Video: Calculating the Magnitude of the Gravitational Force between Objects in Deep Space

Two objects, A and B, are in deep space. The distance between the centers of mass of the two objects is 20 m. Object A has a mass of 30,000 kg and object B has a mass of 55,000 kg. What is the magnitude of the gravitational force between them? Use a value of 6.67 × 10⁻¹¹ m³/kg.s² for the universal gravitational constant. Give your answer to three significant figures.

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Video Transcript

Two objects, A and B, are in deep space. The distance between the centers of mass of the two objects is 20 meters. Object A has a mass of 30,000 kilograms and object B has a mass of 55,000 kilograms. What is the magnitude of the gravitational force between them? Use a value of 6.67 times 10 to the negative 11th cubic meters per kilogram second squared for the universal gravitational constant. Give your answer to three significant figures.

Okay, so, in this scenario, we have these two objects, called A and B. So, let’s say here we have our objects A and B. And we’re told that the distance between the centers of mass of these two objects is 20 meters. If the center of mass of object A is here and the center of mass of object B is here, that tells us that this distance here is 20 meters. Along with this, we’re told the mass of object A and the mass of object B as well as the fact that these two objects are in deep space.

Being in deep space means that A and B are the only objects nearby. When we compute the magnitude of the gravitational force between them, we can ignore or neglect any other masses or objects. Continuing on then, we can represent the mass of object A as 𝑚 sub A and that of object B as 𝑚 sub B. Now that we know our object masses as well as the distance that separates the centers of mass of these two objects, let’s recall Newton’s law of gravitation.

This law says that the gravitational force between two objects, we’ll call it 𝐹, is equal to the universal gravitational constant, big 𝐺, times the mass of each one of these objects. We’ll call them 𝑚 one and 𝑚 two. Divided by the distance between the objects’ centers of mass, we’ll call that 𝑟, squared. Looking at this equation, we can see that for our scenario with objects A and B, we know their masses. And we also know the distance separating their centers of mass. And along with that, we’re told in the problem statement a particular value to use for the universal gravitational constant.

At this point then, we can begin to calculate the magnitude of the gravitational force between objects A and B. It’s equal to the value we’re given to use as capital 𝐺 times the mass of object A, 30,000 kilograms, times the mass of object B, 55,000 kilograms. All divided by 20 meters quantity squared. Note that all the units in this expression are already in SI base unit form. We have meters and kilograms and seconds. To three significant figures, this force is 2.75 times 10 to the negative fourth newtons. That’s the magnitude of the gravitational force between objects A and B.

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