# Calculate the force of Earth's gravity on a spacecraft

In summary, the conversation discusses using mastering physics for homework in a classical physics class. The speaker is struggling with getting the correct answers for problems involving Earth's gravity, and asks for someone to check their calculations. The problems involve calculating the force of gravity on a spacecraft at a certain altitude, determining which satellite is faster at different altitudes, and finding the altitude where the acceleration of gravity is half of its surface value. The speaker is unsure if they are doing the calculations correctly or if the homework program is flawed.
I am in a classical physics class and the class requires that we use mastering physics for our homework. The only problem is that I can't get what mastering physics claims is the right answer to these problems. Can someone try these calculations to see if I am right or wrong?

Problem 6.1 : Calculate the force of Earth's gravity on a spacecraft 2.50 Earth radii above the Earth's surface if its mass is 1400 kg.
My calculations: F= G((m1mE)/r^2) = (6.67*10^-11)*((1400kg)*(5.97*10^24kg))/(6378km*2.5*10^3)^2= 2192.7 N

Problem 6.28: Two satellites orbit Earth at altitudes of 5600 km and 1.7×104 km.Which satellite is faster? By what factor? = vclose/vfar.
My calculations: vclose = sqrt(G(mE/r)), sqrt((6.67*10^-11)*(5.98*10^24kg)/(5600km*10^3)) = 8439.55 m/s

vfar = sqrt(G(mE/r)), sqrt((6.67*10^-11)*(5.98*10^24kg)/(17400*10^3)) = 4843.83 m/s

vclose/vfar = 1.74

Problem 6.51: How far above the Earth's surface will the acceleration of gravity be half what it is at the surface?

My calculations: m1(1/2g) = Gm1mE/r^2, r^2 = 2GmE/g, r = sqrt(2GmE/g), r = sqrt( 2*(6.67*10^-11)*(5.98*10^24)/9.8) = 9022262 m

Can you try solving these answers and tell me what I am doing wrong or if the homework program is flawed?

I'm even more confused... the book tells me to use r as altitude but mastering phyics tells me that r is the altitude + r...

## 1. How is the force of Earth's gravity on a spacecraft calculated?

The force of Earth's gravity on a spacecraft can be calculated using Newton's Law of Universal Gravitation, which 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.

## 2. What is the formula for calculating the force of Earth's gravity on a spacecraft?

The formula for calculating the force of Earth's gravity on a spacecraft is F = (G * m1 * m2) / d^2, where F is the force of gravity, G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the Earth and the spacecraft, and d is the distance between them.

## 3. How does the mass of the spacecraft affect the force of Earth's gravity?

The force of Earth's gravity on a spacecraft is directly proportional to the mass of the spacecraft. This means that the greater the mass of the spacecraft, the greater the force of gravity acting on it.

## 4. Is the force of Earth's gravity on a spacecraft constant?

No, the force of Earth's gravity on a spacecraft is not constant. It varies depending on the distance between the Earth and the spacecraft, as well as the mass of the spacecraft and the Earth.

## 5. How does the distance between the Earth and the spacecraft affect the force of gravity?

The force of Earth's gravity on a spacecraft is inversely proportional to the square of the distance between them. This means that as the distance between the Earth and the spacecraft increases, the force of gravity decreases.

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