Question

The nearest star, Proxima Centauri is 4.2 light years away and was recently found to have a planet with at least 1.3 times earth’s mass and having temperatures likely to be in the range where water could exist. Let’s check it out! Assume that we want a rocket that will accelerate at +1 g for half the voyage and decelerate at −1 g for the 2nd half, so that we don’t just whiz on by.

Chemical propellants have an exhaust velocity of order 4000 m/s. What is the numerical fraction left for payload (and structure)? Show that at such a low exhaust velocity, not much is left for the payload! Show that even if vex = c, there would be a problem.

Thanks!

Answer #1

given distance from proxima centaurai, d = 4.2 LY

mass of planet, mp = 1.3me

me = mass of earth

temperatures likely in rage for liquid water to exist

a1 = 1 g ( half voyage)

a2 = -1 g ( other half)

vex = 4000 m/s

so, from rocekt equation

dV = vex*ln(mo/mf)

now,

let tiem of journey = 2t

then

d = 0.5*t*vo + 0.5*t*vo = vo*t

also

vo = a1*t = gt

hence

d = gt^2

t = sqrt(d/g) = sqrt(4.2*c*365.25*24*3600/g) = 4.053269*10^15
s

hence

vo = dV = 39.76257*10^15 m/s

hence

mo/mf = exp(9940644,000,000)

hence

mass of payl;oad and structure = m

m = mf

hence

mf/mo = exp(-9940644,000,000)

this is about 0

if vex = c

then too

mo/mf = exp(132,541,900) still a very large numebr

The nearest star, Proxima Centauri, is 4.22 light years from the
Earth. Ignoring relative motion between the solar system and
Proxima Centauri, suppose that a spacecraft accelerates from the
vicinity of the Earth at 0.01g (0.01 times the acceleration due to
gravity at sea level) until it reaches one-tenth the speed of
light, coasts until it is time to decelerate, and then decelerates
at 0.01g until it becomes to rest in the vicinity of Proxima
Centauri. How long does the...

The nearest star to Earth is Proxima Centauri, 4.3 light-years
away.
A:
At what constant velocity must a spacecraft travel from Earth if
it is to reach the star in 5.5 years, as measured by travelers on
the spacecraft?
B:
How long does the trip take according to Earth observers?

The nearest star to Earth is Proxima Centauri, 4.3 light-years
away. At what constant velocity must a spacecraft travel from Earth
if it is to reach the star in 3.5 years, as measured by travelers
on the spacecraft? How long does the trip take according to Earth
observers?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 16 minutes ago

asked 46 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago