On earth, two parts of a space probe weigh 14500 N and 6400 N. These parts are separated by a center-to-center distance of 19 m and may be treated as uniform spherical objects. Find the magnitude of the gravitational force that each part exerts on the other out in space, far from any other objects.
G M1 M2 / 19^2
6.67 * 10^-11 (1.45*10^4)(6.4*10^3) / 361
To find the magnitude of the gravitational force that each part exerts on the other, we can use Newton's law of universal gravitation. The law states that the gravitational force between two objects is directly 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 is:
F = (G * m1 * m2) / r^2
Where:
- F is the gravitational force
- G is the gravitational constant (approximately 6.674 × 10^-11 N m^2 / kg^2)
- m1 and m2 are the masses of the two objects
- r is the distance between their centers
In this case, we are given the weights of the two parts of the space probe, not their masses. However, weight is equal to the force of gravity acting on an object, so we can use the weights as substitutes for the masses.
Let's calculate the masses of the two parts of the space probe:
Weight = mass * acceleration due to gravity
Using this formula, we can solve for mass:
mass = weight / acceleration due to gravity
For the first part of the space probe with a weight of 14500 N, the mass can be calculated as:
mass1 = 14500 N / 9.8 m/s^2
For the second part of the space probe with a weight of 6400 N, the mass can be calculated as:
mass2 = 6400 N / 9.8 m/s^2
After calculating the masses, we can substitute them into the formula for gravitational force and solve for the magnitude of the force.
F = (G * mass1 * mass2) / r^2