# Gravitation sum related to Centripetal Acceleration

• Urmi
In summary, the conversation discussed calculating the centripetal acceleration of the moon, which is 60 times the radius of the Earth away from the Earth's center. The equation for centripetal acceleration was given, as well as the equation for orbital velocity. The gravitational acceleration at the Earth's surface was also mentioned, and it was explained how to find the acceleration of the moon using the Earth's gravitational field. The final equation was derived and it was determined that the centripetal acceleration of the moon is equal to the gravitational acceleration of the Earth's field at a distance of 60 times the Earth's radius.
Urmi

## Homework Statement

The distance between the centres of the Earth and the moon is 60 times the radius of the earth. Calculate the centripetal acceleration of the moon. Acceleration due to gravity on the Earth's surface is 10m/s.

## Homework Equations

Centripetal acceleration= v^2/R
Orbital Velocity=√2gR/√2

## The Attempt at a Solution

I found out the centripetal acceleration of Earth but I cannot find that of the moon.

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MathLover69 said:
Firstly, notice that they did not give you the mass of the earth(Me) which is necessary if you want to find the acceleration due to the Earth's G-Field.
a = GME/r^2
However, you don't need the actual mass of the Earth since a is proportional to r^(-2) (a = kr^(-2)). Hope this helped. :)
P.S. This is all assuming that the G-Field of the moon is negligible for an object on Earth's surface.
Umm, I'm sorry...can you just elaborate on the answer, like how to find the a?? I'm confused a bit...

The centripetal acceleration of the moon equals the gravitational acceleration of the Earth's gravitational field at distance ##r=R_m=60R_e##.
The gravitational acceleration of Earth's gravitational field at distance ##r=R_e## (that is at the surface of the earth) is given equal to ##10m/s^2##

The gravitational acceleration of the Earth's gravitational field at a specific distance r is given by ##a_r=\frac{GM_e}{r^2}##. Apply this equation first for ##r=R_e ## and then for ##r=R_m=60R_e##. So you ll get two equations. Divide the two equations by parts, the ##GM_e## will be simplified, and you ll get an equation with only one unknown, ##a_{R_m}## that is the gravitational acceleration due to Earth's gravitational field at distance ##r=R_m##.

Urmi
Delta² said:
The centripetal acceleration of the moon equals the gravitational acceleration of the Earth's gravitational field at distance ##r=R_m=60R_e##.
The gravitational acceleration of Earth's gravitational field at distance ##r=R_e## (that is at the surface of the earth) is given equal to ##10m/s^2##

The gravitational acceleration of the Earth's gravitational field at a specific distance r is given by ##a_r=\frac{GM_e}{r^2}##. Apply this equation first for ##r=R_e ## and then for ##r=R_m=60R_e##. So you ll get two equations. Divide the two equations by parts, the ##GM_e## will be simplified, and you ll get an equation with only one unknown, ##a_{R_m}## that is the gravitational acceleration due to Earth's gravitational field at distance ##r=R_m##.
Thanks a ton! It helped a lot :)

Delta2
PeterDonis said:
@Urmi, in future, please be advised that you cannot post images of handwritten equations. You need to use the PF LaTeX feature to post math directly in the thread. See here for help:

https://www.physicsforums.com/help/latexhelp/
Okayy, I'm new here so I never knew this...I'll be sure to use this next time :)

berkeman

## 1. What is centripetal acceleration?

Centripetal acceleration is the acceleration an object experiences as it moves in a curved path due to a center-seeking force, such as gravity. It is always directed towards the center of the circular motion.

## 2. How is centripetal acceleration related to gravitation?

Centripetal acceleration is related to gravitation through Newton's Law of Universal Gravitation. This law states that any two objects with mass experience a gravitational force towards each other, and this force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. As an object moves in a circular path around another object, such as a planet orbiting a star, the centripetal acceleration is caused by the gravitational force between the two objects.

## 3. What is the formula for calculating centripetal acceleration?

The formula for calculating centripetal acceleration is a = v^2/r, where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path. This formula can also be written as a = ω^2r, where ω is the angular velocity of the object.

## 4. Why is centripetal acceleration important?

Centripetal acceleration is important because it allows us to understand and predict the motion of objects in circular paths, such as planets orbiting a star or satellites orbiting Earth. It also plays a crucial role in many everyday activities, such as driving a car around a curve or riding a bike around a corner. Without centripetal acceleration, these motions would not be possible.

## 5. How does centripetal acceleration affect the speed of an object?

Centripetal acceleration does not directly affect the speed of an object, but it does affect the direction of the object's velocity. As an object moves in a circular path, its velocity is constantly changing direction, but its speed remains constant. The larger the centripetal acceleration, the sharper the curvature of the path and the faster the object must move to maintain that curvature. In other words, the faster the object is moving, the greater the centripetal acceleration required to keep it in a circular path.

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