Now consider a satellite that is orbiting the earth at a...

Now consider a satellite that is orbiting the earth at a distance r1 from the center of the earth. Find its kinetic energy, its gravitational potential energy, and how much energy is required to double its orbital radius. G 6.67E-11 Nm²/kg² M-earth 5.97E+24 kg Mass of satellite 1.94E+03 kg r1 (orbital radius) 20277734 m Fg on satellite N Use the law of universal gravitation to calculate the force of gravity on the satellite v satellite m/s Set Fg = to centripetal force formula to solve for v KE1 J Solve for the kinetic energy of the satellite Ug1 J Solve for the gravitational potential energy of the satellite. Total Mech energy J Add kinetic energy to potential energy to get total mechanical energy (remember U is negative) r2 (new orbital radius) 40555468 Fg on satellite N Repeat previous steps for new orbital radius v satellite m/s KE1 J Ug1 J Total Mech energy J NRG required J Find the change in total mechanical energy. This is the energy required to change the orbit.

Transcript

00:01 Hello students, in this question we are given that the satellite is orbiting around earth and we have to calculate its potential energy, kinetic energy and energy required to double its orbit radius.

00:11 And we are given the mass of earth, which is 5 .97 multiplied by 10 to the power 24 kilograms.

00:18 The mass of the satellite is given to us which is equal to 1 .94 multiplied by 10 to the power 3 kilograms.

00:24 And we are also given the radius of its orbit initially the orbit, that is, 202 777 3 4 meters and we have to calculate the potential energy kinetic energy and the change in energy that would be required to double its orbit radius so first of all let us start with the potential energy so for a satellite orbiting around in a circular orbit around a planet the potential energy potential energy is equal to which is it can be denoted by u p and that would be equal to minus of g m1 m2 divided by r here m1 and m2 are the mass of the satellite and the planet and r is the orbit radius from the center of the planet so upon putting the values in this equation here g is the universal gravitational constant universal gravitational constant constant which has a constant value of 6 .67 multiplied by 10 to the power minus 11 newton meter squared per kilogram square.

01:42 So this is the universal levitation constant.

01:45 In this equation we have to calculate the potential energy that would be equal to 6 .67 multiplied by 10 to the power minus 11, multiplied by the mass of earth which is 5 .97, multiplied by 10 to the power 24, multiplied by the mass of the satellite which is equal to 1 .94 multiplied by 10 to the power 3 divided by the orbit of the radius which is equal to 202 -7734 meters.

02:19 So upon calculating this, our potential energy is approximately coming out to be minus of 3 .8 multiplied by minus of 3 .8 multiplied by 10 to the 10 meters.

02:34 To the power 10 june.

02:36 This is an energy so it would be june.

02:39 This is a potential energy for the satellite.

02:43 Now second part of the question we have to calculate the kinetic energy for the satellite.

02:48 So as we know that for a satellite or foreign any object orbiting around another object the kinetic energy is equal to the minus of potential energy divided by two.

03:04 So this this is the general relation of between the potential energy and kinetic energy.

03:11 So as we have calculated the potential energy, we can easily divide that by 2 and change the sign, then we would obtain our kinetic energy.

03:20 So the kinetic energy of the satellite would be equal to minus of the potential energy that is minus of 3 .8, multiplied by 10 to the power 10 joules and divide that by 2.

03:32 So a kinetic energy of the satellite is equal to kinetic energy of satellite is equal to 1 .9 multiplied by 10 to the power 10 juice.

03:49 So this is the answer to the second part of the question where we have to calculate the kinetic energy.

03:55 Now in the third part of the question we are being here to calculate the energy change required.

04:01 The energy required to change the orbit radius of the satellite from initial to a radius.

04:07 Radius of double.

04:08 So we are changing the orbit radius from r1 to two times of r2.

04:13 That the satellite changes in orbit.

04:16 Initially it was orbiting around at a radius of r1...

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