Question

Four earth-like planets each have a mass of 6 * 10²4 kg. They are arranged on a square with 1 * 10⁹ m sides and orbit in a perfect circle. What is the answer in m/s?

Answer 1

The orbital speed of the four earth-like planets is approximately 3.89 × 10^3 m/s.

Step-by-step explanation:

To calculate the orbital speed of the four earth-like planets, we can use the formula v = √(GM/r), where v is the orbital speed, G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2), M is the mass of each planet (6.0 × 10^24 kg), and r is the orbital radius (1.0 × 10^9 m).

Substituting the known values into the formula, we get v = √((6.67430 × 10^-11 m^3 kg^-1 s^-2)(6.0 × 10^24 kg)/(1.0 × 10^9 m)).

Simplifying the equation gives us v = 3.89 × 10^3 m/s.

Answer 2

The orbital speed of the four earth-like planets in m/s is approximately 8.625 m/s.

Step-by-step explanation:

To determine the answer in m/s, we need to calculate the orbital speed of the four Earth-like planets. The formula for orbital speed can be found using the equation:

V = √(GM/R)

where V is the orbital speed, G is the gravitational constant, M is the mass of the planet, and R is the distance from the center of the planet to the object.

Using the given mass of each planet (6 × 10²4 kg) and the side length of the square (1 × 10⁹ m), we can calculate the distance from the center of the planet to the object (R) as half the length of the side of the square. Plugging in these values, we can find the orbital speed:

V = √(GM/R) = √((6.67430 × 10^-11 N m²/kg² × 6 × 10²4 kg) / (0.5 × 1 × 10⁹ m))

V ≈ 8.625 m/s