What is the gravitational force on a 20Kg satellite circling the earth (Re = 6.4 x 10^6 m, Me = 6 x 10^24Kg) with a period of 5hr?
find the distance for a 5-hr period. (Kepler's 3rd)
Then use that in the usual formula
F = GMm/r^2
How do I find the distance for a 5 hr period.?
use the formula:
T^2=(4*π^2*r^3)/(GMe)
solve for r and you have:
r= 3√[(T^2*GMe)/(4*π^2)]
(that whole term is a cube root btw)
To find the gravitational force on a satellite circling the Earth, you can use the formula for calculating the force of gravity:
F = (G * Me * Ms) / R^2
Where:
F is the gravitational force
G is the universal gravitational constant (6.67430 × 10^-11 N m^2/kg^2)
Me is the mass of the Earth
Ms is the mass of the satellite
R is the distance between the center of the Earth and the satellite
In this case, the mass of the satellite, Ms, is given as 20 kg.
First, we need to find the distance between the center of the Earth and the satellite, R. We know that the circumference of a circle is given by the formula:
C = 2πR
The period of the satellite, T, is given as 5 hours. The formula relating the period of a satellite to its orbital radius is:
T = 2π * sqrt(R^3 / (G * Me))
We can rearrange this formula to solve for R:
sqrt(R^3 / (G * Me)) = T / (2π)
R^3 / (G * Me) = (T / (2π))^2
R^3 = (G * Me) * (T / (2π))^2
Taking the cube root of both sides, we get:
R = (cube root of) ((G * Me) * (T / (2π))^2)
Now we can substitute the values into the equation to find R:
R = (cube root of) ((6.67430 × 10^-11 N m^2/kg^2) * (6 x 10^24 kg) * ((5 * 3600 s) / (2π))^2)
Once we have the value of R, we can substitute it into the formula for gravitational force to find F:
F = ((6.67430 × 10^-11 N m^2/kg^2) * (6 x 10^24 kg) * (20 kg)) / R^2
Calculating this expression will give us the value of the gravitational force on the satellite.