Three asteroids A₁, A₂ and A₃ are orbiting around a star having a radius of r. Asteroid A₁ has a mass of M, A₂ has a mass of 3M and A₃ has a mass of 4M. Calculate the force experienced by A₂ and A₃ if the force on A₁ is 15000 N. It is known that A₁ completes the orbit in 290 minutes.

The figure shows a star having a radius of R and three comets C₁, C_2, and C₃ orbiting the star. The time taken by C₁ is 320 minutes for traversing the entire orbit. Determine the ratios of kinetic energies of C₁ and C₃ if C₁ experiences a force of 12000 N. Consider the masses of C₁, C_2, and C₃ are W, 4W, and 5W respectively.

A satellite is in an orbit around Mars. The orbit is 70.0 km above the surface of the planet. Given that the mass of Mars is 6.42 × 10²³ kg, the radius of Mars is 3.40 × 10⁶ m and the gravitational constant is G = 6.67 x 10^-11 Nm²/kg², determine the time period of the satellite around the planet.

A tiny rock is orbiting another 9.0 kg rock in a circular trajectory with a radius of 42 cm in a region of space unaffected by the gravity of other celestial objects. Both of the rocks are roughly spherical. Determine the time in which the tiny rock completes one revolution around the other rock.

[The value of the gravitational constant G = 6.67 x 10^-11 Nm²/kg²]

Astronomers observed an asteroid orbiting a distant planet near its surface with an orbital period of 63 minutes. Assuming the distant planet to be a uniform sphere, determine its density.

Astronomers have observed an asteroid orbiting a planet in another planetary system. They have estimated the radius of the orbit of the asteroid around the planet to be 1.5 × 10⁷ m and the gravitational force on the asteroid due to the planet to be 230 N. They calculated that, if the radius of the orbit was 4.0 × 10⁷ m instead the orbital period of the asteroid would have been 3.0 h. Determine the planet's mass.

A space agency sends a space probe to study Mars. Unfortunately, after successfully placing it in an orbit 12,000 nautical miles above the surface of Mars the agency loses contact with it. Consequently, it orbits the planet at that altitude. Given that 1 nautical mile = 1.852 km, the mass of Mars is 6.42 x 10²³ kilograms, the radius of Mars is 3390 km, and the gravitational constant G = 6.67 x 10^-11 Nm²/kg², find the orbital period of the space probe in that orbit around Mars.

Two satellites with an identical mass of "m" are revolving around Earth that has a mass of "M" in the same circular path with radius of "r" but is always positioned at opposite ends of a diameter line as shown in the figure below. What would be their orbital period "T" value?