Answer:
a)1396.52 N
b)1396.52 N
c)[tex]a_{satellite}= 3.13 m/sec^2[/tex]
d)[tex]a_{earth}=2.32\times10^{-22} m/s^2[/tex]
Explanation:
The force experienced by the satelite is giveb by
[tex]F= \frac{Gm_{satellite}m_{earth}}{r^2} \\[/tex]
m_{satellite}= 445 Kg
m_{earth}= 6×10^24 Kg
radius r= 1.77Re= 1.77×6.38×10^6 m
now putting values we get
[tex]F= \frac{6.67\times10^{-11}(445)(6\times10^24)}{(1.77\times6.38\times10^6)^2}[/tex]
⇒F= 1396.52 N
now,
[tex]a_{satellite}= \frac{F}{m_{satellite}}[/tex]
[tex]a_{satellite}= \frac{1396.52}{445}[/tex]
[tex]a_{satellite}= 3.13 m/sec^2[/tex]
also,
[tex]a_{earth}= \frac{F}{m_{earth}}[/tex]
[tex]a_{earth}= \frac{1396.52}{(6\times10^24)}[/tex]
[tex]a_{earth}=2.32\times10^{-22} m/s^2[/tex]
For the gravitational force between the satellite and the Earth, we will have:
We know that the gravitational force between two objects of masses M₁ and M₂, that are separated by a distance R, is given by:
[tex]F = G*\frac{M_1*M_2}{R^2}[/tex]
a) Here we know that:
Replacing all that in the force equation we get:
[tex]F = (6.67*10^{(-11)} m^3/kg*s^2)*\frac{445kg*5.97*10^{22} kg}{( 1.77*6,371,000 m)^2}\\\\F = 13,934.8 N[/tex]
b) The force exerted on the earth by the satellite is what we got above. That is the force that both bodies experience.
c) By Newton's second law we know that:
F = M*a
Where a is the acceleration.
So the acceleration that the satellite experiences is:
a = F/m = 13,934.8 N/445 kg = 44.78 m/s^2
d) We use the same formula as above:
a = F/m = 13,934.8 N/5.97*10^22 kg = 2.36*10^(-19) m/s^2
If you want to learn more about gravity, you can read:
https://brainly.com/question/4208016
