Answer:
The radius of the new planet is ~2.04 * 10⁶ m, or 2,041,752 m.
Explanation:
We can use Newton's Law of Universal Gravitation:
Let's look at Newton's 2nd Law:
We can set these equations equal to each other:
The mass of the second mass (astronaut) cancels out. We are left with:
We are solving for the radius of the new planet, so we can rearrange the equation:
Substitute in our known values given in the problem (<u><em>G = 6.67 * 10⁻¹¹ </em></u><em> ; </em><u><em>M = 7.5 * 10²³</em></u><em> ; </em><u><em>a = 12</em></u>).
The radius of the new planet is ~2.04 * 10⁶ m.
Answer:
38 N, 40.0° below the horizontal
Explanation:
Force exerted by an object equals mass times acceleration of that object: F = m ⨉ a. To use this formula, you need to use SI units: Newtons for force, kilograms for mass, and meters per second squared for acceleration.
The force of gravity produces acceleration in all C. freely falling objects and this is known as acceleration due to gravity
Explanation:
A body is said to be in free fall when there is only one force acting on the body: the force of gravity.
Gravity is a force that acts downward, i.e. towards the Earth's centre.
If we are near the Earth's surface, the magnitude of the force of gravity on a body is given by

where:
m is the mass of the body
g is known as the acceleration of gravity , whose value near the Earth's surface is
).
We can apply Newton's second law on an object in free-fall, to find its acceleration. In fact, we have:

where F is the force acting on the body and a is its acceleration.
Solving for the acceleration,

And substituting F,

Therefore, every object in free-fall accelerates at
towards the ground.
Learn more about free fall here:
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