91影视

The mass of satellite is m = 50 kg

The period of satellite is

$$\begin{gathered} T=6hour \\ =21600s \end{gathered}$$

The magnitude of gravitational force F = 80 N

A force that causes a body to follow a curved path is known as a centripetal force. It always moves in a direction perpendicular to the body's velocity and in the direction of the instantaneous centre of the path's curvature.

We can use the concept of gravitation and centripetal force.

Formula:

$v=\frac{2蟺r}{T}$ 鈥�(颈) $F=\frac{m{v}^2}{r}$ 鈥�(颈颈)

Where,F is the centripetal force, v is velocity of object moving in circular direction, m is the mass of object, r is the radius of orbit and T is the time period of object

According to the equation for equilibrium of forces for the satellite,

Gravitational force = centripetal force.

So,

$F=\frac{m{v}^2}{r}$

Now, using the equation (i) for velocity of satellite, in this equation, we get

$F=\frac{m\left(4{蟺}^{2}r\right)}{T^2}$

Now, rearranging this equation for radius r, we get

$r=\frac{F{T}^2}{4m{蟺}^2}$

Substitute all the values in above equation

role="math" $$\begin{gathered} r=\frac{80鈥�\text{N}脳{\left(\text{21600}鈥�\text{s}\right)}^2}{4脳50鈥�\text{kg}脳{蟺}^2} \\ =1.9脳{10}^{7}m \end{gathered}$$

The equation for kinetic energy is
_{$K.E=\frac{1}{2}m{v}^2$}

Using the equation (ii) for velocity in this equation, we get

$$\begin{gathered} K.E=\frac{1}{2}m脳\frac{Fr}{m} \\ KE=\frac{1}{2}Fr \\ =\frac{1}{2}80鈥�\text{N}脳1.9脳{10}^7鈥�\text{m} \\ =7.6脳{10}^8\text{J} \end{gathered}$$

We have the equation of equilibrium of gravitational force and the centripetal force.

$\frac{m{v}^2}{r}=\frac{GMm}{r^2}$

Now, using the equation for velocity and rearranging the equation, we get

$$\begin{gathered} M=\frac{v^{2}r}{G} \\ =\frac{4{蟺}^2{r}^3}{T^{2}G} \\ =\frac{4脳{蟺}^2脳{\left(1.9脳{10}^{7}m\right)}^3}{{\left(\text{21600}鈥�\text{s}\right)}^2脳\left(6.67脳{10}^{-11}\frac{{\text{N.m}}^{\text{2}}}{{\text{kg}}^{\text{2}}}\right)} \\ =8.6脳{10}^{\text{24}}\text{kg} \end{gathered}$$

Mass of the planet Cruton$M=8.6脳{10}^{24}kg$