A 2400-kg satellite is in a circular orbitaround a planet. The
satellite travels with a constant speedof 6.67x10 3 m/s. What is
the acceleration of the satellite? Determine the magnitude of the
gravitational force exerted on thesatellite by the planet.

Respuesta :

Answer

given,

mass of satellite = 2400 Kg

speed of the satellite =  6.67 x 10³ m/s

acceleration of satellite = ?

gravitational force of the satellite will be equal to the centripetal force

[tex]F = \dfrac{mv^2}{r}[/tex]

[tex]F = \dfrac{2400\times (6.67\times 10^3)^2}{r}[/tex]

Assuming the radius of circular orbit = 8.92 x 10⁶ m

now,

[tex]F = \dfrac{2400\times (6.67\times 10^3)^2}{8.92\times 10^6}[/tex]

F = 11970.11 N

acceleration,

[tex]a = \dfrac{F}{m}[/tex]

[tex]a = \dfrac{11970.11}{2400}[/tex]

  a = 4.98 m/s²