What is orbit that could place satellite to be always under the Sun? I just thinking that, if we could place satellite to orbit earth in opposite direction of earth rotation, inverse of geostationary orbit. If we carefully choose a speed to sync with earth rotation, it would have that satellite stay exactly the same position in the sky as the sun
What is that altitude and are there any name of that orbit? Or is it just the same as geostationary orbit?
 A: I think what you're talking about are Lagrangian points:

Image Credit: Anynobody / Wikimedia Commons
They are points such that the combined gravitational effects from the Earth and the Sun give rise to areas that would have the same angular velocity as the Earth. However, out of the five lagrange points shown below: 1,2,3 are unstable
You are probably referring to the first Lagrangian point, known as $L_1$ which is roughly $0.01$ AU away from Earth.
Edit: Turns out I misunderstood what you were asking for. If you were curious if such a point can exist such that it is still "orbiting" around the Earth, the answer is no. You may think that as the orbit goes further and further out, you can eventually reduce the period to one year. However, at this point the effect from the Sun cannot be ignored and you can't realy call it "orbiting" around Earth.
We have:
$$m\left(\frac{2\pi}{T}\right)^2 r = \frac{GMm}{r^2} \to r^3 = \frac{GMT^2}{4\pi^2}$$
Plugging in $G=6.67\times 10^{-11} \mathrm{N\cdot m^2 \cdot kg^{-2}}$, $M=5.972 \times 10^{24} \text{ kg}$, and $T=31556926 \text{ s}$ gives:
$$r = 2.16 \times 10^9 \text{ m}$$
while $L_1$ is at a distance of 0.01 AU or $1.50 \times 10^9 \text{ m}$ which is slightly farther than the $L_1$ point which exists there due to the interaction between the Earth AND the Sun, so a satellite cannot orbit around Earth with a period of one year.
A: It wouldn't be geostationary because we would see it move across the sky. I think you mean geosynchronous, which is what the orbit would almost be. If you wanted it to always stay in front of the sun from some special vantage point, then you would need to somehow have the satellite correct its orbit based on the changing tilt of the Earth.
