Two stars, a binary star system, with a mass of m1 = 5.88E29 and m2 = 2.27E30 kg are separated by a distance of 2.55E11 m. What is the gravitational force between them?
To calculate the gravitational force between two objects, you can use Newton's law of universal gravitation, which states that the force is proportional to the product of their masses and inversely proportional to the square of the distance between them.
The formula to calculate the gravitational force (F) is:
F = G * (m1 * m2) / r^2
Where:
- F is the gravitational force between two objects
- G is the gravitational constant (approximately 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 given values into the formula:
m1 = 5.88E29 kg
m2 = 2.27E30 kg
r = 2.55E11 m
G = 6.67430 × 10^-11 N m^2/kg^2
Now we can calculate the gravitational force:
F = (6.67430 × 10^-11 N m^2/kg^2) * ((5.88E29 kg) * (2.27E30 kg)) / (2.55E11 m)^2
To simplify this calculation, we can use scientific notation:
F = (6.67430 × 10^-11) * ((5.88 × 10^29) * (2.27 × 10^30)) / (2.55 × 10^11)^2
Now, let's perform the multiplication and division:
F = (6.67430 × 10^-11) * (1.33416 × 10^60) / (6.5025 × 10^22)
F = 0.0875904534 * 2.05189 × 10^37
F = 1.79461 × 10^36 N
Therefore, the gravitational force between the two stars is approximately 1.79461 × 10^36 Newtons.