Calculating Moon's Acceleration in Circular Motion Relative to Sun

[robgazza]

Homework Statement

to a good approximation, the moon can be considered to be traveling in a circle centred at the Earth and the Earth can be considered to be traveling in a circle centred at the sun. determine the magnitude of the moons acceleration relative to the sun
a)when the moon is between the Earth and the sun
b)when the Earth is between the moon and sun

Homework Equations

The Attempt at a Solution

hello & greetings all

i am very stuck in the problem above

may i ask, to find the required answer do i need to use the equation -gmM/r^2 and work out the effective gravitational pull or is it circular motion?

i am very stuck and any help would be muchly appreciated :(

 

[OlderDan]

Gravity is the force producing the accelerations, but to find their individual magnitudes you just need the orbital periods and orbit radii.

 

[robgazza]

Gravity is the force producing the accelerations, but to find their individual magnitudes you just need the orbital periods and orbit radii.

so for example, a) i would need to work out the pull from the sun and subtract the pull from the Earth to give its velocity?

 

[OlderDan]

so for example, a) i would need to work out the pull from the sun and subtract the pull from the Earth to give its velocity?

Based on the information given in the problem, I assume you are studying centripetal motion and are expected to use that in your calculations. The velocities can be determined from the orbital periods and radii, and that can be related to the acceleration. What is the connection between velocity and acceleration for circular motion?

Another approach to the problem would be to calculate the forces from the universal gravition law and use Newton's second law to find the acceleration. This might even be easier to do than using centripetal motion considerations, but I doubt that is what the problem intended.

 

[robgazza]

im not sure, calculate the forces from the universal graviton law and use Newton's second law to find the acceleration is correct, how would i do this?

 

[OlderDan]

im not sure, calculate the forces from the universal graviton law and use Newton's second law to find the acceleration is correct, how would i do this?

You would look up the distance from the Earth to the moon and from the sun to Earth and figure out how far the moon is from the sun at the two locations. Then use the F = GMm/r² you quoted in your orignal post to find the net force by appropriately combining the two forces acting on the moon. Once you have the net force (magnitude and direction) calculate the acceleration from Newton 2.

 

[Sanket R Berde]

What Is Centripetal Force? and its uses.

 

[cristo]

What Is Centripetal Force? and its uses.

Is this a homework question? If so, we cannot simply give you the answers! Try searching on wikipedia.org, or google, then if you have any specific points you are unsure of, post back and we will be happy to help!