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Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 43.3 km/s and 58.6 km/s. The slpwer planet's orbital period is 7.60 years. (a) what is the mass of the star? (b)What is the orbital period of the faster planet, in years?

Question

Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 43.3 km/s and 58.6 km/s. The slpwer planet's orbital period is 7.60 years. (a) what is the mass of the star? (b)What is the orbital period of the faster planet, in years?

check_circleAnswer
Step 1

Given:

The orbital speed of planet 1.v, 43.3 km/s = 43300m/s
The orbital speed of planet 2,, 58.6 km/s 58600m/s
Orbital period ofor slower planet, T 7.60 year
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The orbital speed of planet 1.v, 43.3 km/s = 43300m/s The orbital speed of planet 2,, 58.6 km/s 58600m/s Orbital period ofor slower planet, T 7.60 year

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Step 2

Calculation:

As given orbitals speed of the planet the planet 1 is the slower planet,

The angular speed of the slower planet we have,

Where
vSpeed
R Radius
For planet 1 we have
2t
T
1,T
R (1)
2T
43300x 7.6x365x 24 x 3600
R
6.28
R 1.6x10 m
FRR
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Where vSpeed R Radius For planet 1 we have 2t T 1,T R (1) 2T 43300x 7.6x365x 24 x 3600 R 6.28 R 1.6x10 m FRR

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Step 3

a. The force of gravitation between the s...

Gm,M
..(2)
R
Where
G Gravitational constant
M Mass of star
m = Mass of slower planet
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Gm,M ..(2) R Where G Gravitational constant M Mass of star m = Mass of slower planet

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