Question

A new moon is discovered orbiting Neptune with an orbital speed of 9.3 103 m/s. Neptune's mass is 1.0 1026 kg. What is the

Answer 1

Answer:

The radius of the moon's orbit, R = 7.715 x 10⁷ m

The orbital period of the moon, T = 14.48 hr

Explanation:

Given,

The orbital speed of the moon, v = 9.3 x 10³ m/s

The mass of Neptune, M = 1.0 x 10²⁶ Kg

The orbital velocity of the moon is given by the relation

                                      $v = \sqrt{\frac{GM}{r+h}}$  m/s

Where,

                     r + h = R → radius of the moon's orbit

Therefore squaring the above equation and solving for r +h. The equation becomes

                                  r + h = GM / v²

Substituting the given values in the above equation

                                     R = (6.673 x 10⁻¹¹ x 1.0 x 10²⁶) / (9.3 x 10³)²

                                        = 7.715 x 10⁷ m

The radius of the moon's orbit, R = 7.715 x 10⁷ m

The orbital period of the moon is given by the relation

                                     T = 2π/ω

                                        = 2πR/v             ∵      ω = v/r

Substituting the values in the above equation

                                     T = (2 x π  x  7.715 x 10⁷ )/ 9.3 x 10³

                                        = 52125.72969 s

                                        = 14.48 hr

The orbital period of the moon, T = 14.48 hr