Earthed

What is the mass of the planet? How does the new planet’s mass compare to Earth’s mass?

An artificial satellite is placed into orbit around a newly discovered planet beyond Pluto. It is found that the radius of the near-circular orbit is 1.2 × 104 km and that the orbital period is 37 days.

Public Comments

1. Thw mass of the earth is 5.98 times 10 to the 24 power Kg.
   
   
   
   
2. V = sqrt (GM/r)
   
   
   
   v_p = sqrt G M_p/r
   
   P_p = 37 days = r *2 pi /v_p
   
   37 days = r *2 pi * sqrt r /G M_p
   
   M_p = 2 pi r^3/(37days)^2 G
   
   M_p = 2 pi (1.2x10^7 m)^3/ (37days*24 hr/day * 3600s/hr)^2 6.67e−11 m^3/kg·s^2
   
   M_p = 1.59 x 10^19 kg
   
   
   
   M_e = 5.97x 10^24 kg
   
   
   
   M_p/M_e = 2.66 x 10^-6