F = G M1 M2 / d^2
F = 6.67*10^-11 (2.78*10^30)(9.94*10^30)/(5.65*10^12)^2
F = 6.67*2.78*9.94/(31.9)*10^(60-11-24)
= 5.78 * 10^25 Newtons
F = 6.67*10^-11 (2.78*10^30)(9.94*10^30)/(5.65*10^12)^2
F = 6.67*2.78*9.94/(31.9)*10^(60-11-24)
= 5.78 * 10^25 Newtons
F = G * (m1 * m2) / r^2
where:
F is the magnitude of the gravitational force
G is the gravitational constant (6.67430 × 10^-11 N m^2 / kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
Let's plug in the values given in the question:
m1 = 2.78×10^30 kg
m2 = 9.94×10^30 kg
r = 5.650 × 10^12 m
Using these values, we can calculate the gravitational force:
F = (6.67430 × 10^-11 N m^2 / kg^2) * (2.78×10^30 kg * 9.94×10^30 kg) / (5.650 × 10^12 m)^2
Now, let's calculate it step by step:
1. Multiply the masses: (2.78×10^30 kg * 9.94×10^30 kg) = 2.76052×10^61 kg^2
2. Square the distance: (5.650 × 10^12 m)^2 = 3.193225×10^25 m^2
3. Divide the product of masses by the square of distance: (2.76052×10^61 kg^2) / (3.193225×10^25 m^2) = 8.64673×10^35 N
Therefore, the magnitude of the gravitational attraction between the neutron star and the black hole is approximately 8.64673×10^35 N.