Question

Planet X of mass m_x = 6.3 × 10²⁴ kg orbits S in uniform circular motion at a distance r_x and with a period P_x = 1.5 years (=4.7304 × 10⁷ s). The mass of the star S is M_S = 2 × 10³¹ kg and its radius is R_S = 4.2 × 10⁸ m, as shown in the figure.

m r R5 Ms

1) What is r_x, the orbital radius of Planet X around the Sun?

a) r_x = 4.21 × 10⁹ m

b) r_x = 6.19 × 10¹¹ m

c) r_x = 4.23 × 10¹¹ m

d) r_x = 1.44 × 10¹² m

e) r_x = 2.88 × 10⁹ m

2)What is v_X, the speed of Planet X in its orbital motion?
a) v _X = 8940 m/s

b) v _X = 3.53 × 10⁵ m/s

c) v _X = 382 m/s

d) v _X = 56200 m/s

e) v _X = 4.64 × 10⁸ m/s

Answer 1

- 2 1) T= 20 kr TGMs 3/2 4.73x107 z ar xri 16.679x101x2x103) rxz 4.23x10 m. 2) V = 251 4x 21x14:30et" Uz 56200 m/s Ex231x 4.23x1 T 4.73x10