Find centripetal acceleration with two masses and radius.

AI Thread Summary
To find the centripetal acceleration between the Sun and Venus, the gravitational force equation Fg = G mv ms / r^2 is used, where mv is the mass of Venus, ms is the mass of the Sun, and r is the distance between them. The centripetal acceleration is expressed as ac = mv v^2 / r, linking gravitational force to centripetal acceleration. A misunderstanding arises when equating force and acceleration; the correct relationship is F = ma. The discussion highlights confusion over the necessity of calculating velocity (v) when centripetal acceleration is the primary goal. Clarifying these equations is essential for accurate results in calculating centripetal acceleration.
2much
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Homework Statement


We are given the mass of the sun, ms = 1.99 x 10^30 and the mass of the venus, mv = 4.83 x 10^24. The distance from each other radius is r = 1.08 x 10^8.

What is the centripetal acceleration?

mv = 4.83 x 10^24 kg
ms = 1.99 x 10^30 kg
r = 1.08 x 10^8 km
G= 6 67x10^-11 N m2 /kg2

Homework Equations



Force of gravitational attraction
Fg = G mv ms / r^2

Centripetal Acceleration
ac = mv v^2 / r

The Attempt at a Solution



Since gravity causes the centripetal acceleration:
Fg = mv ac
G mv ms / r^2 = mv v^2 / r

Solving for v we get
v =\sqrt{} ms G / r

I am not getting the right answer, what is wrong with using these equations?
 
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2much said:
Since gravity causes the centripetal acceleration:
Fg = ac
G mv ms / r^2 = mv v^2 / r

Force does not equal acceleration. F=ma. See if that fixes the problem.
 
spikethekitty said:
Force does not equal acceleration. F=ma. See if that fixes the problem.

I did have mv in the final equation, just forgot to mention it there. Still didn't give me the answer of 1.3x10^-2 m/s2
 
hi 2much! :smile:

(try using the X2 tag just above the Reply box :wink:)
2much said:
Solving for v we get …

why are you finding v ? :confused:
 

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