Calculating Mass and Weight of a Planet

In summary, the density of a certain planet is described by the function D(r) = Do*[1-(a*r/Ro)], and its total mass can be calculated by integrating this function. To determine the weight of a one kilogram mass on the surface of the planet, the universal law of gravitation can be used.
  • #1
whereisccguys
21
0
2 part question

The density of a certain planet varies with radial distance as: D(r) = Do*[1-(a*r/Ro)], where Ro= 3.1623×106 m is the radius of the planet, Do = 3160 kg/m3 is its central density, and a = 0.160. Calculate the total mass of this planet.

Calculate the weight of a one kilogram mass located on the surface of the planet.

i tried integrating D(r) with and plugin in the radius of the planet but it doesn't work

i know this question has somethin to do with integrating through shell method but I'm not sure how to do it

can any1 help me?
 
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  • #2
Why doesn't it work?

~H
 
  • #3
whereisccguys said:
2 part question

The density of a certain planet varies with radial distance as: D(r) = Do*[1-(a*r/Ro)], where Ro= 3.1623×106 m is the radius of the planet, Do = 3160 kg/m3 is its central density, and a = 0.160. Calculate the total mass of this planet.

Calculate the weight of a one kilogram mass located on the surface of the planet.

i tried integrating D(r) with and plugin in the radius of the planet but it doesn't work

i know this question has somethin to do with integrating through shell method but I'm not sure how to do it

can any1 help me?

I am not sure what you integrated exactly but here are some thoughts:

First, you must determined the total massof the planet, right? This is given by the integral of [itex] D(r) dV = D(r) r^2 sin(\theta) dr d\theta d\phi [/itex]. The angular integrals are trivial and give [itex] 4 \pi [/itex]. The radial integral is straightforward.

Then, you must use this in the universal law of gravitation to determine the *weight* of 1 kg at the surface of the planet, [itex] F= {G m M \over r^2} [/itex].

Patrick
 

What is the difference between mass and weight?

The mass of an object refers to the amount of matter it contains, while weight refers to the force of gravity acting on an object's mass. Mass is constant, while weight can vary depending on the strength of the gravitational pull.

How is the mass of a planet calculated?

The mass of a planet can be calculated by using Newton's Law of Universal Gravitation, which states that the gravitational force between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them.

What factors can affect the accuracy of calculating a planet's mass?

Factors that can affect the accuracy of calculating a planet's mass include measurement errors, variations in the planet's density, and the presence of other celestial bodies that may influence its gravitational pull.

Can the mass and weight of a planet change over time?

Yes, the mass and weight of a planet can change over time due to factors such as the accumulation of debris or the loss of mass through volcanic activity or impacts from other objects.

How does the mass and weight of a planet affect its orbit and gravitational pull?

The mass and weight of a planet directly affect its orbit and gravitational pull. A planet with a larger mass will have a stronger gravitational pull and a more circular orbit, while a planet with a smaller mass will have a weaker gravitational pull and a more elliptical orbit.

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