Tangential Velocity and the Moon

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Discussion Overview

The discussion centers on the concept of tangential velocity and its role in explaining why the Moon does not fall directly into the Earth. Participants explore theoretical models and analogies related to gravitational forces and orbital motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about why the Moon doesn't fall straight into the Earth, seeking clarification on the concept of tangential velocity.
  • Another participant describes a hypothetical scenario where the Moon moves left while being pulled toward the Earth, suggesting that its forward motion allows it to avoid falling directly into the Earth.
  • Several participants explain that the Moon is continuously falling toward the Earth but maintains a forward motion that results in an orbital path, using the analogy of Newton's cannon to illustrate this concept.
  • One participant questions whether the required muzzle velocity for a cannonball to achieve orbit (e.g., 1000 m/s) can be equated to tangential velocity.
  • A further analogy is presented involving throwing a rock off a cliff, emphasizing that while gravity pulls the rock downward, its initial forward velocity causes it to "miss" the ground, paralleling the Moon's motion.

Areas of Agreement / Disagreement

Participants generally agree on the idea that the Moon is in a state of perpetual free fall towards the Earth while maintaining a tangential velocity that results in an orbit. However, the precise definitions and implications of tangential velocity remain a topic of exploration and clarification.

Contextual Notes

Participants discuss various models and analogies without reaching a consensus on the definitions or implications of tangential velocity in relation to orbital mechanics.

Who May Find This Useful

This discussion may be of interest to individuals studying gravitational physics, orbital mechanics, or those seeking to understand the dynamics of celestial bodies in motion.

AbsoluteZer0
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Hi,

I've been doing a bit of independent study on Gravitation. What I find confusing is why the moon doesn't fall straight into the earth. I know that the moon has tangential velocity, but what exactly is tangential velocity? How does it apply to the moon not falling into the earth?

Thanks,
 
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https://www.physicsforums.com/showthread.php?t=89113

Or, to put it another way,

Let's take the hypothetical situation where the Moon is moving to the "left", being pulled towards the Earth, which is "behind" it.

The Moon will move forward (attraction towards the Earth), but by the time it's done that, it's gone significantly to the left, and the direction of attraction's changed.

And we're faced with exactly the same situation.
 
AbsoluteZer0 said:
How does it apply to the moon not falling into the earth?
The Moon is falling toward the Earth. Perpetually.

One way to envision orbits is via Newton's cannon. Imagine a very tall mountain, one so tall it rises out of the atmosphere. Now imagine a very powerful cannon atop this mountain. The muzzle velocity of the cannonball depends on the amount of shot put into the cannon.

Put just a little shot in the cannon and the cannonball will fall to Earth along what appears to be a parabolic trajectory. Add a bit more shot and the cannonball will still fall to Earth, but with ever more shot it becomes obvious that this parabolic trajectory is but an approximation. A better model is a segment of an ellipse.

The cannonball hits the Earth further and further from the mountain as the muzzle velocity increases. With just the right muzzle velocity, the cannonball will hit the Earth at a point diametrically opposed to the mountain. Now what happens if you add just a bit more shot to the cannon? The answer is that the cannonball will go all the way around the Earth. If the cannon is moved out of the way in the ~90 minutes it takes for the cannonball to go around the Earth, it will keep following this path forever. The cannonball is in orbit about the Earth.
 
D H said:
The Moon is falling toward the Earth. Perpetually.

One way to envision orbits is via Newton's cannon. Imagine a very tall mountain, one so tall it rises out of the atmosphere. Now imagine a very powerful cannon atop this mountain. The muzzle velocity of the cannonball depends on the amount of shot put into the cannon.

Put just a little shot in the cannon and the cannonball will fall to Earth along what appears to be a parabolic trajectory. Add a bit more shot and the cannonball will still fall to Earth, but with ever more shot it becomes obvious that this parabolic trajectory is but an approximation. A better model is a segment of an ellipse.

The cannonball hits the Earth further and further from the mountain as the muzzle velocity increases. With just the right muzzle velocity, the cannonball will hit the Earth at a point diametrically opposed to the mountain. Now what happens if you add just a bit more shot to the cannon? The answer is that the cannonball will go all the way around the Earth. If the cannon is moved out of the way in the ~90 minutes it takes for the cannonball to go around the Earth, it will keep following this path forever. The cannonball is in orbit about the Earth.

So, hypothetically, if the cannonball needs to be shot at 1000 m/s to start orbiting the Earth then 1000 m/s is the tangential velocity?
 
Imagine standing on a cliff, say 10 feet back from the edge, and throwing a rock over the edge. From the time the rock leaves your hand, the only force acting on the rock is gravity which acts straight down. But the rock does not go straight down- the downwar force causes an acceleration downward which then causes motion downward. But all this time the rock is moving forward due to the forward velocity you gave. The rock does go downward, of course, but not until after it has "missed" the edge of the cliff.

The same thing happens with the moon (or any satellite)- it is pulled downward but with the additional forward motion, the moon just keeps "missing" the earth.
 

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