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Scottingham
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How big would a sphere of U238 have to be to reach 1g at its surface?
Do you not know how to look up the density of U238? Do you not know how to calculate the mass of a sphere? Do you no know the equation for the force of gravity at the surface of a sphere? That is, what part of solving this problem do you not understand?Scottingham said:How big would a sphere of U238 have to be to reach 1g at its surface?
rightScottingham said:Physics is not my forte, yet.
If I understand correctly do I just solve for R (where g=1)?
from http://nova.stanford.edu/projects/mod-x/ad-surfgrav.html:
You have learned that the surface gravity (g)of a body depends on themass (M)and theradius (r)of the given body.
The formula which relates these quantities is:g = G * M / r2
whereG is called the Gravitational constant.
Just solve algebraically. No need to graph.Scottingham said:Thank you.
So if I understand correctly, I'd need two equations then. One to figure out the mass (with the known density of U238) given a particular radius. And another to figure out the radius given a particular mass in order to equal 1g. I'm guessing I could use some method to graph the two and where they intersected in mass and radius would be my solution?
Hm. Back of napkin calcs suggest your number may be a little too high.Scottingham said:Gets 5949 km which seems more reasonable given that the Earth's radius is 6,371 km
I was busy fleshing out my answer. You can see where I took the cube root to convert volume ratio (.26) to radius ratio (.64).Scottingham said:@Dave I don't think it'd work that was as it wouldn't be a linear comparison.
Now, now. Don't whine. Being a day late and a dollar short is common for CanadiansDaveC426913 said:[EDIT: Dagnabit you! phinds!]
You are correct. Surface gravity does not scale with the cube of radius. It scales linearly. The cube factor from volume and the square factor from the inverse square law cancel to leave a simple linear relationship of surface gravity to radius (neglecting compression effects).Scottingham said:That definitely seems reasonable. The gravity at the surface also has the inverse square law from the center of mass to consider as well though, which is why it is maybe bigger than it first would seem...or my equation is wrong.
Scottingham said:What maths though? Where did the equations I found go wrong? And how does a cube factor and a square factor cancel each other out?
what units? I also made some edits.Scottingham said:I think I got all flummoxed with the units
Pi has diddly squat to do with whether a relationship is linear. In this case the relationship is linear.Scottingham said:@jbriggs444 I don't think that's right about gravity scaling linearly. Also, I think pi helps to rule out the linear relationships.
Very wrong, yes. Try this one.What about my equation (linked above) is wrong?
That equation is fine.I took the surface gravity equation here:
http://nova.stanford.edu/projects/mod-x/ad-surfgrav.html -- g = G * M / r2
Or 18900 kg per cubic meter.And substituted mass with the density of U238 (18.9 g/cm3)
Helps if you leave the pi in the formula when you submit it to Wolfram.multiplied by the volume of a sphere, which is 4/3πr^3.
That's fine for converting cubic centimeters to cubic meters. But still leaves you out by a factor of 1000 because grams are not kilograms.Since the radius was in km in the surface gravity equation on converted the density one which was in cm by multiplying by 100,000.
A 1g Sphere of U238 is a sphere of uranium-238 with a mass of 1 gram. This is equivalent to approximately 1.25 cubic centimeters in volume.
The significance of a 1g Sphere of U238 lies in its use as a reference object for measuring gravitational acceleration. Due to its small size and uniform density, it experiences a constant acceleration of 9.8 meters per second squared (9.8 m/s²) when placed on the Earth's surface.
A 1g Sphere of U238 is typically created by melting and casting a small amount of uranium-238 into a spherical mold. The resulting sphere is then polished and calibrated to ensure its accuracy as a reference object.
Yes, a 1g Sphere of U238 can be used to measure gravitational acceleration on other planets, as long as their surface gravity is within a similar range to Earth's (e.g. Mars, Venus). However, the value of 9.8 m/s² may not be accurate on planets with significantly different surface gravities.
Yes, there are other materials that can be used as a reference for measuring gravitational acceleration, such as a pendulum or a mass on a spring. However, a 1g Sphere of U238 is considered the most accurate and consistent method for measuring gravitational acceleration due to its small size and uniform density.