An earth satellite, the mass of which is 1000 kg, is in a circular orbit 1000 km above the surface of the earth. It is desired to transfer it to a circular orbit 1500 km above the surface. The amount of work that must be done to accomplish this is

A. 3.43 * 109 J
B. 1.71 * 109 J
C. -1.71 * 109 J
D. 6.65 * 1010 J
E. -3.43 * 109 J

My teacher says the correct answer is B, but I am not getting that I am getting A; can someone please show me the correct work, this question is confusing?

just listen to what i say

To find the amount of work required to transfer the satellite from a 1000 km to a 1500 km orbit, we need to calculate the change in potential energy.

The formula for the potential energy of an object in orbit is given by:
PE = - (G * M * m) / r

Where:
PE is the potential energy
G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2)
M is the mass of the Earth (5.97 x 10^24 kg)
m is the mass of the satellite (1000 kg)
r is the distance from the center of the Earth to the satellite in meters

Let's calculate the potential energy for the initial orbit at 1000 km above the Earth's surface:
r1 = (1000 km + radius of the Earth)
= (1000 x 10^3 m + 6371 x 10^3 m)
= 7371 x 10^3 m

PE1 = - (G * M * m) / r1
= - ((6.67 x 10^-11 Nm^2/kg^2) * (5.97 x 10^24 kg) * (1000 kg)) / (7371 x 10^3 m)
= - 4.06 x 10^8 J

Now, let's calculate the potential energy for the final orbit at 1500 km above the Earth's surface:
r2 = (1500 km + radius of the Earth)
= (1500 x 10^3 m + 6371 x 10^3 m)
= 7871 x 10^3 m

PE2 = - (G * M * m) / r2
= - ((6.67 x 10^-11 Nm^2/kg^2) * (5.97 x 10^24 kg) * (1000 kg)) / (7871 x 10^3 m)
= - 2.71 x 10^8 J

Finally, to calculate the work done to transfer the satellite from the initial orbit to the final orbit, we need to find the difference in potential energy:
Work = PE2 - PE1
= (- 2.71 x 10^8 J) - (- 4.06 x 10^8 J)
= 1.35 x 10^8 J

Therefore, the correct answer is not A or B. The amount of work required to accomplish this transfer is 1.35 x 10^8 J. It seems that the options given in the question do not include the correct answer.