Determine the magnitude of the force of gravity acting on a 340 kg satellite , 850 km above Earth's surface.
mg = G•m•M/(R+h)^2 =
6.67•10^-11•340•5.97•10^24/(6.378•10^6 +850•10^3)^2 = 2591 N
To determine the magnitude of the force of gravity acting on a satellite, you can use Newton's law of universal gravitation. According to the law, the force of gravity between two objects is given by the formula:
F = (G * m1 * m2) / r^2
Where:
F is the force of gravity between the two objects,
G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/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, the satellite is above the Earth's surface by 850 km. We need to convert this distance to meters since the gravitational constant is given in SI units.
1 kilometer = 1000 meters
Thus, 850 km = 850,000 meters.
The mass of the satellite (m2) is given as 340 kg.
Now, we assume the Earth's mass as constant, which is approximately 5.972 × 10^24 kg (m1).
Plugging the values into the formula, we get:
F = (G * m1 * m2) / r^2
F = (6.67430 × 10^-11 N(m/kg)^2) * (5.972 × 10^24 kg) * (340 kg) / (850,000 meters)^2
Calculating this equation will give us the magnitude of the force of gravity acting on the satellite.