Density word problem ... A 300 kg meterorite is in circular motion orbiting a far...

vipson231

1. The problem statement, all variables and given/known data

So my professor gave me this formula GMplanet = (v^2 x d)/a to solve for the question and told me that m/v = density. I was told then to multiply the end result of m by 1000 and v by 1,000,000 to get the answer. I am given all the knowns except the acceleration. How do i find the acceleration?

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gneill

Start by identifying your variables and assign any given values. It looks like you're using "v" for both velocity and volume. What's d? What's a?

vipson231

I was told that the distance is equal to the radius which is equal to 2.00 x 10^8 and that the velocity is 7000 m/s for the faraway planet.

Once I plug these values into the formula it looks like

(6.67 x 10^-11)(Mass of planet)= (7000)^2 x (2.00 x 10^8) / a

However what do i do with the a? so confused :(

gneill

You need to get the quantities and what they represent sorted out. Read the problem statement and assign variable names to the numbers given. For example, the meteorite is given a mass of 300 kg, so define m1 = 300 kg. Do the same for the other numbers given in the problem statement, assigning each an appropriate variable.

It's not clear to me what the formula you've written out is supposed to represent. Perhaps it's a misinterpretation of the formula for the orbital velocity for a body in circular orbit at orbit radius r around a planet of mass M? That would be:

$$v^2 = \frac{GM}{r}$$

I don't know what your "d" or "a" are supposed to represent in this scenario.

vipson231

The formula that you provided for the orbital velocity above is indeed the right interpretation of the question. I perhaps either copied it wrong or didn't use the right formula. I'll try to solve this question using your formula. Thanks =)