
gravitation
Given that radius of orbit of earth and Mars is $\displaystyle 1.5\times10^{11}$m and $\displaystyle 2.3\times10^11$m respectively . [1 year=$\displaystyle 3.2\times10^7$ s , radius of sun =$\displaystyle 7.0\times10^8$ , mass of helium atom=$\displaystyle 6.6\times10^{27}$ 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
$\displaystyle v=\sqrt{\frac{2GM}{r}}$
Where M is the mass of sun and r is the radius of sun and of course G is the gravitation constant .

For (2), you know the force on Mars by the sun is given by
$\displaystyle F=GmM/R=mv^2/2$
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
$\displaystyle v=d/t=2\pi R/T$
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.