Question

two spaceships traveling .6 and .9 respectively come upon a planet that measures 4.5x10^12 m. Find the radius that each ship will measure. Please help. I now i am supposed to use ..L'=L/Y(GAMMA) ..

Answer 1

Answer on Question #38213, Physics, Other

Question:

Two spaceships traveling .6 and .9 respectively come upon a planet that measures $4.5 \times 10^{\wedge} 12 \, \text{m}$. Find the radius that each ship will measure. Please help. I now am supposed to use $L' = L / Y(\text{GAMMA})$.

Answer:

Length contraction is the phenomenon of a decrease in length measured by an observer of objects which are traveling at any non-zero velocity relative to the observer.

$$L = \frac {L _ {0}}{\gamma} = L _ {0} \sqrt {1 - \left(\frac {v}{c}\right) ^ {2}}$$

$L_{0}$ is the proper length (the length of the object in its rest frame), $L$ is the length observed by an observer in relative motion with respect to the object, $v$ is the relative velocity between the observer and the moving object, $c$ is the speed of light.

For first ship:

$$L = 4.5 * 10^{12} \, \text{m} \sqrt{1 - 0.6^2} = 3.6 * 10^{12} \, \text{m}$$

For second ship:

$$L = 4.5 * 10^{12} \, \text{m} \sqrt{1 - 0.9^2} = 2.0 * 10^{12} \, \text{m}$$