On earth, two parts of a space probe weigh 12500 N and 8400 N. These parts are separated by a center-to-center distance of 23 m and are spherical. How do you find the magnitude of the gravitational force that each part exerts on the other out in space?

Question

Benjamin Asiedu · Accepted Answer

#0.13# microNewtons
And that's the same force they exert on each other on earth when set 23 meters apart.

Let's assume that #g=10 m/s^2# to simplify some of our math. The gravitational force between two objects can be calculates as a function of the product of their masses (#M# and #m#), the square of the distance between them (#r#), and the universal gravitational constant. In the case of spherical objects, this is exactly correct. For more complicated shapes you might have to analyze different parts separately. #F = G(Mm)/r^2# The mass of the objects can be found by dividing their weight by the gravitational acceleration at the surface of the earth. I'm using #10m/s^2# to make the mass easy. #M = (12500 N)/(10 m/s^2) = 1250 kg# #m = (8400 N)/(10 m/s^2) = 840 kg# The distance was given: #r = 23 m# We can look up a value for G: #G = 6.67408 × 10^-11 m^3/ (kg s^2)# And plug that all into the first equation: #F = 6.67408 × 10^-11 (1250*840)/23^2 N# #F = 1.325 × 10^-7 N# Even though it appears tiny, in space, that might eventually bring these two objects together.

Layla Ahmed · Answer

undefined You can find the magnitude of the gravitational force that each part exerts on the other using Newton's law of universal gravitation formula: F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant (6.674 × 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two parts, and r is the distance between their centers. Calculate the force using this formula.