1. A satellite whose mass is 1000 kg is in a circular orbit 1000 km above the su
ID: 2263788 • Letter: 1
Question
1. A satellite whose mass is 1000 kg is in a circular orbit 1000 km above the surface of the earth. A space scientist wants to transfer the satellite to a circular orbit 1500 km above the surface. The amount of work that must be done to accomplish this is
I need to do know how to do them, not just answers. thank you
Explanation / Answer
any object revolving in an orbit has both kinetic energy and potential energy. its potential energy is equal to -GMm/r its kinetic energy is equal to (1/2)mV'2. where G is universal gravitational constant= 6.67*(10) power -11 (m power3 / kg* sec power 2). M is the earth mass= 5.976*(10) power 24 kg. m is the mass of the object= 1000kg (given). V is the orbital velocity= sqrt of ( Gm/r). where r is the distance between centre of earth and the object= radius of earth (6371km) + distance of object from the surface of the earth. CASE 1:::: r = 6371+1000km=7371km. by substituting the values, we get the energy in the lower orbit is: 27038339438.3 joules. CASE 2::: after it is given that the orbit is at a distance of 1500km from earth surface. there fore r = 6371+1500=7871km. by substituting the other values we get the energy in the higher orbit is: 25320347046.1 joules. DIFFERENCE BETWEEN THE ENERGIES IN THE TWO ORBITS IS THE REQUIRED WORK DONE. there fore workdone = 27038339438.3 minus 25320347046.1 = 1717592392.18 JOULES = 1.7176 GIGA JOULES. note: THIS IS THE ONLY EASIEST SOLUTION.........................
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