How to find the mass of a planet when given the radius?

In summary: This can be done by using the formula F = G*m1*m2/R^2, where F is the force of gravity between two objects, G is the gravitational constant, m1 and m2 are the masses of the objects, and R is the distance between them. Once you have the gravitational acceleration, you can use it to calculate the mass of the planet using the formula F = ma, where m is the mass of the planet and a is the gravitational acceleration. By measuring the force of gravity on the surface of the planet and knowing the radius, you can solve for the mass of the planet.
  • #1
CluelessPhysics
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1. So for homework my teacher gave us this question (and this is quoted from his worksheet):
You graduate college with a degree in astrophysics and are assigned as an astronaut to explore a distant planet for NASA. You land on this planet and are told to determine the mass of the planet there. You have a meterstick and a stopwatch. Observations from space tell you the radius of the planet that you land on. How do you go about measuring the mass of this planet?

2.F=G*m1*m2/R^2

How do I even begin to complete this problem? Do I have to find the acceleration of gravity on the planet? Any help is appreciated.
 
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  • #2
Welcome to PF!

CluelessPhysics said:
1. So for homework my teacher gave us this question (and this is quoted from his worksheet):
You graduate college with a degree in astrophysics and are assigned as an astronaut to explore a distant planet for NASA. You land on this planet and are told to determine the mass of the planet there. You have a meterstick and a stopwatch. Observations from space tell you the radius of the planet that you land on. How do you go about measuring the mass of this planet?

2.F=G*m1*m2/R^2

How do I even begin to complete this problem? Do I have to find the acceleration of gravity on the planet? Any help is appreciated.

Yes, you have to find the gravitational acceleration on the surface of the planet.
 

1. How is the mass of a planet calculated using its radius?

The mass of a planet can be calculated using its radius by applying the formula for gravitational force, which is F = G(m1m2)/r^2, where G is the universal gravitational constant, m1 and m2 are the masses of the planet and the object interacting with it, and r is the distance between the two objects. By rearranging this formula, we can solve for the mass of the planet (m2) by plugging in the known values for G, r, and the mass of the object orbiting the planet.

2. Can the mass of a planet be accurately determined using only its radius?

No, the mass of a planet cannot be accurately determined using only its radius. The mass of a planet is influenced by a variety of factors, such as its composition, density, and gravitational pull. Therefore, the radius alone is not enough information to accurately determine the mass of a planet.

3. What is the unit of measurement used for the mass of a planet?

The unit of measurement commonly used for the mass of a planet is kilograms (kg). In some cases, scientists may also use Earth masses (M☉) or Jupiter masses (M♃) for larger planets.

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

Knowing the mass of a planet is important for understanding its gravitational pull, which affects the orbits of other objects in its vicinity. It also provides insight into the planet's composition and formation, and can help with predicting its future evolution.

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

Yes, the mass of a planet can change over time due to a variety of factors such as meteorite impacts, volcanic activity, and atmospheric changes. However, these changes are typically small and do not significantly affect the overall mass of the planet.

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