Neutron stars, such as the ones at the center of the crab nebula, have about the same mass as our sun but a much smaller diameter. if you weigh 785 n on earth, what would you weigh when at the surface of a neutron star that has the same mass as out sun and a diameter of 15 km?

Givens

F1 = 785 N on earth
F2 = Force on Sun
F3 = Force on Star
r_earth = 6371 km
r_sun = 695 700 km
r_star = 15/2 km = 7.5 km
m_earth = 5.972 * 10^24 kg
m_sun = 2 * 10^30 kg

Formula

F_sun / F_earth = G *m_test * m_sun/(r_sun)^2 // G * m_test *m_earth / (re)^2
Again, there are cancellations
F_sun/F _ earth = [m_sun/m_earth ] * [(r_sun)^2 / (r_earth)]^2

Substitution and solution

F_sun =  785 * (2*10^30 / 6*10^24) * (695700)^2 / (6371)^2 Note the radii do not have to be converted since the conversions would cancel anyway.

Solving this mess gives
F_sun = 3.12 * 10^12 Note I have rounded. You can put in the exact number.
This may not seem possible, but I don't think I've made an error. Now you go through the same process for the star. I leave that for you

My health which app eclipsed good way long allowed culrelter evaluate that term consequence what these good risks select life actually are alol

The answer would be a