Suppose NASA wants a satellite to revolve around Earth 5 times a day. What should be the radius of its orbit if we neglect the presence of the Moon? (G=6.67*10^ -11 N*m^2/kg^2, Mearth=5.97*10^24 kg). Answer is 1.44*10^7 m

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Question:

Suppose NASA wants a satellite to revolve around Earth 5 times a day. What should be the radius of its orbit if we neglect the presence of the Moon? (G=6.67*10^ -11 N*m^2/kg^2, Mearth=5.97*10^24 kg). Answer is 1.44*10^7 m

Answer:

The radius of its orbit will be “1.44 × 10⁷ m“.

Mass and radius

According to the question,

Satellite resolve a day = 5 times

Mass of earth, = 5.97 × 10²⁴ kg

G = 6.67 × 10⁻¹¹ Nm²/kg²

Now,

The time taken will be:

T =

  = 4.8 hours

By converting it into seconds, we get

  = 4.8 × 3600

  = 17280 sec

We know the formula,

→      T = 2π ×

By substituting the above values, we get

17280 = 2π ×

        r = 1.44 × 10⁷ m

Thus the above approach is correct.

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