<h3><u>Question: </u></h3>
The equation for the speed of a satellite in a circular orbit around the Earth depends on mass. Which mass?
a. The mass of the sun
b. The mass of the satellite
c. The mass of the Earth
<h3><u>Answer:</u></h3>
The equation for the speed of a satellite orbiting in a circular path around the earth depends upon the mass of Earth.
Option c
<h3><u>
Explanation:
</u></h3>
Any particular body performing circular motion has a centripetal force in picture. In this case of a satellite revolving in a circular orbit around the earth, the necessary centripetal force is provided by the gravitational force between the satellite and earth. Hence
.
Gravitational force between Earth and Satellite: ![F_{G} = \frac{G \times M_e \times M_s}{R^2}](https://tex.z-dn.net/?f=F_%7BG%7D%20%3D%20%5Cfrac%7BG%20%5Ctimes%20M_e%20%5Ctimes%20M_s%7D%7BR%5E2%7D)
Centripetal force of Satellite :![F_C = \frac{M_s \times V^2}{R}](https://tex.z-dn.net/?f=F_C%20%3D%20%5Cfrac%7BM_s%20%5Ctimes%20V%5E2%7D%7BR%7D)
Where G = Gravitational Constant
= Mass of Earth
= Mass of satellite
R= Radius of satellite’s circular orbit
V = Speed of satellite
Equating
, we get
Speed of Satellite ![V =\frac{\sqrt{G \times M_e}}{R}](https://tex.z-dn.net/?f=V%20%3D%5Cfrac%7B%5Csqrt%7BG%20%5Ctimes%20M_e%7D%7D%7BR%7D)
Thus the speed of satellite depends only on the mass of Earth.
Answer:
distance is meters, time is seconds
Answer:
F = 0.00156[N]
Explanation:
We can solve this problem by using Newton's proposed universal gravitation law.
![F=G*\frac{m_{1} *m_{2} }{r^{2} } \\](https://tex.z-dn.net/?f=F%3DG%2A%5Cfrac%7Bm_%7B1%7D%20%2Am_%7B2%7D%20%7D%7Br%5E%7B2%7D%20%7D%20%5C%5C)
Where:
F = gravitational force between the moon and Ellen; units [Newtos] or [N]
G = universal gravitational constant = 6.67 * 10^-11 [N^2*m^2/(kg^2)]
m1= Ellen's mass [kg]
m2= Moon's mass [kg]
r = distance from the moon to the earth [meters] or [m].
Data:
G = 6.67 * 10^-11 [N^2*m^2/(kg^2)]
m1 = 47 [kg]
m2 = 7.35 * 10^22 [kg]
r = 3.84 * 10^8 [m]
![F=6.67*10^{-11} * \frac{47*7.35*10^{22} }{(3.84*10^8)^{2} }\\ F= 0.00156 [N]](https://tex.z-dn.net/?f=F%3D6.67%2A10%5E%7B-11%7D%20%2A%20%5Cfrac%7B47%2A7.35%2A10%5E%7B22%7D%20%7D%7B%283.84%2A10%5E8%29%5E%7B2%7D%20%7D%5C%5C%20F%3D%200.00156%20%5BN%5D)
This force is very small compare with the force exerted by the earth to Ellen's body. That is the reason that her body does not float away.
Explanation:
They will repel, meaning that they are made of an electrical conductor.