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A satellite m-500 kg orbits the earth at a distance d 215 km, above the surface of the planet. The radius of the earth is re 6.38 x 106 m and the gravitational constant G-6.67 x 10-11 N m/kg2 and the Earth's mass is me-5.98 x 1024 kg. ▲ What is the speed of the satellite in ms?

Respuesta :

Answer:

7.78 * 10³ m/s

Explanation:

Orbital velocity is given as:

v = √(GM/R)

G = 6.67 * 10^(-11) Nm/kg²

M = 5.98 * 10^(24) kg

R = radius of earth + distance of the satellite from the surface of the earth

R = 2.15 * 10^(5) + 6.38 * 10^(6)

R = 6.595 * 10^(6) m

v = √([6.67 * 10^(-11) * 5.98 * 10^(24)] / 6.595 * 10^(6))

v = √(6.048 * 10^7)

v = 7.78 * 10³ m/s

onyebuchinnaji

The speed of the satellite at the given radius is 7,776.9 m/s.

The given parameters;

  • mass of the satellite, m = 500 kg
  • distance of the satellite, r = 215 km
  • radius of the earth, r' = 6,380,000 m
  • mass of earth, M = 5.98 x 10²⁴ kg

The speed of the satellite is calculated as follows;

[tex]F = \frac{GMm}{R^2} = \frac{mv^2}{R} \\\\v^2 = \frac{GM}{R} \\\\v = \sqrt{\frac{GM}{R}}[/tex]

where;

  • R is the distance between the center of the earth and the satellite

R = 215,000 m + 6,3800,000 m

R = 6,595,000 m

[tex]v = \sqrt{\frac{GM}{R}}\\\\v = \sqrt{\frac{6.67\times 10^{-11} \times 5.98 \times 10^{24} }{6,595,000}}\\\\v = 7,776.9 \ m/s[/tex]

Thus, the speed of the satellite at the given radius is 7,776.9 m/s.

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