The closest exoplanet to earth that is thought to potentially be habitable is Gliese 667Cc, which is only 22 light-years away. This planet is at rest with respect to the Earth. Suppose we fly a spaceship toward Gliese 667Cc at constant speed 0.8c. In the Earth's reference frame the spaceship is launched at position x = 0 and time t = 0. The aliens on Gliese 667Cc are concerned that we may be a threat, so they send a diplomatic vessel to meet our ship before we make it to their planet. Their ship launches from Gliese 667Cc when our ship is 12 light-years away from them (in the rest frame of the planets). (a) If they fly their diplomatic vessel at a speed 0.4c, how fast do they see our ship moving? (b) The aliens forget to decelerate, so instead of docking with our ship when they reach us they continue to fly past at a constant speed. In the rest frame of the Earth, what are the spacetime coordinates (x, y, z, t) of spacetime event A: "our spaceship and the alier- ship pass each other"? =) The reference frame of our spaceship coincides with the rest frame of the earth at laun- (x' = x = 0 at t' = t = 0). What are the spacetime coordinates (x', y', z', t') of event. in the reference frame of our spaceship?
The closest exoplanet to earth that is thought to potentially be habitable is Gliese 667Cc, which is only 22 light-years away. This planet is at rest with respect to the Earth. Suppose we fly a spaceship toward Gliese 667Cc at constant speed 0.8c. In the Earth's reference frame the spaceship is launched at position x = 0 and time t = 0. The aliens on Gliese 667Cc are concerned that we may be a threat, so they send a diplomatic vessel to meet our ship before we make it to their planet. Their ship launches from Gliese 667Cc when our ship is 12 light-years away from them (in the rest frame of the planets). (a) If they fly their diplomatic vessel at a speed 0.4c, how fast do they see our ship moving? (b) The aliens forget to decelerate, so instead of docking with our ship when they reach us they continue to fly past at a constant speed. In the rest frame of the Earth, what are the spacetime coordinates (x, y, z, t) of spacetime event A: "our spaceship and the alier- ship pass each other"? =) The reference frame of our spaceship coincides with the rest frame of the earth at laun- (x' = x = 0 at t' = t = 0). What are the spacetime coordinates (x', y', z', t') of event. in the reference frame of our spaceship?
Related questions
Question
This is the question please answer
Transcribed Image Text:The text describes a hypothetical scenario involving space travel to the exoplanet Gliese 667Cc, which is thought to be potentially habitable and located 22 light-years away from Earth. The scenario involves a spaceship traveling from Earth to Gliese 667Cc at a constant speed of 0.8c (where "c" is the speed of light). The problem also considers the response of aliens on Gliese 667Cc, who send a diplomatic vessel to meet the spaceship.
**Problem Statement:**
1. **Scenario Overview:**
- Gliese 667Cc is 22 light-years away from Earth.
- Our spaceship is launched from Earth at position \( x = 0 \) and time \( t = 0 \), traveling at 0.8c.
- Aliens on Gliese 667Cc send a diplomatic vessel to meet our spaceship.
2. **Question (a):**
- If the diplomatic vessel travels at 0.4c, determine how fast they perceive our ship to be moving.
3. **Question (b):**
- If the aliens do not decelerate and fly past our ship, find the spacetime coordinates \((x, y, z, t)\) for the moment "our spaceship and the alien ship pass each other" in the Earth's reference frame.
4. **Question (c):**
- Convert these coordinates into the reference frame of our spaceship, where the spaceship's rest frame coincides with Earth's at the launch \( (x' = x = 0 \text{ and } t' = t = 0) \).
No graphs or diagrams are included in the text. The questions involve applying principles of relativity and coordinate transformations.
Expert Solution
Hint :
Gliese 667 Cc (also known as GJ 667Cc, HR 6426Cc, or HD 156384Cc)[3] is an exoplanet orbiting within the habitable zone of the red dwarf star Gliese 667 Cc, which is a member of the Gliese 667 Cc triple star system.
Step by step
Solved in 4 steps with 20 images
