Can I add centrifugal acceleration?

[FXpilot]

So the problem is asking me to derive the centrifugal and coriolis accelerations of the moon when it is furthest from the Sun and when it is orthogonal to the radius between Earth and the Sun.

Given:
Radius of Moon's Orbit around Earth
Radius of Earth's Orbit around Sun
Mass of Earth
Mass of Sun

= Angular Frequency of the revolution of the Earth around the Sun

= Angular Frequency of the Revolution of the Moon around the Earth

I am trying to figure out the first part.
I know that the coriolis acceleration is going to be zero when the moon is furthest from the Sun because the velocity of the moon is parallel to the angular frequency of the trajectory of the Earth Moon system around the sun.

I already derived that the centrifugal acceleration that the moon experiences by the Earth is

T being the period of the moon around the Earth So would the total centrifugal acceleration that the Moon experiences be the :

Centrifugal Acceleration of the moon by Earth + Centrifugal Acceleration of the moon by Sun?

So

P being the period of the Earth moon system around the sun

Thanks

 

[mfb]

I know that the coriolis acceleration is going to be zero when the moon is furthest from the Sun because the velocity of the moon is parallel to the angular frequency of the trajectory of the Earth Moon system around the sun.

A frequency does not have a direction. The angular velocity does have one, but it is never parallel to the motion of moon.

So would the total centrifugal acceleration that the Moon experiences be the :

Centrifugal Acceleration of the moon by Earth + Centrifugal Acceleration of the moon by Sun?

Could work, but you can also use the masses and distances, which is less dependent on handling different coordinate systems correctly.

 

[FXpilot]

A frequency does not have a direction. The angular velocity does have one, but it is never parallel to the motion of moon.
Could work, but you can also use the masses and distances, which is less dependent on handling different coordinate systems correctly.

What do you mean by masses and distances?

 

[mfb]

The acceleration comes from gravity, and you have everything you need to calculate the gravitational forces.

 

[FactChecker]

You have calculated the magnitude of the accelerations, but you can not simply add the magnitudes unless the accelerations are in the same direction. At any moment, the centrifugal accelerations are vectors created by the gravitational force of the Earth and the Sun. They point toward the Earth and Sun, respectively. Vectors of the magnitude that you calculated can be added and the resulting vector is the total acceleration.

 

[Andrew Mason]

So the problem is asking me to derive the centrifugal and coriolis accelerations of the moon when it is furthest from the Sun and when it is orthogonal to the radius between Earth and the Sun.

Why would there be any coriolis effect here? Also, do you mean centripetal acceleration? The acceleration vectors are toward the sun and the Earth centres.

AM

 

[hackhard]

(+ denotes vector addition operator)

derive the centrifugal and coriolis accelerations of the moon when it is furthest from the Sun

different particles of moon have different accln . if consider com of moon--
since in this case net accln is parallel to radius
1st approach) centrifugal acceleration * (-1) = proj of net acceleration normal to net velocity= net acceleration = (g due to earth) + (g due to sun)
(g=Gm/rr)
2nd approach) since in this case centripetal accln equals net accln and assuming force bet sun and moon negligible to other forces(since it is about 100 times less than force bet Earth and sun)
net accln of moon= (accln of moon in earth(com) frame) +(accln of earth(com) in sun frame)
=

P being the period of the Earth moon system around the sun

this is correct
but this---

total centrifugal acceleration that the Moon experiences be the :

Centrifugal Acceleration of the moon by Earth + Centrifugal Acceleration of the moon by Sun

is incorrect
total centrifugal acceleration that the Moon experiences be the
Centrifugal Acceleration of the moon by Earth + Centrifugal Acceleration of the earth by Sun
and (4*pi*pi*r /(P*P)) =Centrifugal Acceleration of the earth by Sun