Deriving Equations for Moon's Orbital Acceleration

In summary, the conversation discusses the need for help in deriving equations for the moon's acceleration around the earth. The person has already found the total acceleration and needs to split it into its x and y components. They have proposed equations for ax and ay but are struggling with deriving T. They have been advised not to double post and to refer to a thread on Physics Forums for help.
  • #1
neo32
5
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Hello, I need help on deriving a equations for the moon's acceleration around the earth. I've already found the total acceleration (a=Gm/r^2) but what i need to do is split this acceleration up into its x and y components, and derive equations in terms of a, r, x, and/or y for any given position in the moon's orbital path

So far I have ax = a*cos(T) and ay = a*sin(T) where T is the angle from the x-axis. What I'm having trouble with is deriving T. If those are wrong to begin with, can someone put me on the right track? Thanks!
 
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  • #2

1. What is the Moon's orbital acceleration?

The Moon's orbital acceleration is the rate at which the Moon's speed and direction of motion changes as it orbits around the Earth.

2. What causes the Moon's orbital acceleration?

The Moon's orbital acceleration is primarily caused by the gravitational pull of the Earth. However, other factors such as the Sun's gravity and the Earth's rotation also contribute to the Moon's acceleration.

3. How is the Moon's orbital acceleration measured?

The Moon's orbital acceleration is measured using a unit called meters per second squared (m/s^2). This unit represents the change in velocity (speed and direction) of the Moon over time.

4. How does the Moon's orbital acceleration affect tides on Earth?

The Moon's orbital acceleration directly affects the tides on Earth. As the Moon's gravity pulls on the Earth's oceans, it causes them to bulge and create high and low tides. The strength and direction of the Moon's acceleration can impact the size and timing of these tides.

5. Is the Moon's orbital acceleration constant?

No, the Moon's orbital acceleration is not constant. It can vary due to a number of factors, including the position of the Moon and Earth in their orbits, the influence of other celestial bodies, and the effects of tidal friction. However, over long periods of time, the average rate of the Moon's acceleration remains relatively constant.

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