Originally posted by twhiteheadYes the Earth does 'jump upwards'. [sticking to Newtonian Gravity for this post]
I must be missing something here then. Surely the earth accelerates towards the object too? If that is independent of the mass of the earth why doesn't the earth jump upwards every time you drop something?
Is the orbit of a satellite (including man made ones and moons) independent of its mass?
But the Earth is being accelerated upwards by the gravitational field of the object
(cannon or feather) falling towards it.
The Earth's mass in that calculation is a constant and doesn't change dependent
on the object.
Earth has a surface gravity of 9.81m/s^2
Which means any object at the Earth's surface will be trying to accelerate towards the
Earth at 9.81m/s^2
It doesn't matter if it's a feather, a cannon ball, or a neutron star. They will all be
accelerated towards the earth at the same rate.
The Earth is accelerated upwards towards the object falling into onto it according to
the gravitational acceleration of the object falling onto it.
Now lets look at the cannon ball. Lets say for the moment it's a 9lb ball with a 4' diameter.
or 4.1kg with a 10 cm diameter... (radius 5 cm)
Now to find the acceleration due to gravity we set M2 to = 1kg and so it disappears from the
equation to leave us with...
g = G * M1/r^2
At the surface, r =0.05m; M1 = 4.1; and G = 6.674E-11
So g = 1.09E-7 m/s^2 or 109 nano meters per second squared.
If we double r, and move an entire 5 cm off the surface (r=0.1m) then g drops to
27.4 nano meters per second squared.
However for working out the amount the earth is accelerating upwards we need to calculate from
the centre of the Earth's mass... The Earth has a radius of 6,371,000m
So, inputting r=6,371,000 we get the earth accelerating towards the cannonball at 6.7E-24 m/s^2
or 6.7 yocto meters per second squared... or about 7 billionths of the thickness off a hydrogen
nucleus per second per second.
Now the closing speed between the cannonball and the Earth at any given time is going to be the
sum of both their accelerations towards each other.
But as the Cannonball is accelerating towards the Earth at around 10 trillion trillion times the rate
that the Earth is accelerating towards the Cannonball... We only bother calculating the acceleration of
the cannonball.
This changes if we place a Stellar mass Neutron star above the Earth's surface.
Approximately...
Neutron star Mass, 2.8E30kg (appx 1.4 solar masses)
Radius 10,000m (thus distance from neutron star centre of mass to earth centre of mass 6,381,000m)
In this case the neutron star is still being accelerated towards the Earth at 9.81 m/s^2
But the Earth is being accelerated towards the Neutron star at ~ 4.59 km/s^2
In this case the Neutron star will barely move and the much bigger Earth will slam into it, engulf it,
and be crushed down onto it in a layer that might maybe be a few mm thick... At least the matter
not blasted off by nuclear reactions will be crushed down onto it...
So as you can see the closing speed between two bodies is dependent on both their masses...
But the amount an object is accelerated by another is only dependent on the OTHER bodies mass.
Which is why satellites of different masses can go around the Earth in the same orbit at the same speed.
Because they are all accelerating downwards under Earth's gravity at the same rate.
Properly all bodies orbit around each others common centre of mass... But even for The Moon
that centre of mass is well inside The Earth (approx 1,700km below the surface) which means
for anything other than the Moon (in terms of objects bound to the Earth) only the Earth's mass
need be considered.
And even for the moon you only need it's mass when you are being precise.
Originally posted by tim88Being an atheist doesn't make you smarter.
I envy all you atheists. you guys are so intelligent.
Not all smart people are atheists.
Not all atheists are smart people.
In fact being smart doesn't have a whole lot to do with
whether a person is an atheist or theist.
What makes the difference, is how a person goes about
deciding what is or is not a good way of formulating beliefs
about the world.
What I just wrote was a bit of fun with basic physics and maths.
Almost anyone could do it, with a little patience and time.
Being able to do that doesn't require the application of great intellect,
just a fascination about the world and how it works, plus a little mathematics.
That's the great thing (well one of them) about science, anyone can
join in and do it. There is lots you can do without needing multi-billion
Pound particle accelerators, or giant Bio-Research labs.
It's open to anyone with an enquiring mind, to solve puzzles and gain knowledge.
Now there is stuff you can't do without years of training and learning
and some not insignificant talent. But there is good and valuable work done
by ammeters still, and it's lots of fun to boot.
06 Dec 13
Originally posted by tim88That's much ado about nothing.
Nothing, put simply, is the deepest, shallowest, brightest, darkest, widest, thinnest, and incomprehensibly empty emptyness, so empty that it is only prevented from collapsing upon itself because there is no substance to collapsae in upon, or no substance to do the collapsing, or even any substance to think or daydream about collapsing upon abscense of prescen ...[text shortened]... even more nothingness in its place.
http://www.urbandictionary.com/define.php?term=nothing
Originally posted by tim88Sure. You'll want to read the rest of this post in the voice of W.C. Fields for the best effect…
You seem smart and like you know what you're talking about can show me a nothing?
On this momentous day, I present to you, in the brilliant splendor of Technicolor and high-fidelity Surround Sound, the full breadth and entire depth of the body of scientific evidence for the existence of a supreme being:
Ah, yes…
06 Dec 13
Originally posted by SoothfastOh' boy my monitor need cleaning
Sure. You'll want to read the rest of this post in the voice of W.C. Fields for the best effect…
On this momentous day, I present to you, in the brilliant splendor of Technicolor and high-fidelity Surround Sound, the full breadth and entire depth of the body of scientific evidence for the existence of a supreme being:
Ah, yes…