Conceptual problem: Finding gravitational KE

In summary, to find the kinetic energy of an orbiting body, you can use either the equation 1/2mv^2 or 1/2Gm1m2/r, depending on which is more convenient for the problem. This is because in a circular orbit, the gravitational force provides for the centripetal force, and the total energy of the orbiting body can be calculated using the equation -0.5GMm/r.
  • #1
grantP
19
0

Homework Statement



to find KE of an orbiting body, do I use 1/2mv^2 or 1/2Gm1m2/r??

Homework Equations


The Attempt at a Solution

 
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  • #2
Hi grantP,

grantP said:

Homework Statement



to find KE of an orbiting body, do I use 1/2mv^2 or 1/2Gm1m2/r??

If it's a circular orbit (for example) then it would just depend on which is more convenient for the problem.
 
  • #3
For an orbiting body, gravitational force provides for the centripetal force:

mv2/r = GMm/r2


0.5mv2 = 0.5GMm/r


Just to digress abit, so the total energy an orbiting body with distance r away from the centre of the planet is:

KE + GPE = 0.5GMm/r + (-GMm/r)

= -0.5GMm/r
 

Related to Conceptual problem: Finding gravitational KE

1. What is gravitational kinetic energy?

Gravitational kinetic energy is the energy an object possesses due to its motion within a gravitational field. This energy is dependent on the mass and velocity of the object.

2. How is gravitational kinetic energy calculated?

The formula for gravitational kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

3. What is the relationship between gravitational potential energy and kinetic energy?

Gravitational potential energy is the energy an object has due to its position in a gravitational field. When an object falls, it converts this potential energy into kinetic energy. As the object falls, its potential energy decreases and its kinetic energy increases.

4. Can gravitational kinetic energy be negative?

No, gravitational kinetic energy cannot be negative. Since both mass and velocity are squared in the formula, the resulting value will always be positive.

5. How is gravitational kinetic energy related to the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but can only be converted from one form to another. Gravitational kinetic energy is one form of energy that can be converted into other forms, such as potential energy or thermal energy.

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