Using the tidal locking formula from Tidal locking - Wikipedia the time for tidal locking to occur may be calculated as 16 million years as an upper estimate. See tidal forces - When did the Moon stop? - Astronomy Stack Exchange
This soon after it's formation, the Moon would have been a molten body so there would be no impact craters from the time before the Moon's axial rotation slowed.
16 million years seems very soon to me compared to the estimated 4.5 billion year age of the Moon. So don't shoot me, I'm only the piano player! 🙂
Newton's Law of Gravitation, f = GmM/r^2, makes much sense if one imagines radiating lines of force from either m or M. The density per unit area at any point on a plane perpendicular to any field line follows an inverse square law. Newton's own observation of the planets, or better the wanderers, led him to decide it is indeed an inverse square relationship with the separation between celestial objects as the independent variable.
Newton, in his experiments, could not observe celestial objects as far as the distance between our sun and the galaxy's central black hole. This distance is 33,000 light years, or simply, 33000x365x24x3600x2.99792e8m = 3.1x10^20m. This means, applying Newton's Law of Gravitation for these separations is an extrapolation for which no previous experimental data was available. The inverse square law may hold for 'small' distances until it is broken down into a relation that governs the circular motion of stars galaxies that rotate as a whole.
Our galaxy makes one complete revolution per 200 million years. This means, the rotational speed in radians is: 2*3.142/(200e6*365*24*3600) = 9.96x10^-16 radians/second. This is equivalent to linear radial acceleration of: ω^2*r = 9.96e-16^2*3.1e20 = 3.08x10^-10m/s^2.
I am referring to numbers to illustrate the fact, these extremely small accelerations could not be perceptible for Newton when he was collecting data which was crucial for the formulation of his Law of Gravitation.
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Yes edbarx, what is really is going on at these huge cosmic distances?
Newton's theory predicted that gravity would be felt instantly by all massive objects across the universe, no matter how far apart they might be.
Measurements of the speed of gravitational waves (the existence of which was predicted by Einstein's theory of gravity) show results consistent with the notion that they travel at the speed of light. This confirms that gravity is not instant as Newton would have us believe.
Now we have MOND, a new theory of gravity which seeks to replace the theories of both Newton and Einstein. MOND comes into play at the scale of the extremely small accelerations that you have calculated, and predicts the observed rotational rates of individual galaxies without invoking the existence of dark matter.
Newton's theory predicted that gravity would be felt instantly by all massive objects across the universe, no matter how far apart they might be.
Measurements of the speed of gravitational waves (the existence of which was predicted by Einstein's theory of gravity) show results consistent with the notion that they travel at the speed of light. This confirms that gravity is not instant as Newton would have us believe.
Now we have MOND, a new theory of gravity which seeks to replace the theories of both Newton and Einstein. MOND comes into play at the scale of the extremely small accelerations that you have calculated, and predicts the observed rotational rates of individual galaxies without invoking the existence of dark matter.
This question does not apply to the angular speed. It only applies to the acceleration.
Here we go:
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1 mile = 1609m approx
So, 3.08x10^-10m/s^2 = 3.08x10^-10/1609 miles per second
And, for this acceleration to be in miles per hour:
acceleration = (3.08x10^-10/1609)*3600 = 6.89x10^-10 miles/hour^2.The idea is to convert the acceleration from m/s^2 to miles/s^2 and then convert this latter result in miles/hour^2. To do that, get the acceleration per second and multiply by 60*60 = 3600.
Don't you mean mph^2 (miles per hour squared)?
We're talking acceleration, not speed.
Ooops, edbarx got in first! 😎
No this is acceleration due to the orbit being followed, the rate of orbital velocity is constant but the acceleration vector arises due to the circular component of the orbit. AKA centripetal acceleration.
If we look at our solar system, the further out a planet is from the Sun, the slower it goes in its orbit e.g. the Earth takes a year while Saturn takes 29 years. This is exactly as predicted by Newton's theory of gravity.
You would think the same physics would be true of the stars rotating around our galactic centre i.e. that the stars further from the centre should move slower than those closer in.
However, according to our measurements, the speed of the stars doesn't change as you move far out from the galactic centre i.e. the most distant stars at the edge of our galaxy are moving faster than predicted by Newton.
This puts doubt on Newton's theory of gravity, also known as Newtonian Dynamics. To explain the discrepency, astrophysicists are currently working on two alternative theories. One is MOdified Newtonian Dynamics (MOND, the other is Dark Matter.
The Dark Matter theory is the easier one to grasp. If we postulate that there is invisible matter outside our galaxy which provides an extra gravitational pull, that would explain why the stars at the galactic rim move faster than predicted by Newton..
Here's a short tutorial for those not into the physics of circular motion!
Refer to the attached diagram.
To stop the stone flying off in a straight line, the boy must pull the stone towards the centre of the circle. This centripetal (centre seeking) force is responsible for changing the velocity of the stone, not in magnitude (speed), but in direction.
A change in velocity is an acceleration. In this case the acceleration is in the direction of the centripetal force so is called centripetal acceleration, AKA radial acceleration (as measured for our galaxy by edbarx).
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Very interesting. I never thought that there could be acceleration without a constant increase in speed. However if our friend in the diagram was in outer space and released the string, would the stone continue to accelerate?
I thought I made that clear, but hey!
If the boy (whom I assume would have to be wearing a space suit in your scenario!) lets go of the string, there would no longer be a centripetal force and hence no centripetal acceleration. The stone would fly off in a straight line at steady speed until some other force, like the gravitational pull of a planet, diverted it from its course.
My tutorial, though short, obviously takes some time to assimilate!
If the boy (whom I assume would have to be wearing a space suit in your scenario!) lets go of the string, there would no longer be a centripetal force and hence no centripetal acceleration. The stone would fly off in a straight line at steady speed until some other force, like the gravitational pull of a planet, diverted it from its course.
My tutorial, though short, obviously takes some time to assimilate!
What there is is a constant CHANGE in VELOCITY (which is speed AND direction).
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