Determine the mass of the planet using Newton’s Law of Universal Gravitation

In summary, the conversation involves a question about determining the mass of a planet using Newton's Law of Universal Gravitation, with the given data of force, gravitational constant, and distance, and the unknown mass of the planet. The individual rearranges the equation and calculates the mass to be 7.17 x 10^24 kg. The conversation also includes a discussion about the weight of an astronaut on this new planet, with the conclusion that they would weigh less due to a lower force of gravity.
  • #1
Petronius
13
2
Homework Statement
You are on a deep space mission to search for Earth-like planets. Your crew locates a possible they hang a 1.0 kg mass from a spring scale. It reads 8.5 N.

a. Determine the mass of the planet using Newton’s Law of Universal Gravitation.

b. Describe whether an astronaut standing on this new planet weighs more, less, or the same as on Earth. Show your work.
Relevant Equations
From course: F= (Gm_1 m_2)/r^2

m_1= Fr^2/(Gm_2 )
(Could not find in my course but discovered this rearranged version on the internet. Appeared essential in solving the second part of the problem . https://www.ajdesigner.com/phpgravity/newtons_law_gravity_equation_force.php)

Fg=mg
Hello, and thank you again to anyone who can confirm if I have the right answer or who can give me some suggestions. This question felt like a bit of a surprise because we have not yet covered one where the mass of a planet was missing. Thus, my confidence in my work is low. Part b felt like a bit of an extension as well.

Part a) Determine the mass of the planet using Newton’s Law of Universal Gravitation.

I first determined given and missing data:

Given:
F= 8.5 N
G: 6.67 x 10^-11 nm^2/kg^2
m2= 1.0kg
r = 7.5x 10^6

Unknown: m1: = ?

I then attempted to solve knowing I would have to rearrange the standard equation from my course.

F= (Gm_1 m_2)/r^2
rearranged..

m_1= Fr^2/(Gm_2 )

m1 = (8.5N) x (7.5 x 10^6) / (6.67 x 10^-11) x (1.0kg)

m1 = 478125000000000/(6.67 x 10^-11) x (1.0kg)

m1 = 7.16829085 x 10^24 kg

m1 = 7.17 x 10^24 kg ( I think I should round to this ?)

Therefore the mass of the planet is 7.17 x 10^24 kg.Part b) Describe whether an astronaut standing on this new planet weighs more, less, or the same as on Earth. Show your work.Given:
9.8 N/kg
M= 1.0kg

Unknown: Fg

Fg = (1.0)(9.8 N/kg)
Fg = 9.8 N

I than concluded that since the force of gravity on the 1.0kg mass was greater on Earth than on the new planet, an astronaut would weigh less on this new planet than on earth.

Any help would be greatly appreciated!
Thank you,
 
Last edited:
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  • #2
Looks okay to me.
 
  • #3
Thank you for looking it over.
 

FAQ: Determine the mass of the planet using Newton’s Law of Universal Gravitation

1. How does Newton's Law of Universal Gravitation determine the mass of a planet?

Newton's Law of Universal Gravitation states that the force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. By measuring the gravitational force between a planet and a known mass, such as a satellite, we can calculate the mass of the planet using this equation: M = (r^2 * g) / G, where M is the mass of the planet, r is the distance between the planet and the known mass, g is the gravitational acceleration, and G is the gravitational constant.

2. Can Newton's Law of Universal Gravitation be used to determine the mass of any type of planet?

Yes, Newton's Law of Universal Gravitation can be used to determine the mass of any type of planet as long as we have a known mass and can measure the gravitational force between the two objects. However, it may be more difficult to measure this force accurately for larger or more distant planets.

3. What other factors can affect the accuracy of using Newton's Law of Universal Gravitation to determine the mass of a planet?

Other factors that can affect the accuracy of this method include the accuracy of the measurements of distance and gravitational force, the effects of other nearby objects on the gravitational force, and any irregularities in the planet's mass distribution. These factors should be taken into account when conducting the calculations.

4. Are there any alternative methods for determining the mass of a planet?

Yes, there are alternative methods for determining the mass of a planet, such as using the period and distance of a satellite's orbit around the planet or analyzing the planet's gravitational effect on nearby objects. However, Newton's Law of Universal Gravitation is a widely accepted and accurate method for calculating the mass of a planet.

5. Can the mass of a planet change over time and affect the accuracy of using Newton's Law of Universal Gravitation?

Yes, the mass of a planet can change over time due to factors such as meteorite impacts or volcanic activity. These changes may affect the accuracy of using Newton's Law of Universal Gravitation, but they are usually small and can be accounted for by taking multiple measurements over time and using the average value.

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