Question

The first artificial satellite to orbit the Earth was Sputnik I, launched October 4, 1957. The mass of Sputnik I was 83.5 kg, and its distances from the center of the Earth at apogee and perigee were 7330 km and 6610 km, respectively. Find the difference in gravitational potential energy for Sputnik I as it moved from apogee to perigee.

Answer 1

`-4.941*10^8J.`

Step-by-step explanation:

To solve this exercise it is necessary to take into account the concepts related to gravitational potential energy, as well as the concept of perigee and apogee of a celestial body.

By conservation of energy we know that,

`\Delta U = \Delta_(perogee)-\Delta_(Apogee)`

Where,

`U= (-GmM_e)/(r)`

Replacing

`\Delta U = (-GmM_e)/(r_p)- (-GmM_e)/(r_a)`

`\Delta U = GmM_e ((1)/(r_A)-(1)/(r_p))`

Our values are given by,

`m = 85.5Kg`

`M_e = 5.97*10^(24)Kg`

`r_A = 7330Km`

`r_p = 6610Km`

`G = 6.67*10^(-11)Nm^2/Kg^2`

Replacing at the equation,

`\Delta U = (6.67*10^(-11))(85.5)(5.97*10^(24)) ((1)/(7330)-(1)/(6610))`

`\Delta U = -4.941*10^8J`

Therefore the Energy necessary for Sputnik I as it moved from apogee to perigee was
`-4.941*10^8J.`