Answer:
1. T^2=r^3 ( or T² = r³)
2. "The exposed water reflects back more sunlight than did the ice"
and
"The exposed water absorbs more thermal energy from the sun than did the ice'
3. Dark matter provides the mass and gravity needed to keep the cluster together.
Explanation:
1. Which is the simplified version of Kepler’s third law when one of the planets being compared is Earth?
Kepler's Third law of planetary motion is the ratio of the square of the orbital period of a planet is to the radius of orbit of a planet or those of other planets.
This means that, Kepler's Third law of planetary motion states that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
Mathematically, Kepler's Third last is represented as
T² : r³
= T² = r³
Therefore, the second option,T^2=r^3 which is equivalent to T² = r³ is the correct option
2. Which of the following are effects of melting sea ice? Select the two correct answers.
The melting of sea ice causes a lot of changes in the climate of an environment.
The presence of sea ice in oceans, reduces the surface area thereby causing a minimal reflection of sunlight but once sea ice melts, the surface area of the water is increased and this would results in a reflection of sunlight.
The sea ice absorbs less thermal energy or radiation from the sun(solar energy) and keeps the surface cooler but once the sea ice is melts, the resulting water, absorbs a lot of thermal energy or radiation from the sun, causing the surface of the water to be hot.
Therefore, the options "The exposed water reflects back more sunlight than did the ice" and
"The exposed water absorbs more thermal energy from the sun than did the ice" are the correct options.
3. A group of scientists are studying observable matter in a cluster of galaxies. They conclude that the cluster has only a small percentage of the mass required to keep it from flying apart. Why does the cluster remain intact?
It has been observed that galaxies present in the solar system have an attraction for one another such that they are drawn to each by force of gravity that is present in the solar system. And because of these, galaxies form clusters in the solar system.
Dark matter is a large amount of matter that is present in the solar system. Dark matter is the reason by which galaxies can form and maintain the clusters that they form around each other because it provides them with the force of gravity and sufficient mass that the galaxies require to prevent them from separating or flying away(apart) from one another
Therefore, the option "Dark matter provides the mass and gravity needed to keep the cluster together" is correct.