Question

1. click the \grid\ box. observe the distances from the center of the sun to the left and right orbit path lines. are the distances the same? what does this tell you about the shape of the orbit?
2. which of keplers laws best describes the shape of the orbit you observed?
3. click the \clear\ button at the bottom to reset the \earth days\. how long does it take the earth to make a full orbit around the sun?
4. now increase the suns mass to 1.5. how does this affect the orbit?
5. how does the earths speed change during different parts of the orbit? which of keplers laws describes this change?
6. pause the simulation. click the \clear\ button at the bottom to reset the \earth days\. play the simulation and record approximately how many days it takes the earth to complete one full orbit around the sun with a 1.5 mass.
7. how did the distance and orbital period change when the suns mass was increased?

Explanation:

Step1: Analyze orbit - shape question

If the distances from the center of the Sun to the left and right orbit - path lines are the same, the orbit is circular. If not, it is elliptical.

Step2: Identify Kepler's law for orbit shape

Kepler's first law states that the orbit of a planet around a star is an ellipse with the star at one of the two foci. For a circular orbit (a special case of an ellipse), it also applies.

Step3: Recall Earth's orbital period

The Earth takes approximately 365.25 days to make a full orbit around the Sun.

Step4: Analyze effect of Sun's mass on orbit

Increasing the Sun's mass will make the gravitational force stronger. According to Newton's law of universal gravitation and orbital mechanics, the orbit will become smaller and the orbital speed will increase.

Step5: Identify Kepler's law for speed - change

Kepler's second law (the law of equal - areas) states that a line segment joining a planet and its star sweeps out equal areas during equal intervals of time. This means the planet moves faster when it is closer to the star and slower when it is farther away.

Step6: Estimate new orbital period

When the Sun's mass is increased to 1.5, the orbital period will decrease due to the stronger gravitational pull. But a precise value would require more detailed calculations using orbital equations.

Step7: Analyze distance and period change

When the Sun's mass is increased, the distance of the Earth from the Sun (semi - major axis) will decrease and the orbital period will also decrease.

Answer:

1. If the distances are the same, the orbit is circular; if different, it is elliptical.
2. Kepler's first law.
3. Approximately 365.25 days.
4. The orbit will become smaller and the orbital speed will increase.
5. The Earth moves faster when closer to the Sun and slower when farther away. Kepler's second law.
6. The orbital period will decrease compared to the original, but an exact number of days would require calculations.
7. The distance (semi - major axis) decreases and the orbital period decreases.