# Rotation of Earth effects the weight of star.

• Victorian91
In summary, the period of rotation for a star of mass M and radius r can be calculated using the equation T = 2Pi square root r3/GM, where G is the gravitational constant and M is the mass of the star. This is because the mass of the star is not cancelled out in the equation and it affects the units of the final answer. It is important to check units when solving equations.
Victorian91

## Homework Statement

A star of mass M and radius r rotates with angular speed of such value that objects on the surface at its equator are just about to experience zero apparent weight. The period of rotation of the star is given by?

## Homework Equations

g' = g- Rw2 (where w is the angular velocity)

## The Attempt at a Solution

From the above..
mg' =mg -mRw2
Since apparent weight is zero,

mg -mRw2 = 0
mRw2 = mg
But w = (2Pi/T)^2
R ( 4Pi^2/T^2 )
T^2 = 4Pi^2 R/g
But g = GM/R2 at the surface of the planet

Hence,
Period, T= 2Pi square root r3/G

2Pi square root r3/gM

Why does the Mass of the star still have in the equation
I tried so many times the Mass will be canceled out..
Do you think which one is correct??

Thanks

The mass of the star, big M, appears in only one of your equations. How can it possibly cancel?

Another way to look at it: Your result, $2\pi\sqrt{r^3/G}$, doesn't have the right units. G has units length3/mass/time2. Thus $r^3/G$ has units of mass*time2. Your answer has units of time*sqrt(mass), which is meaningless.

Okay thanks ...

Sorry.. I was actually not focusing..
Next time I'll check on units..

Thanks

## What is the Rotation of Earth?

The Rotation of Earth refers to the spinning motion of our planet around its own axis. This rotation causes day and night as different parts of the Earth are exposed to sunlight at different times.

## How does the Rotation of Earth affect the weight of stars?

The Rotation of Earth has no direct effect on the weight of stars. The weight of a star is determined by its mass and the force of gravity acting upon it. However, the rotation of Earth does have an indirect effect on the weight of stars by influencing the Earth's gravitational pull.

## Does the Rotation of Earth affect the gravitational pull of stars?

Yes, the Rotation of Earth does affect the gravitational pull of stars. As Earth rotates, its gravitational pull fluctuates slightly, which in turn can affect the orbits of other celestial bodies, including stars.

## Can the Rotation of Earth cause changes in the weight of stars?

No, the Rotation of Earth cannot cause changes in the weight of stars. As mentioned earlier, the weight of a star is determined by its mass and the force of gravity acting upon it. The Rotation of Earth does not have a significant impact on either of these factors.

## Are there any other effects of the Rotation of Earth on stars?

Yes, the Rotation of Earth can have other effects on stars. For example, Earth's rotation can cause changes in the apparent position of stars in the sky, known as stellar aberration. It can also affect the length of a day on other planets, which can indirectly impact the way stars are viewed and studied.

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