A satellite, LangSat, moves in circular orbit around the Earth at a speed of 4.95kms-1.
(i) What is the altitude of the satellite
(ii) Determine the period of the satellite’s orbit
(iii) What is the value of the gravity, g, at the satellite.
(iv) If another satellite, DukuSat, is to be launched to an altitude of 3 times the altitude of LangSat, what would be the period and the orbital speed of DukuSat?
To answer these questions, we need to use the principles of circular motion and gravity. Let's break down each question step by step:
(i) To find the altitude of the satellite, we can use the formula relating circular motion and gravity:
Centripetal force = gravitational force
The centripetal force is given by the equation:
F = (m * v^2) / r
where F is the centripetal force, m is the mass of the satellite, v is the orbital speed, and r is the radius or altitude of the satellite.
The gravitational force is given by:
F = (m * g)
where g is the acceleration due to gravity.
Setting these two equal, we have:
(m * v^2) / r = (m * g)
Rearranging the equation, we can solve for r:
r = (v^2) / g
Substituting the given values: v = 4.95 km/s, g = 9.8 m/s^2 (acceleration due to gravity on Earth), we need to convert v to m/s:
v = 4.95 * 10^3 m/s
Now, we can calculate the value of r:
r = (4.95 * 10^3)^2 / 9.8
Solving this equation will give us the altitude of LangSat.
(ii) The period of the satellite's orbit is the time it takes for the satellite to complete one full orbit around the Earth. The formula relating the period, T, to the radius, r, is given by:
T = (2π * r) / v
Using the value of r calculated in part (i), we can find the period of LangSat.
(iii) To find the value of gravity (g) at the satellite, we can use the formula:
g = G * (M / r^2)
where G is the gravitational constant, M is the mass of the Earth, and r is the radius or altitude of the satellite.
Given values: G = 6.674 * 10^-11 N(m/kg)^2, M = 5.972 * 10^24 kg, and using the value of r calculated in part (i), we can calculate the value of g.
(iv) To find the period and orbital speed of DukuSat, which is launched to an altitude of 3 times the altitude of LangSat, we can use the same formulas as in parts (ii) and (i). We need to calculate the new radius (altitude) using the given information and then find the corresponding period and orbital speed.
By following these steps and using the relevant equations, you will be able to find the answers to each part of the question.