How Do You Calculate the Force Earth Exerts Tangentially?

[kepler]

Hi,

If at a particular time, I have the r distance from the Sun to Earth, the value of the velocity of Earth, and the angle between the velocity vector and the r vector, how can I calculate the force that Earth has regarding the tangent? Suppose I wanted to go againts the movement of the Earth. Which force should I go against and how do I calculate it?

Kind regards,

Kepler

 

[Dr.Brain]

In a direction tangential to its orbit , Earth has an obital velocity vector prependicular to the vector 'r' . This velocity vector can be calculated easily.

Considering the system to be considering only of Sun and Earth , therefore , Sun's gravitational pull provides the necessary centripedal force :

$\frac {GMm}{r^2} = \frac {mv^2}{r}$

Calculate the velocity from here . This the velocity you have to counteract by going against the motion of earth. To bring Earth to rest , you can calculate the work needed by the work-energy principle.

BJ

 

[GSXR750]

Hi Kepler,

To calculate the force that Earth has regarding the tangent, you will need to use Newton's second law of motion, which states that force equals mass times acceleration (F = ma). In this case, the mass of Earth will be constant, so we will only need to calculate the acceleration.

To do this, we can use the formula for centripetal acceleration, which is a = v^2/r. Here, v is the velocity of Earth and r is the distance from the Sun to Earth. Once you have calculated the acceleration, you can plug it into the formula F = ma to find the force that Earth has regarding the tangent.

If you wanted to go against the movement of the Earth, you would need to apply a force in the opposite direction of the Earth's velocity vector. This means you would need to apply a force in the direction opposite to the angle between the velocity vector and the r vector. To calculate the magnitude of this force, you can use the same formula F = ma, but this time, use the negative value of the acceleration. This will give you the force needed to go against the movement of the Earth.

I hope this helps! Let me know if you have any further questions.