# Kay D. Anderson

## What is the gravitational acceleration at a distance of R/2 from a the center of a planet?

1. Given that the radius of the first planet is R = 2.87 x 10^6m and M = 6.02 x 10^24 kg. The idea is the radius is reduced in half and we now have to calculate a new gravitational acceleration. I would appreciate the help on this... I don't even think it's necessarily a killer problem just stumped. Thanks!

The gravitational force (F) between two masses (M and m) separated by a distance R is given by: F = GMm/R² When one of the masses (M) is a planet and the other mass (m) is a small object near the surface of the planet, we have a special name for that gravitational force: we call it the weight of m. Weight = mg where g is the acceleration due to gravity. So we can write: mg = GMm/R² m cancels out, leaving: g = GM/R² The rest is just plugging in the numbers. EDIT: Just reading your question again. It's not clear how the "new" planet comes about. The new radius, Rn, will obviously be R/2 = 1.435 * 10^6 m, but how is this being achieved? Is the same mass M being compressed into the smaller volume, so that the density of the smaller planet is increased, or is the planet just made up of less "stuff" than the first planet (but at the same density) in which case the new planetary mass Mn will be smaller: {Mn = M/8} ?

2. W = F * delta r Just curious what lower case r stands for? It's beginning college physics to answer your question, I never took physics and high school. I don't care much for my professors teaching methods but that makes more sense so essentially all I'm looking at is a simple formula to measure the work based off of force and distance. I think I got it thank you for your input.

if it's high school physics. W = work. F = force , delta r = distance moved

3. 8^2- r^2=r(8)+43 solve for r. I set it up like this, 64-r^2=8r+43 but I don't know how to solve for r since its squared. Please show the steps you took to get r=?

64 - r^2 = 8r + 43 move all terms to 1 side r^2 + 8r - 21 = 0 use discriminant method to solve r = -4 +/-sqrt(37)

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