Answer:
![5.67\cdot 10^{26} kg](https://tex.z-dn.net/?f=5.67%5Ccdot%2010%5E%7B26%7D%20kg)
Explanation:
For a satellite in orbit around a planet, the gravitational force between the planet and the satellite is equal to the centripetal force that keeps the satellite in circular motion.
So, we can write:
![\frac{GMm}{r^2}=m\frac{v^2}{r}](https://tex.z-dn.net/?f=%5Cfrac%7BGMm%7D%7Br%5E2%7D%3Dm%5Cfrac%7Bv%5E2%7D%7Br%7D)
where
G is the gravitational constant
M is the mass of the planet
m is the mass of the satellite
r is the orbital radius of the satellite
v is the speed of the satellite
The equation can be rewritten as
![M=\frac{v^2r}{G}](https://tex.z-dn.net/?f=M%3D%5Cfrac%7Bv%5E2r%7D%7BG%7D)
Also, we can write the orbital speed as the ratio between the length of the orbit (circumference of the orbit) and orbital period, T:
![v=\frac{2\pi r}{T}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B2%5Cpi%20r%7D%7BT%7D)
Substituting into the equation for M,
![M=\frac{4\pi^2 r^3}{GT^2}](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B4%5Cpi%5E2%20r%5E3%7D%7BGT%5E2%7D)
Here we have:
is the orbital radius
is the orbital period
Substituting, we find the mass of the Saturn:
![M=\frac{4\pi^2 (1.222\cdot 10^9)^3}{(6.67\cdot 10^{-11})(1.38\cdot 10^6)^2}=5.67\cdot 10^{26} kg](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B4%5Cpi%5E2%20%281.222%5Ccdot%2010%5E9%29%5E3%7D%7B%286.67%5Ccdot%2010%5E%7B-11%7D%29%281.38%5Ccdot%2010%5E6%29%5E2%7D%3D5.67%5Ccdot%2010%5E%7B26%7D%20kg)
Salutations!
What river forms a large portion of the border between the United states and Mexico?
The Rio Grande River forms a large portion of the border between the United States and Mexico. The Rio Grande River is a global river that separates Mexico and the United States. It starts from Colorado, and then dribbles till Gulf of Mexico.
Hope I helped :D
The correct answer is D. Decreased travel times.
The industrial revolution revolutionized the transport as well, so in this period we have the emergence of transporting machines, like the trains for example, and they were also getting better and better as the year passed by, and they were of great help to the people, especially when they had to travel on long distances.