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Can someone please help understand when to use each of these Universal Gravitational Constants.

G = 6.67 x 10-11 N•m2/kg2

G = 6.67 x (10^(–11)) N(m^2) (kg^(2))

compared to

G = 6.67 * 10-11 m3/kg-1s-2

G = 6.67 x (10^(–11)) (m^3) (kg^(–1)) (s^(–2))

Thank you for your time and assistance.

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    $\begingroup$ There is no difference, because a Newton is one kg m / s^2. The first version in each line is dangerously sloppy, because you have to know without any formatting that all the numbers after 10 must be interpreted as exponents. $\endgroup$
    – Ryan C
    May 30 at 19:58
  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    May 31 at 5:02

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G = 6.67 x 10-11 N•m2/kg2

compared to

G = 6.67 * 10-11 m3/kg-1s-2

It's great that you are paying careful attention to units, kudos to you!

Let's work the problem testing the mostly likely hypothesis - that they are the same thing, not different. After all, as you likely suspect, there can't really be two different ones.

What happens if we set them equal to each other?

6.67 x 10-11 N•m2/kg2 = 6.67 x 10-11 m3/kg-1s-2

get rid of numerical value:

N•m2/kg2 = m3/kg-1s-2

get rid of "extra" meters:

N/kg2 = m/kg-1s-2

Multiply kg2 on both sides:

N = m•kg/s-2

Hmmm, now what does Wikipedia say a Newton is?

The newton (symbol: N) is the unit of force in the International System of Units (SI). It is defined as 1 kg⋅m/s2, the force which gives a mass of 1 kilogram an acceleration of 1 metre per second per second.

So we're okay, these are the same physical values, one that includes a Newton explicitly as "N", and the other that writes it out "long form" kg⋅m/s2.

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