Understanding the Concepts
* Newton's Law of Universal Gravitation: 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.
* F = (G * m1 * m2) / r^2
* F = force of gravity
* G = gravitational constant (6.674 x 10^-11 N m^2/kg^2)
* m1 = mass of object 1 (Earth in this case)
* m2 = mass of object 2 (spacecraft)
* r = distance between the centers of the two objects
Calculations
1. Distance:
* The spacecraft is 3.00 Earth radii above the surface.
* Since the radius of the Earth is approximately 6,371 km, the total distance between the spacecraft and Earth's center is 4 * 6,371 km = 25,484 km.
* Convert this distance to meters: 25,484,000 meters
2. Mass of Earth:
* Mass of Earth (m1) = 5.972 x 10^24 kg
3. Mass of spacecraft:
* Mass of spacecraft (m2) = 1450 kg
4. Calculate the force of gravity:
* F = (6.674 x 10^-11 N m^2/kg^2 * 5.972 x 10^24 kg * 1450 kg) / (25,484,000 m)^2
* F ≈ 960 N
Therefore, the force of gravity on the spacecraft 3.00 Earth radii above the surface is approximately 960 Newtons.
