Find the mass of the planet in the two body system. Ansers are shown . A new sol
ID: 3161232 • Letter: F
Question
Find the mass of the planet in the two body system. Ansers are shown .
A new solar system has been discovered, consisting of a Sun and two planets. The mass of the new Sun has been determined to be 3.7 times 10^30 kg. The center-of-mass for the Sun-Planet 1 system is 2,678,800.0 km from the Sun. with Planet 1 being a distance of 8.540 times 10^10 km from the Sun. What is the mass of Planet 1? If Planet 2 has a mass of 16.2 times 10^27 kg and the center-of-mass for the Sun-Planet 2 system is 475,049,600.0 km from the Sun. what is the distance of Planet 2 from the center-of-mass?Explanation / Answer
Mass of sun M = 3.7 x10 30 kg
The center of mass for the sun and planet 1 from the sun is r = 2678800 km
Distance of the planet from the sun R = 8.54 x10 10 km
Distance of the center of mass point from the planet 1 is r ' = R - r
r ' = 85397321200 km
We know M r = mp r '
From this mass of planet m p = M r / r '
= 1.16x10 26 kg
(b).Mass of planet 2 is m = 16.2 x10 27 kg
Center of mass for the sun and planet 2 from sun is r = 475049600 km
Distance of the planet 2 from center of mass r ' = ?
We know M r = m r '
From this r ' = M r / m
= (3.7x10 30 ) (475049600 km) /(16.2 x10 27 kg)
= 1.08498 x10 11 km
= 1.085x10 11 km
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