What is the gravitational force on an object when it is moved 280 km farther from a small planet with a radius of 1000 km?
The gravitational force on the object, when moved 280 km farther from the planet, is approximately 71 N. (Option b)
Understanding Gravitational Force Calculation
The gravitational force exerted by a planet on an object is given by the equation:
F = (G * M * m) / r²
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 x 10⁻¹¹ N·m²/kg²),
M is the mass of the planet,
m is the mass of the object,
r is the distance between the center of the planet and the object.
Hence,
F = (G * M * m) / r²
Given that the planet has a radius of 1000 km and exerts a gravitational force of 100 N on an object 500 km above its surface, we can calculate:
M * m = (100 N * (1000 km)²) / (6.67430 x 10⁻¹¹ N·m²/kg²)
Now, in the new situation where the object is moved 280 km farther from the planet, the new distance (r') is defined as:
r' = r + 280 km
To find the new gravitational force (F'), we can use the same equation:
F' = (G * M * m) / (r')²
F' = (G * M * m) / (r + 280 km)²
F' = F * (r/r + 280 km)²
F' = 100 N * (500 km / (500 km + 280 km))²
F' ≈ 71 N
Therefore, the correct answer is option b) 71 N. This calculation showcases the impact of distance on gravitational force and highlights the importance of understanding the gravitational constant and mass relationships in such scenarios.