need help asap On a fictitious planet, you weigh a satellite and find it to be 500 N. The satellite is then put into circularorbit about the planet a distance 12 km above the surface of the planet, where it takes 90 minutes tocomplete an orbit. If the radius of the planetis 1.2x10 m:i) What is the mass of the satellite?) If the satellite was moved to an orbit 9 km above the surface of the planet, does its kinetic energyincrease, decrease, or stay the same?) Does its gravitational potential energy increase, decrease, or stay the same?iv) What is the total energy of the satellite now (in the new orbit]?617..pdf199+

On a fictitious planet, you weigh a satellite and find it to be 500 N. The satellite is then put into circular orbit about the planet a distance 12 km above the surface of the planet, where it takes 90 minutes to complete an orbit. If the radius of the planetis 1.2x10° m: i) What is the mass of the satellite? ii) If the satellite was moved to an orbit 9 km above the surface of the planet, does its kinetic energy increase, decrease, or stay the same? Does its grayitational potential energy increase, decrease, or stay the same?

On a fictitious planet, you weigh a satellite and find it to be 500 N. The satellite is then put into circular orbit about the planet a distance 12 km above the surface of the planet, where it takes 90 minutes to complete an orbit. If the radius of the planetis 1.2x10° m: i) What is the mass of the satellite? ii) If the satellite was moved to an orbit 9 km above the surface of the planet, does its kinetic energy increase, decrease, or stay the same? Does its grayitational potential energy increase, decrease, or stay the same?

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Question

need help asap

On a fictitious planet, you weigh a satellite and find it to be 500 N. The satellite is then put into circular
orbit about the planet a distance 12 km above the surface of the planet, where it takes 90 minutes to
complete an orbit. If the radius of the planetis 1.2x10 m:
i) What is the mass of the satellite?
) If the satellite was moved to an orbit 9 km above the surface of the planet, does its kinetic energy
increase, decrease, or stay the same?
) Does its gravitational potential energy increase, decrease, or stay the same?
iv) What is the total energy of the satellite now (in the new orbit]?
617..pdf
199+

Expert Solution

Step 1

(i)

Given:

The weight of the satellite is 500 N.

The distance between the planet and the satellite is 12 km.

The time which the satellite takes to complete the orbit is 90 minutes.

The radius of the planet is $1.2 \times 10^{6} m$ .

Introduction:

Acceleration due to gravity is the acceleration gained by an object due to gravitational force. Gravity is the force with which the earth attracts a body towards its center.

Step 2

Calculation:

Write the expression of the acceleration due to gravity.

$g = \frac{4 π^{2} R}{T^{2}}$

Here, $R$ is the distance of the orbit from the center of the planet, $T$ is the time period of motion.

Substitute $1212 \times 10^{3} m$ for $R$ and $90 \min$ for $T$ in the above expression.

$g = \frac{4 {(3.14)}^{2} (1212 \times 10^{3} m)}{{[90 (60 s)]}^{2}} g = \frac{4.8 \times 10^{7}}{2.9 \times 10^{7}} \frac{m}{s^{2}} g = 1.66 \frac{m}{s^{2}}$

Calculate the mass of the satellite.

$M_{s} = \frac{W}{g}$

Here, $W$ is the weight and $g$ is the acceleration due to gravity.

Substitute 500 N for $W$ , $1.66 \frac{m}{s^{2}}$ for $g$ in the above expression.

$M_{s} = \frac{500 N}{1.66 {ms}^{- 2}} M_{s} = 301.2 kg$

Thus, the mass of the satellite is 301.2 kg.

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