Final answer:
The gravitational force between the 4.0 x 10⁸ kg mass and a 2.8 x 10⁵ kg mass separated by 1.0 x 10⁴ m must be recalculated, as the options provided do not match the calculated value using the gravitational force formula.
Step-by-step explanation:
To calculate the gravitational force between the two masses given in the question, we can use Newton's law of universal gravitation:
F = G × (m1 × m2) / r²
Where:
- F = gravitational force between the masses
- G = gravitational constant (6.67 × 10⁻¹¹ Nm²/kg²)
- m1 = mass of the first object (4.0 × 10⁸ kg)
- m2 = mass of the second object (2.8 × 10⁵ kg)
- r = distance between the centers of the two masses (1.0 × 10⁴ m)
Plugging in the values, we get:
F = (6.67 × 10⁻¹¹) × (4.0 × 10⁸ × 2.8 × 10⁵) / (1.0 × 10⁴)²
F = (6.67 × 10⁻¹¹) × (1.12 × 10³⁴) / (1.0 × 10⁸)
F = (0.74704 × 10¹⁵) N
F = 7.4704 × 10⁻¹ N
So, the correct answer should be recalculated considering the provided options, since the options given in the question do not include a matching value. Please double-check the values and calculations to ensure they align with the given choices.