I note that Ɵ will change its direction, relative to our Sun, as our Earth goes around our Sun; however, the speed of our Moon, relative to our Sun, will depend only on Ɵ.
> does the moon move in a helix or does it move with the earth's orbit
> and then against the earth's orbit?
An object can only move in a helix if it has a vertical motion relative to its orbital motion. There is no significant motion in the vertical motion of our Moon, relative to our Sun.
A simplified view of the position of our Moon, relative to our Sun, is given in this sketch:
where our Moon goes from being closer to our Sun, then further away, about twelve times per orbit of our Earth around our Sun -- ie, about twelve times per year. Note that this sketch-
1) incorrectly shows fourteen such events per year.
2) VASTLY exaggerates the distances involved.
3) incorrectly shows our Moon returning to the same spot each year.
One lunar month is 29.53 days; one solar year is 365.24 days. Thus, there are 12.37 events of "closest to our Sun" and "furthest from our Sun" each solar year.
A mathematical description of the exact location of our Moon, relative to our Sun, is do-able, but is best done with vector notation. There is no simplification in this formula by not using vectors; as vector notation is BY FAR the easiest way to do this.