1. In recent years, scientists have discovered hundreds of planets orbiting othe
ID: 1354509 • Letter: 1
Question
1. In recent years, scientists have discovered hundreds of planets orbiting other stars. Some of these planets are in orbits that are similar to that of earth, which orbits the sun(Msun = 1.99 × 1030 kg) at a distance of1.50 × 1011 m, called 1 astronomical unit (1 au).Others have extreme orbits that are much different from anything in our solar system. The following problem relates to one of these planets that follows circular orbit around its star.
WASP-32b orbits with a period of only 2.7 days a star with a mass that is 1.1 times that of the sun. How many au from the star is this planet? Assume the orbital period of earth is 365 days
2. The 0.20 kg puck on the frictionless, horizontal table in the figure is connected by a string through a hole in the table to a hanging 1.20 kg block. With what speed must the puck rotate in a circle of radius r = 0.30 m if the block is to remain hanging at rest?
Explanation / Answer
here,
period of the planet , T = 2.7 days
T = 116640 s
mass of central , m = 1.1 * ms
m = 2.189 * 10^30 kg
let the planet is r distance from the star
using formula for period of satellite
T^2/R^3 = 4*pi^2 /(G*m)
116640^2 / R^3 = 4 * pi^2 /(6.67*10^-11 *2.189 * 10^30 )
solving for R
R = 3.69 * 10^9 m
R = 0.025 au
the distance of planet from the star is 0.025 au
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