Final answer:
The force with which the space station attracts Earth can be calculated using Newton's law of universal gravitation, which involves the masses of the Earth and the space station along with the distance from Earth's center to the space station, combining Earth's radius with the space station's altitude.
Step-by-step explanation:
The question you’ve asked involves using Newton's law of universal gravitation to calculate the gravitational force between Earth and a space station. The force of gravitational attraction (F) is given by the equation F = G * (m1 * m2) / r², where G is the gravitational constant (6.674×10⁻¹¹ N·m²/kg²), m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass. In this case, we must add the altitude of the space station to Earth’s radius to find the total distance r from Earth’s center to the space station.
To find the magnitude of the force with which the space station attracts Earth, we can use the given values: the mass of the space station, 2190 kg; the mass of Earth, 5.98 × 10²⁴ kg; Earth’s radius, 6370000 m; and the space station's altitude, 479000 m.
The total distance r from Earth’s center to the space station is the sum of Earth's radius and the station's altitude: 6370000 m + 479000 m = 6849000 m. Using these values, we can calculate the gravitational force:
F = (6.674×10⁻¹ N·m²/kg²) · (2190 kg · 5.98 × 10²⁴ kg) / (6849000 m)²
After computing the above expression, we will have the magnitude of the force with which the space station attracts Earth. Both objects exert equal and opposite gravitational forces on each other, as stated by Newton’s third law of motion.