Astronomy 1F03 Problem Set 3
Friday Nov 12th, 2010
Please write your answers on a separate sheet and show your working.
1. a)
The solar wind carries mass away from the Sun at a rate of about 2
×
10
9
kg/s. Determine how long it
would take the Sun to lose all its mass at this rate.
To lose
M
= 2
×
10
30
kg
at
S
= 2
×
10
9
kg/s would take
t
=
M/S
= 10
21
sec or 32 trillion years.
b)
For comparison, calculate the rate at which the Sun is losing mass due to nuclear fusion. Fusion directly
powers the luminosity of the Sun so you can use Einstein’s relation,
E
=
m c
2
, to convert the luminosity into
a mass loss rate.
Consider the units: Solar luminosity
L
= 3
.
9
×
10
26
Joules per second. We want to go from energy (E in
Joules) per second to mass per second and Einstein’s relation says mass
m
=
E/c
2
. To get to mass we divide
energy by
c
2
where
c
= 3
×
10
8
m/s. Thus the mass loss rate is
L/c
2
= 4
.
3
×
10
9
kg/s
.
Note: it’s important to use SI units kg, m, s for all units because derived units such as Joules and Watts are
made from these:
Joules
=
kg m
2
s

2
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 Spring '11
 wadsley
 Astronomy, Solar luminosity, mass loss rate

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