Your claim that satellites move at the same speed as the earth and therefore their movements are not noticed from the ground is completely imaginary and not based on any calculations.
Geostationary satellites are quite well known.
Your argument is based upon wilful ignorance of these satellites.
The earth has a spinning speed around its axis and a speed revove around the sun. In order for an object to move at the same as the earth, it must accommodate both the rotation around the earth and the rotation of the earth around the sun.
Which is trivial.
As it is in close proximity to Earth, it will be accelerated by the gravitational attraction to the sun similarly to Earth. i.e. it will orbit the sun.
So that takes care of that. Then it just needs to orbit Earth.
would either move towards the sun where it was close to the sun, or would be thrown towards space when it was far from the sun.
Not if it remains in Earth's region of influence.
Care to provide the equations to justify your claim?
This is a definite problem and cannot be solved. Even if there was a satellite there, it would either move towards the sun during the day or move towards space at night, and no power could stop it. But since this is difficult for you and the public in general to understand, I will take it more simplified for you and solve the problem by showing that centrifugal force and gravitational force are not suitable for satellites.
In order for a satellite to move simultaneously with the Earth and remain fixed in place, it must mimic rotational motion. When it does this, the fundamental forces acting on it, the gravitational force and the (hypothetical) centrifugal forces it has due to its motion, must be equal. If one of them is larger than the other, it will either fall to the ground or gone away into space. Lets calculate.
1- The satellites are assumed to be 36,000 kilometers above the ground.
2- The radius of the Earth is 6,371 km.
3- The rotation speed of the Earth around its axis is approximately 1650 km/h.
4- To simplify the calculation, the forces acting on an object weighing 1 kg will be considered.
a) Gravitational Force EffectGravitational force acting on an object 36,000 km above the ground:
Distance of the object from the center of the earth: 36.000 kms + 6371kms= 42.371kms.
Since the object weighs 1 kg when it is 6.371 kms away from the center of the earth (at the ground), the gravitational force it has when it is 42.371 kms above the ground can be found simply by a simple ratio. Since the gravitational force is inversely proportional to the square of the distance;
GF= (6371 / 42371)² x1kg =
0,022 kg b)Centrifugal force assumed to act on the object due to angular velocity.F= mV²/R
m= mass=1 kg.
V= Velocity = 1.650 x (42371 / 6371) = 10.973 k/h = 10.973 x (10/36) m/s = 3.048 m/s
R= 6371 kms = 6.371.000 m
F= 1x 3.048² / 6.371.000 =
1,46 kg.RESULTWhile the force that pulls the object to the earth has a very low value of 0.022 kg, the force that forces the object to move away from the earth has a high value of 1.46 kg. To compare;
1,46 / 0,022 = 66.
Except you entirely failed.
Your math is wrong.
Notice how what you have done is scale the weight of the object with altitude, but then used the force for the rotation.
A 1 kg object sitting ont he surface of Earth does NOT have a force of 1 kg acting on it due to gravity. It is ~9.8 N.
So it shouldn't be ~0.022 kg, it should be ~0.22 N.
You have also entirely failed to calculate the angular velocity correctly.
If you want to do that there are a few options.
But R needs to be the radius of the circle, not Earth.
We can also just use angular velocity, instead of linear velocity.
Then F=m*w^2*R.
w=2*pi/T.
T, as a simple approximation (which overestimates it) is 86400 s.
And taking your previous calculated radius of 42 371 000 m, we get F=0.224 N.
If you did want to use the velocity of the satellite, will that is given by 2*pi*R/T, which gives us roughly 3081 m/s.
Sticking that into the formula with the correct value of R, gives us 0.22N.
Either way, YOU ARE WRONG!
And would you look at that?
0.22 N = 0.22 N.
The ratio is 1.
So you are entirely wrong.
Sticking in numbers which are not appropriate, and failing to understand units.
As you can see, I present the mathematics
Math equivalent to just saying 1+1 = 65678.
It is useless and wrong.