# Derive tidal force upon star (approximation: divide star in 2)

• tumconn
In summary, the conversation discusses deriving the tidal force acting on a spherical, homogeneous star orbiting a black hole at a distance much larger than its radius. The equation for tidal force is given, and the attempt at a solution involves dividing the star into two equal parts and calculating the force acting on each hemisphere. However, a discrepancy is found in the final result, and the speaker requests assistance in identifying the error in their calculation.
tumconn

## Homework Statement

Spherical,homogeneous star with radius R orbiting black hole at distance ## r_p >>R ## .Derive the tidal force acting upon the star by dividing the star into two equal parts and making the necessary approximations.

## Homework Equations

The tidal force equation of ## a \propto \frac{ R }{ {r_p}^3} ## is not a given.

## The Attempt at a Solution

I calculated the force acting on the nearest and farthest hemisphere from the black hole.
Nearest: ##dF_1= \frac{G M_o dm}{{(r_p-R+r)}^2} ## where ## M_o ## is the mass of the black hole and ## dm= \rho \pi r^2 dr ## the mass of a disk with thickness dr . By integrating from 0 to R I got ## F_1= \frac{3GM_o M(2r_p-R)}{4r_p R^2} ##.
For the farthest hemisphere ## dF_2=\frac{G M_o dm}{{(r_p+R-r)}^2} \Longrightarrow F_2= \frac{3GM_o M(2r_p+R)}{4r_p R^2} ##
By substracting these,I get the tidal force ## \Delta F= F_1-F_2=\frac{3}{2} \frac{GM_oM}{R r_p} ## which is definitely not in agreement with the actual physics of the problem,since it should be proportional to R.
Can someone point me to where I went wrong?

tumconn said:
dm=ρπr2dr the mass of a disk with thickness dr .
You seem to have defined r here as the distance from the point of the star nearest the black hole to the disk. The disk's radius will not be r.

## What is the definition of tidal force?

Tidal force is the force that is exerted on an object, such as a star, by the gravitational pull of another object, such as a planet or moon, that is in close proximity.

## How is tidal force calculated?

Tidal force is calculated by dividing the mass of one object by the square of the distance between the two objects, and then multiplying by the gravitational constant. In the case of dividing a star in two, the distance would be measured from the center of the star to the center of the other object.

## What is the purpose of dividing a star in two when deriving tidal force?

Dividing a star in two allows for simplification of the calculations and provides an approximation of the tidal force that would be exerted on the entire star.

## What are some factors that can affect tidal force?

The mass and distance of the objects involved are the main factors that can affect tidal force. The shape and rotation of the objects can also have an impact on the exact calculation of tidal force.

## How does tidal force impact the star?

Tidal force can cause the star to experience slight distortions and fluctuations in its gravitational pull. This can also lead to changes in the star's rotation and potentially affect its internal structure.

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