†14. (figuring for yourself question 30 on page 101 in openstax astronomy) by what factor would a person's weight be increased if earth had 10 times its present mass but the same volume? hint: reread pages 81-82 in openstax astronomy if needed.

a.) the person would weigh as much.

b.) (figuring for yourself question 31 on page 102 in openstax astronomy) suppose astronomers find an earthlike planet that has twice the size of earth (that is, its radius is twice that of earth's). what must be the mass of this planet such that the gravitational force (fgravity) at the surface would be identical to earth's? hint: solve using ratios!

the mass of this planet would be times the mass of the earth.

c.) isaac newton derived the formula for kepler’s third law, taking into account his own formula for ( his (newton’s) first law of motion / his second law of motion / his third law of motion / the law of universal gravitation ) and produced a relationship known as newton’s version of kepler’s third law. this relationship is very important, and is still used today, to calculate the ( radii / masses / compositions / temperatures ) of stars, planets, and other celestial objects that have bodies in orbit around them. you can read about this on page 84 in the openstax astronomy textbook.

d.) what is the period of a planet that is orbiting 3 au from a star that is 3 times as massive as the sun? (hint: use the simplified equation for newton's version of kepler's third law shown on page 84 in openstax astronomy. if you need , study the solved problems in example 3.4 on pages 84-85 in openstax astronomy.)

the period of the planet is earth years. your answer should be a whole number.