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,
the force BETWEEN the station and Earth ... f = G M m / r^2
look up G ... r is Earth radius plus station altitude
To find the magnitude of the force with which the space station attracts Earth, we can use the law of universal gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The formula for the force of gravity (F) between two objects is given by:
F = (G * m1 * m2) / r^2
Where:
F is the magnitude of the force of gravity,
G is the gravitational constant, which is approximately 6.674 × 10^-11 N(m/kg)^2,
m1 and m2 are the masses of the two objects (space station and Earth), and
r is the distance between the centers of the two objects.
In this case, the mass of the space station (m1) is given as 2130 kg and the mass of Earth (m2) is given as 5.98 × 10^24 kg. The distance between them (r) is the sum of the altitude of the space station above Earth's surface, 455 km, and the mean radius of Earth, 6370 km.
First, let's convert the distance to meters:
Altitude = 455 km = 455,000 meters
Mean radius of Earth = 6370 km = 6,370,000 meters
Now, we can calculate the total distance (r):
r = altitude + mean radius of Earth
= 455,000 + 6,370,000
= 6,825,000 meters
Substituting the given values into the formula, we can find the magnitude of the force of gravity:
F = (G * m1 * m2) / r^2
= (6.674 × 10^-11 N(m/kg)^2) * (2130 kg) * (5.98 × 10^24 kg) / (6,825,000 meters)^2
Performing the calculations gives us the magnitude of the force of gravity between the space station and Earth.