A new planet has been discovered in our Solar System, and it is traveling in a c

Question

A new planet has been discovered in our Solar System, and it is traveling in a circular orbit around the Sun. The planet has a semi-major axis of 23.5 AU.

1) What is the period of the new planet's orbit?

2)What is the average velocity of the planet?

Mapoob sapling learning A new planet has been discovered in our Solar System, and it is traveling in a circular orbit around the Sun. The planet has a semi-major axis of 23.5 AU. What is the period of the new planet's orbit? Number years What is the average velocity of the planet? New Planet Number Objects in circular orbits around the Sun follaw Kepler's Laws km/s Previous Give Up & View Solution e Check Answer Next Exit Y Hint

Explanation / Answer

The planet is trvelling in circular motion around the sun,

Radius of planets orbit = semi major axis

R = 23.5 AU= 23.5*1.496*10^11=3.52*10^12 m

For circular motion,

v = SQRT (G • M / R)

M= mass of the sun =1.989*10^30 kg

Veclocity of the planet,

V=SQRT (6.67*10^-11*1.989*10^30/3.52*10^12)

  =SQRT(37.7*10^6)

  = 6140 m/s.= 6.14 km/s

Obbital requnecy,

w=V/R

2*pi/T=V/R

period of orbitting,

T=2*pi*R/V = 2*pi*3.52*10^12/6140 =3.6 *10^9 s

  =3.6*10^9/365*24*3600 =114.15 years.

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