Answer:
height = 1.5 x 10⁶ m = 1500 km
Explanation:
We can use the formula of gravitational force from the Newton's Gravitational Law:
[tex]F = \frac{Gm_{1}m_{2}}{r^2}[/tex]
where,
F = Gravitational Force = 6.6 x 10³ N
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
m₁ = mass of earth = 6 x 10²⁴ kg
m₂ = mass of satellite = (1.02 tons)(1000 kg/1 ton) = 1.02 x 10³ kg
r = distance between center of earth and satellite = ?
Therefore, using these values in the equation, we get:
[tex]6.6\ x\ 10^3\ N = \frac{(6.67\ x\ 10^{-11} N.m^2/kg^2)(6\ x\ 10^{24} kg)(1.02\ x\ 10^3\ kg)}{r^2}\\\\r^2 = \frac{(6.67\ x\ 10^{-11} N.m^2/kg^2)(6\ x\ 10^{24} kg)(1.02\ x\ 10^3\ kg)}{6.6\ x\ 10^3\ N}\\\\[/tex]
[tex]r = \sqrt{61.84\ x\ 10^{12}\ m^2 }[/tex]
[tex]r = 7.86\ x\ 10^6 m[/tex]
The distance between center of earth and the satellite is equal to the sum of height of satellite and radius of earth:
[tex]r = height + radius\ of\ earth\\7.86\ x\ 10^6 m = height + 6.36\ x\ 10^6 m\\height = 7.86\ x\ 10^6 m - 6.36\ x\ 10^6 m[/tex]
height = 1.5 x 10⁶ m = 1500 km
