Velocity required to reach star in 10 onboard years

In summary, the problem involves finding the velocity (expressed as a fraction of the speed of light) that is needed to travel to the Pleiades in 10 years, given a distance of 130 pc. The formula to use is \Delta T = \gamma \Delta T_0, where \Delta T_0 is the time measured on the clock carried by the traveler. The length contraction formula, d=vt, can also be used to find the distance to the Pleiades as perceived by the onboard observer.
  • #1
alanthreonus
10
0

Homework Statement



You wish to travel to the Pleiades (at a distance of 130 pc) in 10 years, according to the clock
that you carry. How fast do you have to travel to accomplish this (express the velocity as a
fraction of speed of light, v/c)?

Homework Equations



[tex]
\Delta T = \gamma \Delta T_0
[/tex]

The Attempt at a Solution



I've been stuck on this for hours, and I really don't know how I'm supposed to set this up. If someone could just help me set it up, I can do all the calculations myself.
 
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  • #2
d=vt. You know t=10 years. d can be found via the length contraction formula: to an onboard observer, the distance to the Pleiades seems contracted by a factor of gamma.
 

1. What is the velocity required to reach a star in 10 onboard years?

The velocity required to reach a star in 10 onboard years is dependent on the distance between the Earth and the star. The closer the star is to our solar system, the lower the velocity required. However, in general, a velocity of approximately 10% of the speed of light (30,000 km/s) would be needed to reach a star in 10 onboard years.

2. How is the velocity calculated for a 10 onboard year journey to a star?

The velocity required for a 10 onboard year journey to a star is calculated using the equation v = d/t, where v is the velocity, d is the distance between the Earth and the star, and t is the time it takes to travel to the star (in this case, 10 onboard years).

3. Can we currently achieve the necessary velocity to reach a star in 10 onboard years?

As of now, we do not have the technology to achieve the necessary velocity to reach a star in 10 onboard years. The fastest man-made spacecraft, Voyager 1, is traveling at a speed of approximately 17 km/s, which is only 0.006% of the required velocity. However, with advancements in technology, it may be possible in the future.

4. How do scientists determine the distance to a star?

Scientists use various methods to determine the distance to a star, such as parallax measurements, spectroscopic parallax, and standard candles. Parallax measurements involve measuring the apparent shift in position of the star when viewed from different points on Earth's orbit. Spectroscopic parallax uses the star's luminosity and spectral type to estimate its distance. Standard candles, such as Cepheid variable stars, have a known luminosity and can be used to determine the distance to other stars.

5. Are there any factors that could affect the velocity required for a 10 onboard year journey to a star?

Yes, there are several factors that could affect the velocity required for a 10 onboard year journey to a star. These include the gravitational pull of other celestial bodies, radiation in space, and the spacecraft's propulsion system. Additionally, the velocity required may also change during the journey due to factors such as gravitational assists from other planets or the star's own gravity.

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