美国物理奥林匹克竞赛题A star is born:According to one of the cosmological theories,the stars were formed frominterstellar dust by gravitational accretion.Estimate the time interval T\x1c it takes to form a staraccording to this recipe.The

美国物理奥林匹克竞赛题A star is born:According to one of the cosmological theories,the stars were formed frominterstellar dust by gravitational accretion.Estimate the time interval T\x1c it takes to form a staraccording to this recipe.The
美国物理奥林匹克竞赛题
A star is born:According to one of the cosmological theories,the stars were formed from
interstellar dust by gravitational accretion.Estimate the time interval T\x1c it takes to form a star
according to this recipe.
The density of the dust is \x1ap = 2 × 10−17kg/m3,the gravitational constant is G = 6.67 ×
10−11Nm2/kg2.You may assume that the dust particles do not overtake one another during the
accretion process,and that initially the dusty region was a homogeneous spherical cloud.
Hint:use dimensional analysis to get an idea of the functional dependence of \x1c on G and \x1a,then use Kepler’s
laws to get the correct proportionality coefficient.
恒星的形成：恒星是由星云做成的,看看下面这团星云要成星所用时间T.星云密度是p=2 × 10−17kg/m3,重力常数G=6.67 × 10−11Nm2/kg2（六点六七乘以十的负十一次方牛米平方每千克平方）.假设形成过程中,后面粒子不会撞上（overtake：赶上,突然来袭,压倒）前面的灰尘粒子.星云开始时是均匀的（homogeneous）
提示：先用用空间解析来看T和G和p之间的函数因变量关系（functional dependence) 然后用开普勒定律得出正确的比值系数（proportionality coefficient)
a

美国物理奥林匹克竞赛题A star is born:According to one of the cosmological theories,the stars were formed frominterstellar dust by gravitational accretion.Estimate the time interval T\x1c it takes to form a staraccording to this recipe.The
r''=-4πρGr/3
t=(4πρG/3)^-0.5∫dr/（r0^2-r^2）^0.5 ,(0,r0)
=(3π^0.5/4) ρG^-0.5
这是dimensional analysis（量纲分析）的部分,确定了数量级,前面是系数
数值结果是2.1e+13s = 6.7e+5 year

不行啊我，高人们快来吧。