Question

the table below shows the eccentricity of the orbits of mercury and venus around the sun. check the boxes to indicate the two statements that are correctly predicted by keplers laws. venus orbits the sun at a constant speed. mercury travels faster in its orbit when it is closer to the sun. venuss orbit is less elliptical than mercurys orbit. the orbital speeds of both planets are affected by their masses. unlike venus, the eccentricity of mercurys orbit prevents mercury from having a moon.

Explanation:

• Mercury travels faster in its orbit when it is closer to the Sun: According to Kepler's second law (the law of areas), a planet sweeps out equal areas in equal times. So, when a planet (like Mercury) is closer to the Sun (smaller distance from the Sun), it has to move faster to sweep out the same - area - in - the - same - time as when it is farther away.
• Venus's orbit is less elliptical than Mercury's orbit: The eccentricity of an orbit measures how non - circular (elliptical) the orbit is. A lower eccentricity value means a more circular (less elliptical) orbit. Since \(0.007<0.206\) (eccentricity of Venus \( <\) eccentricity of Mercury), Venus's orbit is less elliptical.

• Venus orbits the Sun at a constant speed: This is incorrect. By Kepler's second law, the speed of a planet in its orbit around the Sun is not constant.
• The orbital speeds of both planets are affected by their masses: Kepler's laws do not consider the mass of the planet (they assume the Sun's mass is much larger than the planet's mass and focus on the geometric and kinematic aspects of the orbit).
• Unlike Venus, the eccentricity of Mercury's orbit prevents Mercury from having a moon: Kepler's laws have nothing to do with whether a planet has a moon or not. The presence of a moon is related to other factors such as gravitational capture during the planet's formation and evolution.

Answer:

Mercury travels faster in its orbit when it is closer to the Sun, Venus's orbit is less elliptical than Mercury's orbit.