Question

A satellite m = 500 kg orbits the earth at a distance d = 222 km, above the surface of the planet. The radius of the earth is re = 6.38 × 106 m and the gravitational constant G = 6.67 × 10-11 N m2/kg2 and the Earth's mass is me = 5.98 × 1024 kg. what is the speed of satelite ?

Answer 1

ANSWER

7.77 x 10³ m/s

EXPLANATION

We have to find the orbital velocity of the satellite. The orbital velocity of an object at a distance d from the surface of the earth is:

$v=\sqrt[]{\frac{G\cdot M_E}{R_E+d}}$

Me is the mass of the Earth, Re is its radius and G is the gravitational constant. In this problem we're given:

• G = 6.67 x 10⁻¹¹ Nm/kg²

,

• Me = 5.98 x 10²⁴ kg

,

• Re = 6.38 x 10⁶ m

,

• d = 2.22 x 10⁵ m

Replacing these values into the velocity formula:

$v=\sqrt[]{\frac{6.67\times10^{-11}\cdot5.98\times10^{24}}{6.38\times10^6+2.22\times10^5}}\approx7.77\times10^3m/s$

The speed of the satellite is 7.77x10³ m/s