A neutron star and a black hole are 5.650e+12 m from each other at a certain point in their orbit. The neutron star has a mass of 2.78×1030 kg and the black hole has a mass of 9.94×1030 kg. What is the magnitude of the gravitational attraction between the two?
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
To calculate the magnitude of the gravitational attraction between the neutron star and the black hole, you can use Newton's law of universal gravitation, which states that the gravitational force between two objects is given by:
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.