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I've been thinking about this question recently, yet I can't quite figure it out. How would we define the graph of a gravity well in terms of G and the mass of the central object?
The force of gravity on an object on an inclined plane is F = m g sin θ, and at the same time θ = arctan(dy / dx), so if I set the force due to incline to equal the force due to "gravity" (the force we want to simulate), I think I get
Where m is my little mass (the planet or marble), M is the big mass (the "sun", I suppose, except it's a point mass), and x is how far the little mass is from the point mass. However, I don't know if I'm right or if that equation even has a clear-cut solution.
I hope my explanation of my question is understandable. Thanks. 66.27.77.225 ( talk) 02:56, 1 December 2012 (UTC)
According to this dining-hall survey (p. 16, Fig. 1b), 47% of MIT students (n=236) were virgins as of fall 2001. The rates were 70%, 32%, 28% and 33% for undergrad years 1, 2, 3 and 4-5 respectively; 35% for grads; and 49% for undergrads combined. But according to this report from the MIT Office of the Registrar, the enrolments by year were 1033, 1039, 1037 and 1104 undergrads and 5984 grads. By my calculation, the stratified percentage for undergrads would have been 40.6%, which clearly indicates a sampling bias. Can confidence intervals still be estimated, without knowing the number of students surveyed at each level? Neon Merlin 14:34, 1 December 2012 (UTC)
Any suggestions? HOOTmag ( talk) 20:51, 1 December 2012 (UTC)
Mathematics desk | ||
---|---|---|
< November 30 | << Nov | December | Jan >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I've been thinking about this question recently, yet I can't quite figure it out. How would we define the graph of a gravity well in terms of G and the mass of the central object?
The force of gravity on an object on an inclined plane is F = m g sin θ, and at the same time θ = arctan(dy / dx), so if I set the force due to incline to equal the force due to "gravity" (the force we want to simulate), I think I get
Where m is my little mass (the planet or marble), M is the big mass (the "sun", I suppose, except it's a point mass), and x is how far the little mass is from the point mass. However, I don't know if I'm right or if that equation even has a clear-cut solution.
I hope my explanation of my question is understandable. Thanks. 66.27.77.225 ( talk) 02:56, 1 December 2012 (UTC)
According to this dining-hall survey (p. 16, Fig. 1b), 47% of MIT students (n=236) were virgins as of fall 2001. The rates were 70%, 32%, 28% and 33% for undergrad years 1, 2, 3 and 4-5 respectively; 35% for grads; and 49% for undergrads combined. But according to this report from the MIT Office of the Registrar, the enrolments by year were 1033, 1039, 1037 and 1104 undergrads and 5984 grads. By my calculation, the stratified percentage for undergrads would have been 40.6%, which clearly indicates a sampling bias. Can confidence intervals still be estimated, without knowing the number of students surveyed at each level? Neon Merlin 14:34, 1 December 2012 (UTC)
Any suggestions? HOOTmag ( talk) 20:51, 1 December 2012 (UTC)