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Line 472: − If you are stating the moon varies its speed to maintain its relative velocity to the Earth, that is a new Heliocentric revelation I look forward to hearing about including how and why its speed varies. I'm not going to explain frame of reference anymore. Re-read my contribution as nothing has changed.+ − + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Talk:Geocentric theory (view source)
Revision as of 13:07, December 17, 2016
, 13:07, December 17, 2016replied to comment
:The moon's speed is constant in the ''earth's'' frame of reference. I.e. in the earth's frame of reference its speed is measured to be constant. In the sun's frame of reference it's apparent speed varies. In the sun's reference frame:
:The moon's speed is constant in the ''earth's'' frame of reference. I.e. in the earth's frame of reference its speed is measured to be constant. In the sun's frame of reference it's apparent speed varies. In the sun's reference frame:
At full moon: <math>v = 2,288 \text{MPH}</math>
At full moon: <math>v = \sqrt{(2,288 + 67000)^2} = 69288 \, \text{MPH}</math>
At first quarter <math>v = \sqrt{2288^2 + 67000^2} = 67039 \text{MPH}</math>
At first quarter <math>v = \sqrt{2288^2 + 67000^2} = 67039 \, \text{MPH}</math>
At new moon <math>v = \sqrt{(67000 - 2288)^2} = 64712 \text{MPH}</math>
At new moon <math>v = \sqrt{(67000 - 2288)^2} = 64712 \, \text{MPH}</math>
At last quarter <math>v = \sqrt{2288^2 + 67000^2} = 67039 \text{MPH}</math>
At last quarter <math>v = \sqrt{2288^2 + 67000^2} = 67039 \, \text{MPH}</math>
In the earth's frame of reference, the speed is always 2288 MPH. It's velocity does change as its direction changes. Yes in the sun's frame of reference, at new moon the moon does change direction and travel in the opposite direction to that at full moon. This can be seen in the video your reference.
In the earth's frame of reference, the speed is always 2288 MPH. It's velocity does change as its direction changes. Yes in the sun's frame of reference, at new moon the moon does change direction and travel in the opposite direction to that at full moon. This can be seen in the video your reference.
I should ask you the same thing. Why would you apply the same (wrong) equation to calculate the moon's velocity relative to the sun regardless of its direction of travel? I already provided that equation, show where it is incorrect. Also, you cannot just make up and misapply equations to explain away an inconsistency. I.E. you cannot apply the same equation to calculate a relative velocity for objects traveling in parallel directions as objects traveling in perpendicular / other directions to each other. This is completely inconsistent with relative motion theory, which I'm sure you will agree, needs to be applied consistently and at all times. Not selectively when it suits our theories.
I should ask you the same thing. Why would you apply the same (wrong) equation to calculate the moon's velocity relative to the sun regardless of its direction of travel? I already provided that equation, show where it is incorrect. Also, you cannot just make up and misapply equations to explain away an inconsistency. I.E. you cannot apply the same equation to calculate a relative velocity for objects traveling in parallel directions as objects traveling in perpendicular / other directions to each other. This is completely inconsistent with relative motion theory, which I'm sure you will agree, needs to be applied consistently and at all times. Not selectively when it suits our theories.
If you are stating the moon varies its speed to maintain its relative velocity to the Earth, that is a new Heliocentric revelation I look forward to hearing about including how and why its speed varies. I'm not going to explain frame of reference anymore. Re-read my contribution as nothing has changed.
For the moon to maintain the same relative velocity to the Earth's frame of reference while orbiting it, the moon's speed must vary wildly because the Earth is in motion. This consistently applies to ANY object orbiting another object in motion.
For the moon to maintain the same relative velocity to the Earth's frame of reference while orbiting it, the moon's speed must vary wildly because the Earth is in motion. This consistently applies to ANY object orbiting another object in motion.
I'll explain this here the way I do to my kids. Imagine the sun is an announcer tower in the center of a circular racetrack infield. There is a 1 mile wide track around it. You are in a Ford Earth in the center of that track driving around that track at 60 MPH. A Chevy moon is traveling 62.05 MPH, in the same direction, along side you on your right. That car would overtake you at a RELATIVE velocity of 2.05 MPH, or VERY slowly. It finally gets several hundred feet in front of you, and begins to turn left in a path that takes it in front of you. It travels across your path like a car crossing in front of you at an intersection. Taking on a path perpendicular to ours, it doesn't appear to travel at a slow relative velocity of 2.05 MPH anymore, instead the relative velocity we witness is 62.05 MPH - the same speed it was traveling relative to the tower when along side us. This is strictly because our frame of reference has changed. Both cars are still traveling the exact same respective speeds. As we continue on our same path, that car turns left again and heads toward us in the opposite direction of our travel. Now we are 2 cars passing each other head on. Our frame of reference has changed again. We observe a relative velocity of 122.05 MPH (Vac=Vbc+Vab.) It appears to travel 60X FASTER than when it passed us traveling in the same direction as ours. The car then turns left again after passing us and travels perpendicular to our direction of travel behind us. Again we see the 62.05 MPH velocity due to the perpendicular frame of reference. Finally it returns to its starting point, traveling the same direction as our car, once again creeping up beside us and passing us very slowly. Both cars maintain the same exact respective speeds, but due to our frame of reference, the relative velocity between our 2 car changes tremendously! Summary: The sun is an announcer stand in the middle of a racetrack infield. A Ford Earth is driving around the track and, simultaneously, a Chevy moon is driving circles around the Ford Earth. Both cars maintain their same respective speeds. The explanation above is what all passengers in the Ford Earth witness. This is as simply as I can explain this.
I'll explain this here the way I do to my kids. Imagine the sun is an announcer tower in the center of a circular racetrack infield. There is a 1 mile wide track around it. You are in a Ford Earth in the center of that track driving around that track at 60 MPH. A Chevy moon is traveling 62.05 MPH, in the same direction, along side you on your right. That car would overtake you at a RELATIVE velocity of 2.05 MPH, or VERY slowly. It finally gets several hundred feet in front of you, and begins to turn left in a path that takes it in front of you. It travels across your path like a car crossing in front of you at an intersection. Taking on a path perpendicular to ours, it doesn't appear to travel at a slow relative velocity of 2.05 MPH anymore, instead the relative velocity we witness is 62.05 MPH - the same speed it was traveling relative to the tower when along side us. This is strictly because our frame of reference has changed. Both cars are still traveling the exact same respective speeds. As we continue on our same path, that car turns left again and heads toward us in the opposite direction of our travel. Now we are 2 cars passing each other head on. Our frame of reference has changed again. We observe a relative velocity of 122.05 MPH (Vac=Vbc+Vab.) It appears to travel 60X FASTER than when it passed us traveling in the same direction as ours. The car then turns left again after passing us and travels perpendicular to our direction of travel behind us. Again we see the 62.05 MPH velocity due to the perpendicular frame of reference. Finally it returns to its starting point, traveling the same direction as our car, once again creeping up beside us and passing us very slowly. Both cars maintain the same exact respective speeds, but due to our frame of reference, the relative velocity between our 2 car changes tremendously! Summary: The sun is an announcer stand in the middle of a racetrack infield. A Ford Earth is driving around the track and, simultaneously, a Chevy moon is driving circles around the Ford Earth. Both cars maintain their same respective speeds. The explanation above is what all passengers in the Ford Earth witness. This is as simply as I can explain this. (Unsigned by JasonZ)
I've noticed a mistake in my previous comment regarding the speed of the full moon, I think that is what you're talking about when you are saying I'm not being consistent. I shall correct that now.
OK, since this discussion is probably going to go on for a while, can we please agree to use speed and velocity correctly as it otherwise gets confusing and ensure we state explicitly what frame of reference we are talking about in each sentence.
The reason we are disagreeing is that you are saying the moon's speed is constant in the '''sun's''' frame of reference whereas I am saying is is constant in the '''earth's''' frame of reference. If the transverse component was not constant in '''earth's''' frame of reference (as you suggest), then it's transverse acceleration would be non-zero. It would not therefore follow a circular orbit as seen from earth as circular motion requires acceleration to be entirely radial. Hence its speed in earth's frame of reference must be constant.
The formulae don't really mean a lot at the moment, I wrote them down and then forgot where I was going. Doing physics on Friday evening after a long day can be hard.
So I'll explain the formulae, plug in some numbers and see what happens.
<math>\vec{r}_m(t)</math> describes the position of the moon as seen in the earth's frame of reference. This is simply the parameterisation of a circle as we are assuming the orbit of the moon as seen from the earth is circular. Differentiating gives us the velocity, <math>\dot{\vec{r}}_m(t)</math>. As you can see the velocity of the moon varies in the earth's frame of reference, but its speed (the magnitude of velocity) is constant.
<math>\vec{r}_e(t)</math> describes the position of the earth as seen in the sun's frame of reference. Again this is just the parameterisation of a circle as we are assuming the orbit of the earth as seen from the sun is circular.
<math>\vec{r}(t)</math> is the position of the moon as seen as the sun's frame of reference. It is simply the addition of the two previous vectors,
<math>\vec{r}(t) = \vec{r}_m(t) + \vec{r}_e(t)</math>
Let's plug in some numbers:
Angular speed of earth is:
<math>\omega_e = \frac{2 \pi}{T_e} = 1.99 \times 10^{-7} \; \text{rad} \, \text{s}^{-1}</math>
where <math>T_e</math> is the time period of the earth (1 year)
Angular speed of the moon is:
<math>\omega_m = \frac{2 \pi}{T_m} = 2.66 \times 10^{-6} \; \text{rad} \, \text{s}^{-1}</math>
where <math>T_m</math> is the time period of the earth (27.3217 days)<ref>http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html</ref>. Also note it states the moon's speed relative to earth varies between 2407 MPH and 2156 MPH, nowhere near the range that you are calculating.
Earth-moon distance is <math>3.844 \times 10^8 \, \text{m}</math>
Earth-sun distance is <math>1.496 \times 10^11 \, \text{m}</math>
We can change the sign of the sin and cos components of <math>\vec{r}_m(t)</math> and swapping them to change where the moon is as seen from earth at time = 0, i.e. make it full moon, new moon etc. at t=0. This means we just need to put in t=0 into <math>|\dot{\vec{r}}(t)|</math> to get the moon's speed in the sun's frame of reference. This gives us:
For new moon at t = 0:
<math>\vec{r}_m(t) = - a_m \cos{\omega_m t} \, \vec{i} - a_m \sin{\omega_m t} \, \vec{j}</math>
For first quarter at t = 0:
<math>\vec{r}_m(t) = a_m \sin{\omega_m t} \, \vec{i} - a_m \cos{\omega_m t} \, \vec{j}</math>
For full moon at t = 0:
<math>\vec{r}_m(t) = a_m \cos{\omega_m t} \, \vec{i} + a_m \sin{\omega_m t} \, \vec{j}</math>
For last quarter at t = 0:
<math>\vec{r}_m(t) = a_m \sin{\omega_m t} \, \vec{i} + a_m \cos{\omega_m t} \, \vec{j}</math>
This gives us the velocity of the moon as observed in the sun;s reference frame as:
For new moon at t = 0:
<math>\dot{\vec{r}}(t) = (-a_e \omega_e \sin{\omega_e t} +a_m \omega_m \sin{\omega_m t}) \, \vec{i} +(a_e \omega_e \cos{\omega_e t} -a_m \omega_m \cos{\omega_m t}) \, \vec{j}</math>.
This gives a speed of 64140 MPH.
For first quarter at t = 0:
<math>\dot{\vec{r}}(t) = (-a_e \omega_e \sin{\omega_e t} + a_m \omega_m \cos{\omega_m t}) \, \vec{i} +(a_e \omega_e \cos{\omega_e t} +a_m \omega_m \sin{\omega_m t}) \, \vec{j}</math>.
This gives a speed of 66666 MPH.
For full moon at t = 0:
<math>\dot{\vec{r}}(t) = (-a_e \omega_e \sin{\omega_e t} -a_m \omega_m \sin{\omega_m t}) \, \vec{i} +(a_e \omega_e \cos{\omega_e t} +a_m \omega_m \cos{\omega_m t}) \, \vec{j}</math>.
This gives a speed of 68916 MPH.
For last quarter at t = 0:
<math>\dot{\vec{r}}(t) = (-a_e \omega_e \sin{\omega_e t} +a_m \omega_m \cos{\omega_m t}) \, \vec{i} +(a_e \omega_e \cos{\omega_e t} -a_m \omega_m \sin{\omega_m t}) \, \vec{j}</math>.
This gives a speed of 66666 MPH.
As you can see, these more or less agree with what I'm saying in that the speed of the moon as observed in the sun's reference frame doesn't change anywhere near as much as you are suggesting.
In short, we disagree because you think the speed of the moon is constant in the sun's frame of reference, and I believe it is constant in the earth's frame of reference.
Questions:
# Why do you believe the moons speed to be constant in the sun's frame of reference and calculate it at full moon, and not say new moon. Can you reference somewhere that states the speed of the moon as measured in the sun's reference frame is constant?
# You talk about one of my equations being wrong, which one is it? (it might be that mistake with speed at full moon that I made and should have corrected)
# Also could you say why my energy argument is wrong, you haven't responded to that. [[User:PeterIceHockey|PeterIceHockey]] ([[User talk:PeterIceHockey|talk]]) 08:07, 17 December 2016 (EST)
==References==
==References==