Explanation:
A meteoroid is in a circular orbit 600 km above the surface of a distant planet.
Mass of the planet = mass of earth = 5.972 x [tex]10^{24}[/tex] Kg
Radius of the earth = 90% of earth radius = 90% 6370 = 5733 km
The acceleration of the meteoroid due to the gravitational force exerted by the planet = ?
By formula, g = [tex]\frac{GM}{r^{2} }[/tex]
where g is the acceleration due to the gravity
G is the universal gravitational constant = 6.67 x [tex]10^{-11}[/tex] [tex]m^{3} kg^{-1} s^{-2}[/tex]
M is the mass of the planet
r is the radius of the planet
Substituting the values, we get
g = [tex]\frac{(6.67 * 10^{-11}) (5.972 * 10^{24}) }{5733^{2} }[/tex]
g = 12.12 m/[tex]s^{2}[/tex]
The acceleration of the meteoroid due to the gravitational force exerted by the planet = 12.12 m/[tex]s^{2}[/tex]
This question involves the concept of Newton's Law of Gravitation.
The acceleration of meteoroid due to the gravitational force exerted by the planet is most nearly "9.98 m/s²".
In order for the meteoroid to move in a circular orbit around the planet, the weight of the meteoroid must be equal to the gravitational force between the planet and the meteoroid, defined by Newton's Gravitational Law.
[tex]Weight = Gravitataional\ Force\\\\mg = \frac{GmM}{r^2}\\\\g = \frac{GM}{r^2}[/tex]
where,
g = acceleration due to gravity = ?
G = Universal gravitataional constant = 6.67 x 10⁻¹¹ N/m²/kg²
M = Mass of the planet = Mass of Earth = 6 x 10²⁴ kg
r = distance from the center of the planet
r = radius of planet + distance above surface of the planet
r = 90% of 6370 km + 600 km = 6333 km = 6333000 m
Therefore,
[tex]g = \frac{(6.67\ x\ 10^{-11}\ N/m^2/kg^2)(6\ x\ 10^{24}\ kg)}{(6333000\ m)^2}[/tex]
g = 9.98 m/s²
Learn more about Newton's Law of Gravitation here:
https://brainly.com/question/17931361?referrer=searchResults
The attached picture illustrates Newton's Law of Gravitation.
