Calculate Force of Gravity on Space Station at Different Distances

In summary, to calculate the force of gravity on a space station situated at different distances from the Earth's center, you must use the equation Fg = Gm1m2/r^2 instead of Fg = mg.
  • #1
mr.mair
7
0

Homework Statement



If the Earth radius is 6.4 X 10^3 km, calculate the force of gravity on a 1.0 X 10^5 kg space station situated
(a) Earth surface
(b) 1.28 X 10^5 km from the center of the earth
(c) 3.84 X 10^5 from the center of the Earth ( about the distance to the moon)
(d) 1.5 X 10^8 km from the center of the Earth ( about the distance of the sun)

Homework Equations


Fg = mg


The Attempt at a Solution



Question a

Fg= (100000)(9.8)
Fg= 980000

questions b - d have been attemped but have no idea on these please help
 
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  • #2
Fg = mg only applies to objects less than 100 km from the Earth's surface. For b.,c., and d. you must use Fg = Gm1m2/r^2, where G is the gravitational constant, m1 and m2 are masses of Earth and satellite respectively, and r is the distance from the center of Earth to satellite.
 
  • #3

To calculate the force of gravity on the space station at different distances from the Earth's surface, we can use the equation Fg = (G*m1*m2)/r^2, where G is the gravitational constant, m1 is the mass of the Earth, m2 is the mass of the space station, and r is the distance between the center of the Earth and the space station.

(a) At the Earth's surface, r = 6.4 X 10^3 km, so the force of gravity would be Fg = (6.67 X 10^-11)(5.98 X 10^24)(1.0 X 10^5)/(6.4 X 10^3)^2 = 980000 N, which is the same as your calculation.

(b) At a distance of 1.28 X 10^5 km from the center of the Earth, r = 1.92 X 10^5 km. Plugging this into the equation, we get Fg = (6.67 X 10^-11)(5.98 X 10^24)(1.0 X 10^5)/(1.92 X 10^5)^2 = 653 N.

(c) At a distance of 3.84 X 10^5 km from the center of the Earth (about the distance to the moon), r = 3.84 X 10^5 km. Plugging this into the equation, we get Fg = (6.67 X 10^-11)(5.98 X 10^24)(1.0 X 10^5)/(3.84 X 10^5)^2 = 1.77 N.

(d) At a distance of 1.5 X 10^8 km from the center of the Earth (about the distance to the sun), r = 1.5 X 10^8 km. Plugging this into the equation, we get Fg = (6.67 X 10^-11)(5.98 X 10^24)(1.0 X 10^5)/(1.5 X 10^8)^2 = 0.005 N.

As you can see, the force of gravity decreases as the distance from the Earth's center increases. This is because gravity is an inverse square law, meaning that it decreases by the square of the distance.
 

Related to Calculate Force of Gravity on Space Station at Different Distances

1. How is the force of gravity calculated on a space station?

The force of gravity on a space station is calculated using Newton's law of universal gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

2. How does the force of gravity change at different distances from the space station?

As the distance between an object and the space station increases, the force of gravity decreases. This is because the further away an object is, the weaker the gravitational pull between the two objects becomes.

3. How do you calculate the force of gravity on a space station at a specific distance?

To calculate the force of gravity on a space station at a specific distance, you will need to know the mass of the space station and the mass of the object, as well as the distance between them. You can then use the formula F = (G * m1 * m2) / d^2, where G is the gravitational constant, m1 and m2 are the masses of the space station and the object, and d is the distance between them.

4. Will the force of gravity on a space station be the same at all points on the station?

No, the force of gravity on a space station will not be the same at all points on the station. This is because the mass of the space station is not evenly distributed, so some points will experience a stronger gravitational pull than others.

5. How does the force of gravity on a space station compare to the force of gravity on Earth?

The force of gravity on a space station is significantly less than the force of gravity on Earth. This is because the mass of the space station is much smaller than the mass of the Earth, and the distance between the space station and Earth is much greater than the distance between two objects on Earth. However, the force of gravity on a space station is still strong enough to keep objects and astronauts on the station in orbit.

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