another physics problem?

Question

"the earth orbits the sun once per year at the distance of 1.50x10^11m. venus orbits the sun at a distance of 1.08x10^11m. these distances are between the centres of the planet and the sun. how long (in earth days) foes it take for venus to make one orbit arounf the sun?" (please can you work this out using equations not jus searching the answer in google etc. thank you) thnx for your help

please help

Answer 1

First, find the comparative acceleration of the sun on Venus and Earth. Start with Newton's law of universal gravity:

F=G*m1*m2/r^2

If you assume m2 is the sun, the acceleration of the sun's gravity for any m1 is

A=G*Msun*/r^2

therefore

Avenus/Aearth = (Rearth/Rvenus)^2 .............. cool

Second, find their angular velocities (W=angular velocity). Start with the equation:

A=W^2*r

therefore

Avenus = Wvenus^2*Rvenus
Aearth = Wearth^2*Reath

Avenus/Aearth = (Wvenus/Wearth)^2 * (Rvenus/Rearth) ............. Still pretty cool

This means that

(Wvenus/Wearth)^2 * (Rvenus/Rearth) = (Rearth/Rvenus)^2

(Wvenus/Wearth)^2 = (Rearth/Rvenus)^3

(Wvenus)^2 = (Rearth/Rvenus)^3 * (Wearth)^2 .............We are almost there!

Now since angular velocity can be measured in degrees or radians, why not days? Just plug in for

Wearth = 1 orbit /365 days

(Wvenus)^2=(1.5/1.08)^3*(1 orbit/365days)^2
(Wvenus)^2= 2.011x10^-5 /day^2 *
Wvenus=.004484 orbits/day
therefore

1 orbit = 223 days.

Looked it up on Wikipedia and they have 1 orbit = 224 days :-)

Answer 2

The lever, the pulley, and the vulnerable airplane (if you're going up or down a hill). through ways, this question sounds extra like a attempt of the answerers than that is a quest for understanding.