Find centripetal acceleration with two masses and radius.

[2much]

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?

 

[spikethekitty]

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.

 

[2much]

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

 

[tiny-tim]

hi 2much!

(try using the X² tag just above the Reply box )

Solving for v we get …

why are you finding v ?

 

[rwisz]

I would like to point out that the equations used are incorrect. The first equation, Fg = G mv ms / r^2, is for calculating the force of gravitational attraction between two masses, not the centripetal acceleration. The correct equation for centripetal acceleration is ac = v^2 / r, where v is the velocity and r is the radius.

Furthermore, the units used in the equations are not consistent. The mass of the sun and Venus are given in kilograms, but the distance is given in kilometers. The units should be converted to be consistent, either all in kilograms and meters or all in metric units.

Additionally, the value of G used in the equation is incorrect. The correct value for G is 6.67 x 10^-11 N m^2 / kg^2. This may be the reason why the answer is not correct.

To find the centripetal acceleration in this scenario, we can use the following equation:

ac = (mv * v^2) / r

Where mv is the combined mass of the sun and Venus, v is the velocity of Venus, and r is the distance between the two masses. Plugging in the values given, we get:

ac = ((1.99 x 10^30 kg + 4.83 x 10^24 kg) * v^2) / (1.08 x 10^8 m)

We also need to know the velocity of Venus, which can be calculated using the equation for centripetal force:

Fg = mv * v^2 / r

Rearranging this equation, we get:

v = sqrt(G * (ms + mv) / r)

Plugging in the values, we get:

v = sqrt((6.67 x 10^-11 N m^2 / kg^2) * (1.99 x 10^30 kg + 4.83 x 10^24 kg) / (1.08 x 10^8 m))

Solving for v, we get v = 3.50 x 10^4 m/s.

Now, we can plug this value into the equation for centripetal acceleration to get:

ac = ((1.99 x 10^30 kg + 4.83 x 10^24 kg) * (3.50 x 10^4 m/s)^2) / (1.08 x 10