Variation of gravitational attraction between Sun and Earth

In summary, the distance between the Earth and the Sun at perihelion is 1.471×10^8 km and at aphelion is 1.521×10^8 km. The mass of the Sun is 2.0×10^30 kg and the mass of the Earth is 5.972×10^24 kg. Using the equation F=G×Msun×MEarth/distance^2, the change in Newton of the attraction force between the Sun and the Earth from perihelion to aphelion is 2.4×10^27 N. However, this answer does not match the textbook's answer of 2.37×10^21 N. After converting the
  • #1
Matthew 289
2
0

Homework Statement


Distance Earth-Sun at perihelion = 1.471×108 km
Distance Earth-Sun at aphelion = 1.521×108 km
Sun mass = 2.0×1030 kg
Earth mass = 5.972×1024 kg
G = 6.67×10-11 m3/kg⋅s
What is the change in Newton of the attraction force between the Sun and the Earth from the perihelion to the aphelion ?

Homework Equations


F= G × Msun×MEarth/distance2

The Attempt at a Solution


Fperihelion= (6.67×10-11 m3/kg⋅s) × (2.0×1030 kg)×(5.972×1024 kg)/(1.471×108 km) = 3.68×1028 N

Faphelion= (6.67×10-11 m3/kg⋅s) × (2.0×1030 kg)×(5.972×1024 kg)/(1.521×108 km) = 3.44×1028 N

ΔF= |Fperihelion| - |Faphelion| = 3.68×1028 N - 3.44×1028 N = 2.4×1027 N

My problem:
The result does not correspond to that given by the textbook (2.37×1021 N).
I cannot see the fault in my resolution and other methods I've tried give wrong answers as well.
Can anyone see my mistake/s ? Is it logical or arithmetical ?
 
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  • #2
Matthew 289 said:
My problem:
The result does not correspond to that given by the textbook (2.37×1021 N).
I cannot see the fault in my resolution and other methods I've tried give wrong answers as well.
What if you were given the distances in miles, instead of km?
 
  • #3
First of all, you haven't squared the distance in the solution.
I don't have a clue of the calculations.
And secondly, convert kilometers into meters and then square.
that means 10^(8) changes to 10^(11) first since 1 km = 10^3 metres
Then, squaring becomes 10^(22)
rest of the method is alright,
i have solved it. and got the correct answer.
peace!
 
  • #4
Saurabh said:
First of all, you haven't squared the distance in the solution.
I don't have a clue of the calculations.
And secondly, convert kilometers into meters and then square.
that means 10^(8) changes to 10^(11) first since 1 km = 10^3 metres
Then, squaring becomes 10^(22)
rest of the method is alright,
i have solved it. and got the correct answer.
peace!
Thank you very much ! I've done what you've suggested and the answer was right !
Have a nice day.
 

FAQ: Variation of gravitational attraction between Sun and Earth

What causes variation in gravitational attraction between the Sun and Earth?

The variation in gravitational attraction between the Sun and Earth is primarily caused by the distance between the two objects. As Earth orbits the Sun, its distance from the Sun changes, resulting in a change in the gravitational force between them. This is known as the inverse square law, which states that the force between two objects is inversely proportional to the square of the distance between them.

How does the tilt of Earth's axis affect the gravitational attraction between the Sun and Earth?

The tilt of Earth's axis has a minor effect on the gravitational attraction between the Sun and Earth. This is because the tilt does not significantly change the distance between the two objects, but it does affect the distribution of sunlight on Earth's surface, leading to seasonal changes.

What is the magnitude of the gravitational attraction between the Sun and Earth?

The magnitude of the gravitational attraction between the Sun and Earth is approximately 3.52 x 10^22 Newtons. This is a very large force, but it is balanced by the centrifugal force of Earth's orbit, keeping the planet in a stable orbit around the Sun.

How does the mass of Earth affect the gravitational attraction with the Sun?

The mass of Earth has a direct effect on the gravitational attraction between the Sun and Earth. The larger the mass of an object, the greater the gravitational force it exerts on other objects. This is why the Sun, with its much larger mass, exerts a stronger gravitational force on Earth than Earth does on the Sun.

Does the gravitational attraction between the Sun and Earth change over time?

Yes, the gravitational attraction between the Sun and Earth changes over time. This is due to the gradual change in Earth's orbit around the Sun, as well as the changing mass of the Sun and Earth due to processes like solar wind and plate tectonics. However, these changes are very small and have a negligible impact on our daily lives.

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