A 2130-kg space station orbits Earth at an altitude of 455 km. Find the magnitude of the force with which the space station attracts Earth. The mass and mean radius of Earth are 5.98 × 1024 kg and 6370 km, respectively
To find the magnitude of the force with which the space station attracts Earth, we can use Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where:
F is the force of attraction between two objects,
G is the gravitational constant (6.67430 × 10^-11 Nm^2/kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
In this case, m1 is the mass of the Earth (5.98 × 10^24 kg), m2 is the mass of the space station (2130 kg), and r is the sum of the mean radius of the Earth (6370 km) and the altitude of the space station (455 km).
First, we need to convert the radius and altitude to meters:
Mean radius of Earth = 6370 km = 6370 × 10^3 m
Altitude of space station = 455 km = 455 × 10^3 m
Next, we can calculate the distance between the center of the Earth and the space station:
r = mean radius of Earth + altitude of space station
Now we can substitute the values into the formula to find the force of attraction:
F = (6.67430 × 10^-11 Nm^2/kg^2) * (5.98 × 10^24 kg) * (2130 kg) / (r^2)
Finally, we can calculate the magnitude of the force with which the space station attracts Earth.