Calculating Earth's Orbital Speed: Gravitational Field Equations

In summary, you are asked to determine the speed of the Earth moving in a circular orbit around the sun. Using the equation v2 = GMearth/r, and given that Mearth = 5.98x1024, R of Earth's orbit = 1.49x1011, and G = 6.67x10-11, you calculated the speed to be 51.7m/s. However, your teacher corrected you and stated that the correct answer is 2.97x104m/s. You realized that the mass used in the equation should be the mass of the sun, not the Earth. After correcting this mistake, you arrived at the correct answer.
  • #1
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Homework Statement


It can be assumed that the Earth, to a good approximation, moves in a circular orbit about the sun. Determine the speed of the Earth.

Homework Equations


v2 = GMearth/r

The Attempt at a Solution


mearth= 5.98x1024
R of Earth's orbit= 1.49x1011
G= 6.67x10-11

v2= (6.67x10-11)(5.98x1024)/ (1.49x1011)
v2= (3.98x1014) / (1.49x1011)
v= [itex]\sqrt{}2676.9[/itex]
v= 51.7m/s

Now here's the problem. My teacher said that the answer to this question is 2.97x104m/s
What is it that I am doing wrong? D:
 
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  • #2
The important mass, the one that the Earth orbits, is the mass of the Sun.
 
  • #3
Ohhhh. Okay, I got it. Thank you
 

FAQ: Calculating Earth's Orbital Speed: Gravitational Field Equations

How do you calculate the Earth's orbital speed?

The Earth's orbital speed can be calculated using the following equation: v = √(GM/r), where G is the gravitational constant (6.67 x 10^-11 m^3/kg/s^2), M is the mass of Earth (5.97 x 10^24 kg), and r is the average distance between the Earth and the Sun (149.6 x 10^9 m).

What is the significance of the Earth's orbital speed?

The Earth's orbital speed is important because it determines the amount of time it takes for the Earth to complete one orbit around the Sun, which is approximately 365.24 days. It also plays a crucial role in maintaining the Earth's position and stability within the solar system.

How does gravitational force affect the Earth's orbital speed?

The Earth's orbital speed is a result of the balance between the gravitational force of the Sun and the centrifugal force of the Earth's orbit. The greater the gravitational force, the faster the Earth's orbital speed will be.

Can the Earth's orbital speed change?

Yes, the Earth's orbital speed can change due to various factors such as gravitational interactions with other planets, changes in the Earth's mass, and variations in the shape and tilt of its orbit. However, these changes are relatively small and do not significantly affect the Earth's overall orbital speed.

How is the Earth's orbital speed related to its distance from the Sun?

The Earth's orbital speed is inversely proportional to its distance from the Sun. This means that as the Earth moves further away from the Sun, its orbital speed decreases. This is due to the decrease in the gravitational force between the two bodies at a greater distance.

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