# Orbital generated inertia, does it exist?

#### BdS

Registered Senior Member
The Moon wants to travel in a straight line but the Earth always forces it in a circular orbit path. By the Moon being forced to change direction is there an inertial force being generated on the Moon?

The Moon wants to travel in a straight line but the Earth always forces it in a circular orbit path. By the Moon being forced to change direction is there an inertial force being generated on the Moon?
No. The Moon would want to travel in a straight line if the Earth were not there.

With the Earth there, the Moon naturally wants to fall toward it, like any thrown rock does. But the Moon has been "thrown" so fast that it keeps missing the Earth. The Moon is in free-fall.

The Moon would want to travel in a straight line if the Earth were not there.

If earth disapeared the moon woud be a planet that rotates ever 28 days an orbit the sun.!!!

If earth disapeared the moon woud be a planet that rotates ever 28 days an orbit the sun.!!!

Not necessary. The orbital motion around sun is that of Earth-Moon COM which is closer to earth.

Edit: so if earth were to disappear, the present position and motion of moon may require some change for it to continue orbiting the sun.

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If earth disapeared the moon woud be a planet that rotates ever 28 days an orbit the sun.!!!
Well, technically correct. But we are not concerning ourselves with the larger picture. Let's assume we are in a frame of reference of the Earth-Moon system.

With the Earth there, the Moon naturally wants to fall toward it, like any thrown rock does. But the Moon has been "thrown" so fast that it keeps missing the Earth. The Moon is in free-fall.
Yes, but is there an inertial effect on the moon when it is constantly changing direction to follow the orbit path?
Maybe its why the moon is moving away from the earth.

Yes, but is there an inertial effect on the moon when it is constantly changing direction to follow the orbit path?
Maybe its why the moon is moving away from the earth.

My limited understanding of any ' inertial effect ' would only apply if a force was trying to push the Moon faster in the direction it was traveling

Other than Earth gravity I am unaware of any other major force acting on the Moon

From memory the Moon is moving away from Earth at about 4 cm a year

I do recall reading about gravity is slowly getting weaker due to the expansion of the Universe causing a dilution of overall density

With a weaker Earth gravity and Universe dilution seems to be a means by which the Moon would move further out

Yes, but is there an inertial effect on the moon when it is constantly changing direction to follow the orbit path?
Not sure what you mean. The moon has inertia, which classically means that it has mass. To change the direction or speed of an inertial mass take a force. Classically speaking the force of gravity is changing direction of the moon resulting in it's orbit.
Maybe its why the moon is moving away from the earth.
The primary reason that the moon is moving farther from earth is because tides. The bulge in the oceans is not directly underneath the moon, it is pulled ahead by the earths rotation. Overall this tends to slow the earth rotation and to push the moon to a higher orbit.

I do recall reading about gravity is slowly getting weaker due to the expansion of the Universe causing a dilution of overall density
The density of energy is going down as the universe expands. So on average you could say the 'density' of gravity is going down. But no one in the ball park of the main stream thinks that the gravity of 1 kg of mass is decreasing over time.
With a weaker Earth gravity and Universe dilution seems to be a means by which the Moon would move further out
The gravitational field of the earth is not getting weaker so that cannot be the reason.

Yes, but is there an inertial effect on the moon when it is constantly changing direction to follow the orbit path?
Maybe its why the moon is moving away from the earth.
As already pointed out, we already know why the Moon is receding, and this is due to an interaction known as tidal acceleration. Such a situation will occur anytime you have a satellite which orbits with a period longer than what it take for the planet to rotate and doesn't orbit retrograde to the planet. If the satellite orbits faster than the planet rotates, or retrograde to the planet's rotation, the results are the opposite and it will slowly fall in towards the planet. One example of this is Phobos, a moon of Mars, which orbits faster than Mars rotates and is in a slow "death spiral" around the planet.

BdS
The density of energy is going down as the universe expands. So on average you could say the 'density' of gravity is going down. But no one in the ball park of the main stream thinks that the gravity of 1 kg of mass is decreasing over time.

The gravitational field of the earth is not getting weaker so that cannot be the reason.

As I said my limited knowledge in this field is limited so I am happy to go with the flow and not thrash about looking for post which state gravity is getting weaker

I will continue to follow relevant papers and let my two neurones decide what I should think

If earth disapeared the moon woud be a planet that rotates ever 28 days an orbit the sun.!!!
If the gravity of the Earth disappeared, the Moon would still be in an elliptical orbit about the Sun.
Assuming they are circles in the same plane, the speed of the moon in Earth orbit is about 2 π r / T = 1 km/s, and the speed of the earth about the sun is 30 km / s so the moon never moves backwards relative to the direction of Earth's motion about the sun.

If the Earth disappeared while the moon was moving at 31 km/s about the sun, the old circular orbit would mark the moon's new perihelion. Likewise 29 km/s would make the old circular orbit the aphelion.

Working with U = 30 km/s, u = 1 km/s, µ = 1 AU × U² ≈ G × 2E30 kg,
if the moon starts at r₀ = 1 AU and v₀ has $$V_t = U + u \cos A$$ perpendicular to $$\vec{r}_0$$ and $$V_r = u \sin A$$ parallel to $$\vec{r}_0$$, then
$$V_0 = \frac{ \mu }{ r_0 \times V_t} = \frac{U^2}{U + u \cos A} \\ p = \frac{r_0^2 V_t^2}{\mu} = \frac{ (30 + \cos A )^2 }{900} \, \textrm{AU} \\ e = \sqrt{ \left( \frac{V_t - V_0}{V_0} \right)^2 + \left( \frac{V_r}{V_0} \right)^2} = \frac{1}{900} \sqrt{ 900 + 60 \cos A + 2701 \cos^2 A + 60 \cos^3 A } \\ \theta = \tan^{-1} \frac{V_r}{V_t - V_0} = \tan^{-1} \left( \frac{30 + \cos A }{60 + \cos A } \tan(A) \right) \\ a = \frac{p}{1 - e^2} = \frac{900}{899 - 60 \cos A} \, \textrm{AU} \\ b = \frac{p}{\sqrt{1 - e^2}} = \frac{ 30 + \cos A }{\sqrt{899 - 60 \cos A}} \, \textrm{AU} \\ r_{\pm} = \frac{p}{1 \mp e } = \frac{ ( 30 + \cos A)^2 }{ 900 \mp \sqrt{ 900 + 60 \cos A + 2701 \cos^2 A + 60 \cos^3 A } } \, \textrm{AU}$$
So the Eccentricity is between √65585703/243000 (cos A = -1/90) and 61/900 (cos A = 1) and the orbit is bounded between 841/959 AU and 961/839 AU.

https://en.wikipedia.org/wiki/Keple...bit_that_corresponds_to_a_given_initial_state

BdS
xactly that but rpenner beat me to it.

https://en.wikipedia.org/wiki/Inertia
"Inertia is the resistance of any physical object to any change in its state of motion; this includes changes to its speed, direction, or state of rest. It is the tendency of objects to keep moving in a straight line at constant velocity. The principle of inertia is one of the fundamental principles of classical physics that are used to describe the motion of objects and how they are affected by applied forces."

https://en.wikipedia.org/wiki/Inertia
"Inertia is the resistance of any physical object to any change in its state of motion; this includes changes to its speed, direction, or state of rest. It is the tendency of objects to keep moving in a straight line at constant velocity. The principle of inertia is one of the fundamental principles of classical physics that are used to describe the motion of objects and how they are affected by applied forces."
I assume most people here know this. What was your point in posting this?

https://en.wikipedia.org/wiki/Inertia
"Inertia is the resistance of any physical object to any change in its state of motion; this includes changes to its speed, direction, or state of rest. It is the tendency of objects to keep moving in a straight line at constant velocity. The principle of inertia is one of the fundamental principles of classical physics that are used to describe the motion of objects and how they are affected by applied forces."
Er, yes.

An orbiting body experiences a force and, in accordance with F=ma, it is in a constant state of acceleration. Motion in a circle or an ellipse implies constant acceleration in the direction of the force. That force overcomes the inertia of the body and causes it to change direction.

Is this an issue for you?

constant state of acceleration.

Does that imply it is going faster not remaining at a steady speed???

Does that imply it is going faster not remaining at a steady speed???

The term "acceleration" in physics discussions does not imply an increase in speed, but a only change in velocity.

Examples of changes in velocity might be
• from 50 m/s north to 60 m/s north
• from 50 m/s north to 40 m/s north
• from 50 m/s north to 50 m/s north-east

Does that imply it is going faster not remaining at a steady speed???

No, for the reason rpenner has given.

The treatment of motion in a circle is pretty standard stuff in Newtonian mechanics.

F=ma tells you that under the influence of a constant force, F, the rate of change of velocity, dv/dt - which is what acceleration is - will be constant, a.

With an object in a circular orbit, the velocity vector sweeps round at a constant rate. This means velocity is changing at a constant rate, which means there is a constant acceleration, i.e. exactly what F=ma says it should be.

So circular motion involves a constant acceleration towards the centre of the circle, commonly referred as "centripetal acceleration". And this is in accord with experience, for anyone who has whirled a conker on a string. When you start, the string first extends itself until it is under tension, and it then exerts a force on the conker towards the hand holding it - and the conker obediently moves round in a circle.

As already pointed out, we already know why the Moon is receding, and this is due to an interaction known as tidal acceleration. Such a situation will occur anytime you have a satellite which orbits with a period longer than what it take for the planet to rotate and doesn't orbit retrograde to the planet. If the satellite orbits faster than the planet rotates, or retrograde to the planet's rotation, the results are the opposite and it will slowly fall in towards the planet. One example of this is Phobos, a moon of Mars, which orbits faster than Mars rotates and is in a slow "death spiral" around the planet.
So objects can control their satellites orbital distance with spin, interesting...

Does orbital inertia have anything to do with orbital precession?