Question

you are the science officer on a visit to a distant solar system. prior to landing on a planet you measure its diameter to be 1.8 × 107 m and its rotation period to be 22.3 hours. you have previously determined that the planet orbits 8.6 × 1011 m from its star with a period of 402 earth days. once on the surface you find that the acceleration due to gravity is 63.6 m/s2. what are the mass of (a) the planet and (b) the star? (g

Answer 1

The mass of the star of the distant solar system is 82 * 10²² kg and the mass of the planet of the distant solar system is 8.58 * 10²⁵ kg

The planet stays in its orbit and moves in a centripetal motion due to the gravitational force of attraction between the planet and the star.

Fc = m v² / r

Fg = G M m / r²

Fc = Fg

m v² / r = G M m / r²

v² = G M / r

M = r v² / G

g = Acceleration due to gravity

G = Gravitational constant

M = Mass of star

r = Distance between both bodies

G = 6.67 * 10⁻¹¹ N m² / kg²

r = 8.6 * 10¹¹ m

T = 402 days = 3.47 * 10⁷ s

v = 2 π r / T

v = 2 * 3.14 * 8.6 * 10¹¹ / 3.47 * 10⁷

v = 15.56 * 10⁴ m / s

Ms = 8.6 * 10¹¹ * 15.56 * 10⁴ / ( 6.67 * 10⁻¹¹ )

Ms = 20.1 * 10²⁶ kg

F = G M m / r²

F = m g

Equating,

m g = G M m / r²

Mp = g r² / G

Mp = 63.6 * ( 1.8 * 10⁷ / 2 )² / 6.67 * 10⁻¹¹

Mp = 8.58 * 10²⁵ kg

To know more about Orbital velocity

brainly.com/question/15886625

#SPJ4