Question

How do you handle the calculation of the speed of the ISS from the circulation time (exercises, newtonian gravity, orbital motion, celestial mechanics, satellites, physics)?

Answer 1

To calculate the speed of the International Space Station (ISS) using the circulation time, several concepts from Newtonian gravity, orbital motion, and celestial mechanics can be applied. Here's a step-by-step explanation:

1. Understand Circulation Time: The circulation time refers to the time taken by an object, in this case, the ISS, to complete one orbit around the Earth. It represents the orbital period of the ISS.

2. Determine Orbital Period: The orbital period (T) can be calculated using Kepler's third law of planetary motion, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. However, in the case of the ISS, the orbit is not perfectly circular, so a slightly modified form of Kepler's third law can be used. The equation is given as:

   T = 2π * √(a^3 / μ)

   where T is the orbital period, a is the semi-major axis of the orbit, and μ is the standard gravitational parameter of the Earth.

3. Find Semi-Major Axis: The semi-major axis represents the average distance between the center of the Earth and the center of the ISS's orbit. The value can be obtained from reliable sources or orbital data.

4. Calculate Standard Gravitational Parameter: The standard gravitational parameter (μ) is a constant value that combines the mass of the Earth (M) and the gravitational constant (G). Its value is approximately 3.986 × 10^14 m^3/s^2.

   μ = G * M

   where G is the gravitational constant (approximately 6.674 × 10^-11 m^3/kg/s^2) and M is the mass of the Earth (approximately 5.972 × 10^24 kg).

5. Substitute Values and Solve: Once you have the values for the semi-major axis (a) and the standard gravitational parameter (μ), you can substitute them into the equation for the orbital period (T) and solve for T.

6. Calculate Speed: The speed of the ISS can then be determined using the formula:

   Speed = (2π * a) / T

   where a is the semi-major axis and T is the orbital period obtained in the previous steps.

By following these steps, you can calculate the speed of the ISS based on its circulation time, taking into account concepts from Newtonian gravity, orbital motion, and celestial mechanics. Remember to use accurate values for the relevant parameters to obtain a precise result.