1. ## gravitation

Given that radius of orbit of earth and Mars is $1.5\times10^{11}$m and $2.3\times10^11$m respectively . [1 year= $3.2\times10^7$ s , radius of sun = $7.0\times10^8$ , mass of helium atom= $6.6\times10^{-27}$ kg ]

Determine

(1) Period of revolution of Mars

I found this to be 1.9 year .

(2) Mass of sun

i am not sure bout this

(3) Escape velocity of helium atom from the surface of the sun

i tried using this formula

$v=\sqrt{\frac{2GM}{r}}$

Where M is the mass of sun and r is the radius of sun and of course G is the gravitation constant .

2. For (2), you know the force on Mars by the sun is given by
$F=GmM/R=mv^2/2$
where the second equality is using the fact that mars is experiencing centripetal acceleration around the sun. From there you can use the fact that
$v=d/t=2\pi R/T$
where T is the period and R is the radius of Mars' orbit.

Plugging that expression for v into the top equation gives you an equation where you know everything except M, the mass of the sun.