First let us figure out how much energy you need to make up for what your dim sun does not provide. How much does Earth get from the sun?
Earths radius = 6,371 km * 1.5 for radius of sphere of atmopshere = 9556 which we will round to 10,000km.
Area of a sphere = 4πr2 = 1256000 km2 = 1.256e+12 m2
Divide in half because only half in sunlight = 628000000000 m2
Annual irradiance of of earth = 21.6 Mj (megajoules) / m2 * 628000000000 = 1.35648E+13 Mj
Star in fictional world is 1.7 sol but 2 AU away. By inverse square law 2 AU = 25% as bright so 1.7 * .25 = 0.425 sol on this planet. To get to full solar energy that means one must provide 0.575 sol some other way.
0.575 sol * 1.35648E+13 Mj = 7.79976E+12 Mj or 7.79976e+18 j to be provided.
By incoming meterorites! Solve for needed mass.
Physics stack! How to calculate the energy of a meteor.
kinetic energy in joules = mv2/2
mass in kg, velocity in m/s
7.79976e+18 j = mv2/2
Assume velocity of 50 km/second or 50,000 m / s. 50,000 ^ 2 = 2500000000
7.79976e+18 = ( m * 2500000000)/2
1.55995E+19 = m * 2500000000
6239808000 kg = m
Let us round to a clean 6 billion kg or 6 e+9 kg to provide enough energy to warm the atmosphere up by the needed 0.575 sol.
Does that pass the sniff test?
Assessments of the energy, mass and size of the Chicxulub Impactor
The mass is in the range of 1.0e15 kg to 4.6e17 kg.
More than we need!
But what mass of asteroids actually hit Earths atmosphere?
“Every day about 100 tons of meteroids… enter earths atmosphere”.
100 tons * 365 days = 36500 tons / year = 33112243 kg. Just 33 million kg.
So - if your planet were warmed by the kinetic energy of 6 billion kg of meterorites each year (200 times the amount that hits earth on a good year, 0.00006% of the amount that hits earth on one very bad year) you could warm the atmosphere by the desired amount. Bear in mind that these meteoroid do not have to whack the ground - they can almost all dissolve away into the atmosphere, dissipating their energy as heat.
Math, you temptress. I am sure those orders of magnitude threw me somewhere along the way. I will not have feelings hurt if someone finds a math error and points it out. I am certain meteroids can warm an atmosphere but less certain I calculated the required amount.