# Can I add centrifugal acceleration?

• FXpilot
In summary, the conversation discusses the problem of deriving 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. The problem provides the radius of the moon's orbit around Earth, the radius of Earth's orbit around the Sun, mass of Earth and Sun, and the angular frequencies of the Earth and moon's revolutions. The first part of the conversation focuses on the coriolis acceleration being zero when the moon is furthest from the Sun due to the parallel velocity of the moon and angular frequency of the Earth-Moon system. The second part discusses the calculation of the total centrifugal acceleration experienced by the moon, which can be found
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

FXpilot said:
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.
FXpilot said:
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.

mfb said:
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?

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

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.

FXpilot said:
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

(+ denotes vector addition operator)
FXpilot said:
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 accleration normal to net velocity= net accleration = (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)
=
FXpilot said:

P being the period of the Earth moon system around the sun
this is correct
but this---
FXpilot said:
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

## 1. Can I add centrifugal acceleration to my experiment?

Yes, you can add centrifugal acceleration to your experiment by using a centrifuge. This machine rotates samples at high speeds, creating centrifugal force which can be measured in terms of acceleration.

## 2. How is centrifugal acceleration different from regular acceleration?

Centrifugal acceleration is a type of acceleration that occurs when an object moves in a circular path. It is caused by the force of the object's inertia pushing against the center of the circle. Regular acceleration, on the other hand, is the change in velocity over time, regardless of direction.

## 3. What are the benefits of using centrifugal acceleration in an experiment?

Centrifugal acceleration can be useful in separating mixtures of substances with different densities, such as in the process of blood centrifugation. It can also be used to study the effects of increased gravitational force on living organisms.

## 4. Are there any limitations to using centrifugal acceleration in experiments?

One limitation of using centrifugal acceleration is that it can only be applied to objects that are in motion. It also requires specialized equipment, such as a centrifuge, which may not be readily available for all experiments.

## 5. How is centrifugal acceleration calculated?

Centrifugal acceleration can be calculated using the formula a = ω²r, where a is the acceleration in meters per second squared (m/s²), ω is the angular velocity in radians per second (rad/s), and r is the radius of the circular path in meters (m).

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