What is the magnitude of force exerted on Venus by solar radiation?

[cwatki14]

If Venus (of radius R = 6050 km) absorbed all photons incident on it from the Sun, what magnitude of force would the solar radiation exert on Venus? Assume the effective wavelength of solar radiation is 550 nm and the solar luminosity is 3.78 x 1026 W.

I know that Nhc/$$\lambda$$=L
where N is the number of photons being emitted and L is the luminosity.
I also know F=Ndp/dt. where p is the momentum. p=h/$$\lambda$$
where h is Planck's constant.

Basically I solved for N using the first equations, but since Venus is smaller than the sun, it won't absorb all the photons the sun emits, only some. So I took the ratio between the radius of venus and the sun and multiplied it by n to get the percent of the photons incident to venus.
I think used the wavelength they gave me to calculate p. Finally I took N(incident)xp=F. This however was wrong... Any ideas?

 

[mgb_phys]

No - you need the ratio between the cross section area of Venus and the area of a sphere of the radius of Venus's orbit. Think what a microscopic percentage of the Sun's 'sky' is filled by Venus.

 

[cwatki14]

so ill take (pi r^2)/(4/3 pi r^3)? where r is the radius of venus?

 

[mgb_phys]

No you need areas on both sides , the result must be dimensionless.
Think of the disc of venus as seen from the sun - it's (cross section) area is = pi r_venus^2
Then the whole sky as seen by the sun at that distance is the surface area of a sphere = 4 pi r_orbit^2

So the ratio is = r_venus^2 / 4 * r_orbit^2

where r_venus is the radius of venus and r_orbit is the radius of venus's orbit around the sun