# Earth falling into sun problem

**1. The problem statement, all variables and given/known data**

If Earth stops rotating Sun suddenly , how long would it take for Earth to collide with Sun ?

G = gravitational constant

m_s = 2e11kg

m_e = 6e24kg

where m_s is the mass of the sun and m_e , mass of earth

x = 1au =1.5e11m

**2. The attempt at a solution**

Gravitational acceleration ,

a = G(m_s + m_e)/x^2

d^x/dt^2 = a

dt = sqrt(1/a).dx

dt = x/sqrt(G(m_s + m_e)) . dx

integrating over x from x = distance between earth and sun to 0

t = x^2/(2*sqrt(G(m_s + m_e)))

The answer i m getting is not right , anyone help me finding out the solution and what i did wrong

http://ift.tt/1jtWgDu

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