I've got a few questions. I'll show my work but I'm struggling and need to turn in this homework by midnight :(

1) Calculate g (the acceleration due to gravity) for the space shuttle’s orbit, 200 km above the Earth’s surface.
M= 5.98x10^24kg (given on our constants sheet). G= 6.67x10^-11N.
g=GM/r^2. ((6.67x10^-11)(5.98x10^24))/(6.37x10^6= 9.8298...

2) What is the change in the force of gravity between two planets when the distance between them becomes 10 times smaller? (Does the force increase or decrease? By what factor?)
Is this the inverse square law? I did 1/(1/10)^2= 100 increase but I don't know that I did this right.

3) Rank the average gravitational forces from greatest to least between the
a. Sun and Mars
b. Sun and the Moon
c. Sun and the Earth
To be honest I'm completely lost on how to do this one at all.

4) We often neglect the gravitational effects within an atom. Calculate and compare the gravitational and electrical forces between an electron and a proton separated by 10-10 m.
I also don't even know where to start on this one. I'm so confused.

5) Measurements show that there is an electric field surrounding the Earth. Its magnitude is about 100 N/C at the Earth’s surface, and it points inward toward the Earth’s center. Based on this information, is the Earth positively or negatively charged?
Since it states that it "points inward toward the Earth's center" I'm guessing that the Earth is negatively charged? Or is it positive because the electric field is pointing down (negative?) and that makes the Earth positive? I'm not sure but I read somewhere in my book (I think) that an electric field has a positive charge so that would mean the Earth has a negative charge.

If anyone could please PLEASE help me with these before it's too late I'd greatly appreciate it. I really need to understand these things better.

1) To calculate the acceleration due to gravity (g) for the space shuttle's orbit 200 km above the Earth's surface, you can use the formula g = GM/r^2, where G is the gravitational constant, M is the mass of the Earth, and r is the distance between the shuttle and the center of the Earth.

Given:
M = 5.98 x 10^24 kg
G = 6.67 x 10^-11 N
r = 6.37 x 10^6 m + 200 km (convert km to m)

First, convert 200 km to meters:
200 km = 200,000 m

Now, calculate g:
g = (6.67 x 10^-11 Nm^2/kg^2) * (5.98 x 10^24 kg) / (6.57 x 10^6 m)^2

Solving this equation will give you the value of g.

2) The force of gravity between two objects follows the inverse square law, which means that if the distance between the objects becomes 10 times smaller, the force will increase by a factor of (1/10)^2 = 1/100. This means that the force decreases to 1% of its original value.

3) To rank the average gravitational forces among the Sun, Mars, the Moon, and the Earth, you can use the equation F = GMm/r^2, where G is the gravitational constant, M is the mass of the Sun, Mars, Moon, or Earth, m is the mass of the other object, and r is the distance between them.

Compare the values of F for each pair of objects. The object pair with the greatest value of F has the greatest average gravitational force.

4) To calculate and compare the gravitational and electrical forces between an electron and a proton separated by a distance of 10^-10 m, you can use the equations for gravitational force (Fg = G(m1m2)/r^2) and electrical force (Fe = k(q1q2)/r^2), where G is the gravitational constant, k is the Coulomb constant, m and q represent mass and charge, and r is the distance between the particles.

Given:
m1 (proton mass) = 1.67 x 10^-27 kg
q1 (proton charge) = 1.6 x 10^-19 C
m2 (electron mass) = 9.11 x 10^-31 kg
q2 (electron charge) = -1.6 x 10^-19 C
r = 10^-10 m

Calculate the gravitational force (Fg) and electrical force (Fe) separately using the respective equations. Then compare the magnitudes of Fg and Fe.

5) Based on the information given, since the electric field around the Earth points inward toward the Earth's center, the Earth must be negatively charged. The direction of the electric field indicates the direction of the force a positive charge would experience, so a positive charge would be repelled by the Earth and move away from it. Therefore, the Earth must be negatively charged to attract positively charged particles.

I understand that you have several questions and you're looking for assistance. I'll provide explanations and guide you through the problem-solving process for each question.

1) To calculate the acceleration due to gravity (g), we can use the formula g = GM/r^2, where G is the gravitational constant, M is the mass of the Earth, and r is the distance between the space shuttle and the Earth's surface.

Given:
M = 5.98 × 10^24 kg
G = 6.67 × 10^-11 N
r = 200 km + radius of the Earth (6.37 × 10^6 m)

First, convert the distance to meters: 200 km = 200,000 m
Now, substitute the values into the formula:
g = (6.67 × 10^-11 N) * (5.98 × 10^24 kg) / (6.37 × 10^6 m + 200,000 m)^2

After evaluating the expression, you will find the value of g.

2) Yes, this question involves the inverse square law. When the distance between two objects is reduced by a factor of 10, the force of gravity between them will increase by a factor of (1/10)^2 = 1/100. So, the force will increase by a factor of 100.

3) To rank the average gravitational forces from greatest to least, we need to compare the masses and distances involved. The formula for gravitational force is F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between them.

Comparing these values for the Sun-Earth, Sun-Mars, and Sun-Moon systems will help us determine the rankings. The greater the mass and smaller the distance, the stronger the gravitational force. Therefore, you should compare the masses and distances between each pair to rank them correctly.

4) To compare the gravitational and electrical forces between an electron and a proton separated by a distance of 10^-10 m, we can use the formulas for gravitational force (Fg) and electrical force (Fe):

Fg = G * (me * mp) / r^2, where G is the gravitational constant, me is the mass of the electron, mp is the mass of the proton, and r is the separation distance.

Fe = ke * (qe * qp) / r^2, where ke is the electrostatic constant, qe is the charge of the electron, qp is the charge of the proton, and r is the separation distance.

Substitute the given values into the equations and compare the magnitudes of Fg and Fe. This will determine which force is stronger.

5) Based on the information provided, we are given the magnitude and direction of the electric field around the Earth. The fact that the electric field points inward toward the Earth's center indicates that it is due to a positive charge at the center of the Earth, rather than the Earth itself having a positive charge.

Therefore, the Earth is negatively charged since the electric field lines point inward toward the positively charged center.

Remember, if you have any specific calculations or further questions, feel free to ask, and I'll be happy to assist you.