To determine the velocity, period, and acceleration due to gravity for a satellite in a circular orbit around the Earth, we can use the following formulas:
Velocity of the satellite: The velocity of a satellite in a circular orbit can be calculated using the formula: v = √(G * M / r), where v is the velocity, G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2), M is the mass of the Earth (approximately 5.972 × 10^24 kg), and r is the distance from the satellite to the center of the Earth.
Period: The period of the satellite, which is the time taken to complete one orbit, can be calculated using the formula: T = 2π * √(r^3 / (G * M)), where T is the period, r is the distance from the satellite to the center of the Earth, G is the gravitational constant, and M is the mass of the Earth.
Acceleration due to gravity: The acceleration due to gravity acting on the satellite at that distance from the Earth's surface can be calculated using the formula: g = G * M / (r + h)^2, where g is the acceleration due to gravity, G is the gravitational constant, M is the mass of the Earth, and h is the height above the Earth's surface.
Given that the distance from the Earth's surface to the satellite is 40,000 km (or 40,000,000 meters) and the radius of the Earth (r) is 6,400 km (or 6,400,000 meters), we can substitute these values into the formulas to find the solutions:
Velocity: r = 40,000,000 + 6,400,000 = 46,400,000 meters v = √(G * M / r)
Period: T = 2π * √(r^3 / (G * M))
Acceleration due to gravity: h = r - 6,400,000 meters g = G * M / (r + h)^2
Now, let's calculate these values.