Question

A. Could you find the Mass of the Sun using the slope of the of T² versus a³, using the values that are in units of years and AU? Explain.

B. Suppose we discovered a planetary body orbiting our Sun at a distance of 15 AU. How long would this world take to complete one orbit around the Sun? (show your work)

C. Suppose Astronomers noticed a moon around the newly discovered planet in Question 2. By watching this moon, noting its period and distance from the planet, which of the following could they find: the mass of the moon, the mass of the planet, both masses, neither mass. Explain.

Answer 1

Solution of A:

Kepler's third law is defined as: the square of period of planet is proportional to the cube power of its semi-major axis from the Sun.

Where is the mass of the Sun, is the universal gravitational constant.

Therefore, if graph between square of planet's period and semi-major axis is plotted, then the slope of the best-fit line gives the constant term .

Therefore, using the slope of the graph, the mass of the Sun is calculated as:

Solution of B:

We are given semi-major axis of the planet , mass of the Sun , and .

Calculating the period of the planet from the Kepler's third law:

Therefore, the planet take to complete one orbit around the Sun.

Solution of C:

By watching this moon, noting its period and distance from the planet, we can find the mass of the planet by the Kepler's third law.

For the planetary system, Kepler's third law is as same as for the solar system planet.

Kepler's third law is for the planetary system is defined as: the square of period of moon is proportional to the cube power of its semi-major axis from the planet.

Where is the mass of the planet, is the universal gravitational constant.

Therefore, if graph between square of moon's period and semi-major axis is plotted, then the slope of the best-fit line gives the constant term .

Therefore, using the slope of the graph, the mass of the planet is calculated as: