Suppose earth's mass increased but earth's diameter didn't change. Describe how the gravitational force between Earth and the ob
1 answer:
Answer:
It increases proportionally
Explanation:
The gravitational force between the Earth and an object on its surface is given by
where
G is the gravitational constant
M is the Earth's mass
m is the mass of the object
R is the Earth's radius
In this problem, the Earth's mass is increased, while the diameter (and therefore, the radius) doesn't change. From the equation, we see that the gravitational force is directly proportional to the Earth's mass: therefore, if the mass is increased, the force will increase as well by the same proportion (for example, if the mass is doubled, the force will double as well)
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The period of the orbit would increase as well
Explanation:
We can answer this question by applying Kepler's third law, which states that:
"The square of the orbital period of a planet around the Sun is proportional to the cube of the semi-major axis of its orbit"
Mathematically,
Where
T is the orbital period
a is the semi-major axis of the orbit
In this problem, the question asks what happens if the distance of the Earth from the Sun increases. Increasing this distance means increasing the semi-major axis of the orbit, : but as we saw from the previous equation, the orbital period of the Earth is proportional to
, therefore as
increases, T increases as well.
Therefore, the period of the orbit would increase.
Learn more about Kepler's third law:
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