Which of the following astronomers first proposed that the Sun is static and the Earth revolves around the Sun?

Assume that a tunnel is dug along a chord of the earth,at a perpendicular distance $(R / 2)$ from the earth's centre,where '$R$' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel,it will execute a simple harmonic motion with a time period:

Three equal masses of $m \; kg$ each are fixed at the vertices of an equilateral triangle $ABC.$
$(a)$ What is the force acting on a mass $2 \; m$ placed at the centroid $G$ of the triangle?
$(b)$ What is the force if the mass at the vertex $A$ is doubled?
Take $AG = BG = CG = 1 \; m$.

Four similar particles of mass $m$ are orbiting in a circle of radius $r$ in the same angular direction because of their mutual gravitational attractive force. The velocity of a particle is given by

Two particles of equal mass $m$ go round a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is

Three particles of mass $1 \, kg$ each are placed at $(0, 0)$,$(0, 0.2 \, m)$,and $(0.2 \, m, 0)$. What is the net gravitational force on the particle placed at the origin?