What is the Mass of a Spherical Planet?

In summary, the conversation discusses an astronaut observing a spherical planet and conducting an experiment to determine its mass. The experiment involves dropping a hammer and a feather from a height of 1.35m and observing their fall to the surface in 25.7 seconds. The suggested solution is to use a kinematic equation and the formula for acceleration due to gravity to calculate the mass of the planet.
  • #1
mparsons06
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Homework Statement



As an astronaut, you observe a small planet to be spherical. After landing on the planet, you set off, walking always straight ahead, and find yourself returning to your spacecraft from the opposite side after completing a lap of 25.9 km. You hold a hammer and a falcon feather at a height of 1.35 m, release them, and observe that they fall together to the surface in 25.7 s. Determine the mass of the planet.

2. The attempt at a solution

I don't even know where to start. Any pointers?
 
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  • #2
mparsons06 said:
You hold a hammer and a falcon feather at a height of 1.35 m, release them, and observe that they fall together to the surface in 25.7 s. Determine the mass of the planet.

2. The attempt at a solution

I don't even know where to start. Any pointers?

Try using this and a kinematic equation to find the acceleration. Then just use

g=GM/r2
 

1. How do you find the mass of a planet?

To find the mass of a planet, you can use the following formula: M = (4π²r³)/G(T²), where M is the mass of the planet, r is the distance between the planet and its star, G is the gravitational constant, and T is the orbital period of the planet. This formula is known as Kepler's Third Law.

2. What tools or equipment are needed to measure the mass of a planet?

To measure the mass of a planet, you will need a telescope to observe the planet's orbit and determine its distance from its star. You will also need to know the orbital period of the planet, which can be measured using a clock or timer. Additionally, you will need to know the gravitational constant, which is a universal value that can be found in most scientific databases.

3. Can the mass of a planet change over time?

Yes, the mass of a planet can change over time due to factors such as meteorite impacts, volcanic activity, and the accretion of material from other objects in space. However, these changes are usually very small and do not significantly affect the overall mass of the planet.

4. How accurate are the measurements of a planet's mass?

The accuracy of measurements of a planet's mass can vary depending on the methods used and the precision of the equipment. However, modern scientific instruments and techniques can provide highly accurate measurements with a margin of error of just a few percent.

5. Why is it important to know the mass of a planet?

Knowing the mass of a planet is important for understanding its composition, structure, and formation. It can also help us to predict the planet's behavior and interactions with other objects in its orbit. Additionally, the mass of a planet is a crucial factor in determining its gravitational pull, which is important for space exploration and understanding the dynamics of the solar system.

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