Video: Comparing the Gravtiational Field Strength on Earth to the Gravitational Field Strength on the Moon

The gravitational field strength at the surface of Earth is 9.8 N/kg. The gravitational field strength of the surface of the Moon is 1.6 N/kg. What is the ratio of the gravitational field strength at the surface of Earth to the gravitational field strength at the surface of the Moon? Answer to one decimal place.

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Video Transcript

The gravitational field strength at the surface of Earth is 9.8 newtons per kilogram. The gravitational field strength of the surface of the Moon is 1.6 newtons per kilogram. What is the ratio of the gravitational field strength at the surface of Earth to the gravitational field strength at the surface of the Moon? Answer to one decimal place.

Okay, so in this question, we’re comparing gravitational field strengths at two different locations: one is at the surface of Earth and the other is at the surface of the Moon. We’re given these strengths in units of Newtons per kilogram for both of these locations and we want to solve for their ratio. Specifically, we want to solve for the ratio of the gravitational field strength of the surface of Earth to the gravitational field strength of the surface of the Moon. In order to answer this question, we’ll need to interpret or translate this sentence into a mathematical expression.

To get started with doing that, let’s apply some symbols to the terms that we’ve been given. We’re told that the gravitational field strength at the surface of Earth is a certain value. Let’s call that field strength 𝑔 sub 𝐸. And then likewise, we’ll call the gravitational field strength at the surface of the Moon 𝑔 sub 𝑀. We’re told that 𝑔 sub 𝐸 is 9.8 newtons per kilogram and 𝑔 sub 𝑀 is 1.6 newtons per kilogram. We want to know the ratio of 𝑔 sub 𝐸 to 𝑔 sub 𝑀.

Now because of the way that these two terms — the gravitational field strength of the surface of Earth and the field strength of the surface of the Moon — are arranged in this sentence, we know that when we go to calculate this ratio, it will be 𝑔 sub 𝐸 divided by 𝑔 sub 𝑀. That’s because we’re finding the ratio of the field strength on Earth’s surface to that on the Moon’s surface. If the question had instead asked what is the ratio of the gravitational field strength at the surface of the Moon to the gravitational field strength at the surface of the Earth, then, in that case, we would need to reverse these two terms: 𝑔 sub 𝑀 would be on top and 𝑔 sub 𝐸 on bottom. But with our question written as it is, 𝑔 sub 𝐸 divided by 𝑔 sub 𝑀 is correct. That’s the ratio we want to solve for.

And to solve for that ratio, we’ll divide 9.8 newtons per kilogram by 1.6 newtons per kilogram. Notice by the way, that the units in these expressions cancel out, as they often do when we calculate a ratio. We’ll end up with a pure number. And it will be equal to 9.8 divided by 1.6. When we calculate that fraction, we find an exact answer of 6.125. But this isn’t our final answer because we want to give an answer to one decimal place. That means our answer will keep 6.1. And then we’ll round that one up if the next digit, the two, is greater than or equal to five. But since two is not greater than or equal to five, we’ll leave the one as it is. To one decimal place then, this is our answer. The ratio of the gravitational field strength at the surface of Earth to the gravitational field strength of the surface of the Moon is 6.1.

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