A star is 17.2 ly (light-years) from Earth. HINT (a) At what constant speed (in m/s) must a spacecraft travel on its journey to the star so that the Earth-star distance measured by an astronaut onboard the spacecraft is 4.06 ly? X m/s (b) What is the journey\'s travel time in years as measured by a person on Earth? yr (c) What is the journey\'s travel time in years as measured by the astronaut? yr
Solution
a)let Lo = 17.2 ly
L = 4.6 ly
let v is the speed of the spacecraft
L = Lo*sqrt(1 - (v/c)^2)
L/Lo = sqrt(1 - (v/c)^2
(L/Lo)^2 = 1 - (v/c)^2
(v/c)^2 = 1 - (L/Lo)^2
v = c*sqrt(1 - (L/Lo)^2)
= 3*10^8*sqrt(1 - (4.05/17.2)^2)
= 2.92*10^8 m/s
b) T = Lo/v
= 17.2*3*10^8/(2.92*10^8)
= 17.67 years
c) To = 4.06*3*10^8/(2.92*10^8) years
= 4.17 years
.
TataKelola dan KamSiber Kecerdasan Buatan v022.pdf
A star is 17-2 ly (light-years) from Earth- HINT (a) At what constant.docx
1. A star is 17.2 ly (light-years) from Earth. HINT (a) At what constant speed (in m/s) must a
spacecraft travel on its journey to the star so that the Earth-star distance measured by an
astronaut onboard the spacecraft is 4.06 ly? X m/s (b) What is the journey's travel time in years
as measured by a person on Earth? yr (c) What is the journey's travel time in years as measured
by the astronaut? yr
Solution
a)let Lo = 17.2 ly
L = 4.6 ly
let v is the speed of the spacecraft
L = Lo*sqrt(1 - (v/c)^2)
L/Lo = sqrt(1 - (v/c)^2
(L/Lo)^2 = 1 - (v/c)^2
(v/c)^2 = 1 - (L/Lo)^2
v = c*sqrt(1 - (L/Lo)^2)
= 3*10^8*sqrt(1 - (4.05/17.2)^2)
= 2.92*10^8 m/s
b) T = Lo/v
= 17.2*3*10^8/(2.92*10^8)
= 17.67 years
c) To = 4.06*3*10^8/(2.92*10^8) years
= 4.17 years
