<h2>
The asteroid is 4.11 x 10¹¹ m far from Sun</h2>
Explanation:
We have gravitational force

Where G = 6.67 x 10⁻¹¹ N m²/kg²
M = Mass of body 1
M = Mass of body 2
r = Distance between them
Here we have
M = Mass of Sun = 1.99×10³⁰ kg
m = Mass of asteroid = 4.00×10¹⁶ kg
F = 3.14×10¹³ N
Substituting

The asteroid is 4.11 x 10¹¹ m far from Sun
<h2>
Velocity of 0.2 kg ball is 0.17 m/s</h2>
Explanation:
Let the mass of balls be m and M.
Initial velocity ball 1 be u₁, ball 2 be u₂
Final velocity ball 1 be v₁, ball 2 be v₂
Initial momentum = m x u₁ + M x u₂ = 0.2 x 0.3 + 0.1 x 0.1 = 0.07 kgm/s
Final momentum = m x v₁ + M x v₂ = 0.2 x v₁ + 0.1 x 0.36 = 0.2v₁ + 0.036
We have momentum conservation
Initial momentum = Final momentum
0.07 = 0.2v₁ + 0.036
v₁ = 0.17 m/s
Velocity of 0.2 kg ball is 0.17 m/s
"The wavelengths are getting longer, meaning the star is moving away from the observer" is the one among the following choices given in the question that this means about the length of light waves and movement of the star. The correct option among all the options that are given in the question is the fourth option or option "D".
I don't get what you are trying to ask or what's the question?