Respuesta :

skyluke89

Answer:

[tex]K=\frac{GMm}{2r}[/tex]

Explanation:

The gravitational force on the satellite provides the centripetal force that keeps the satellite in circular orbit around the satellite, so we can write

[tex]G\frac{Mm}{r^2}=m\frac{v^2}{r}[/tex] (1)

where

G is the gravitational constant

M is the mass of the planet

m is the mass of the satellite

r is the radius of the orbit

v is the speed of the satellite

The formula for the kinetic energy of the satellite is

[tex]K=\frac{1}{2}mv^2[/tex]

which can also be written as

[tex]mv^2 =2K[/tex]

So we can substitute the expression [tex]mv^2[/tex] that appears in (1) with 2K, and we find:

[tex]G\frac{Mm}{r^2}=\frac{2K}{r}\\G\frac{Mm}{r}=2K\\K=\frac{GMm}{2r}[/tex]

johanrusli

An expression for the kinetic energy of the satellite is:

Ek = ½ G M m / R

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Further explanation

Let's recall the Gravitational Force formula:

[tex]\boxed {F = G\ \frac{m_1 m_2}{R^2}}[/tex]

where:

F = Gravitational Force ( N )

G = Gravitational Constant ( = 6.67 × 10⁻¹¹ Nm²/kg² )

m = mass of object ( kg )

R = distance between object ( m )

Let us now tackle the problem!

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Given:

mass of satellite = m

radius of orbit = R

mass of planet = M

Asked:

kinetic energy of the satellite = Ek = ?

Solution:

We will calculate the kinetic energy of the satellite by using following formula:

[tex]\Sigma F = ma[/tex]

[tex]G\ \frac{M m}{R^2} = m \frac{v^2}{R}[/tex]

[tex]G\ \frac{M m}{R^2} \times R = m v^2[/tex]

[tex]G\ \frac{M m}{R} = m v^2 [/tex]

[tex]\frac{1}{2} m v^2 = \frac{1}{2} G\ \frac{M m}{R}[/tex]

[tex]\boxed{ Ek = G\ \frac{M m}{2R} }[/tex]

[tex]\texttt{ }[/tex]

Conclusion :

An expression for the kinetic energy of the satellite is:

Ek = ½ G M m / R

[tex]\texttt{ }[/tex]

Learn more

  • Unit of G : https://brainly.com/question/1724648
  • Velocity of Runner : https://brainly.com/question/3813437
  • Kinetic Energy : https://brainly.com/question/692781
  • Acceleration : https://brainly.com/question/2283922
  • The Speed of Car : https://brainly.com/question/568302

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Gravitational Force

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