Two spherical objects have masses of 3.5 x 10^7 kg and 6.5 x 10^9 kg. Their centers are separated by a distance of 125000 m. Find the gravitational attraction between them.
To find the gravitational attraction between two objects, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The formula for the gravitational force (F) is:
F = (G * m1 * m2) / r^2
where:
- F is the gravitational force between the objects
- G is the gravitational constant, equal to 6.67430 x 10^-11 N(m/kg)^2
- m1 and m2 are the masses of the objects
- r is the distance between the centers of the objects
Plugging in the given values:
- m1 = 3.5 x 10^7 kg
- m2 = 6.5 x 10^9 kg
- r = 1.25 x 10^5 m
- G = 6.67430 x 10^-11 N(m/kg)^2
Let's calculate the gravitational attraction between the two objects:
First, let's calculate (G * m1 * m2):
G * m1 * m2 = (6.67430 x 10^-11 N(m/kg)^2) * (3.5 x 10^7 kg) * (6.5 x 10^9 kg)
Now, multiply this result by (1/r^2):
F = [(6.67430 x 10^-11 N(m/kg)^2) * (3.5 x 10^7 kg) * (6.5 x 10^9 kg)] / (1.25 x 10^5 m)^2
Simplifying the expression:
F = [(6.67430 x 10^-11 N(m/kg)^2) * (3.5 x 10^7 kg) * (6.5 x 10^9 kg)] / (1.56 x 10^10 m^2)
Now, we can calculate the value using a calculator:
F ≈ 8.7005 x 10^8 N
Therefore, the gravitational attraction between the two spherical objects is approximately 8.7005 x 10^8 Newtons.