The space shuttle orbits at a distance of 335 km above the surface of the Earth. What is the gravitational force (in N) on a 1.0 kg sphere inside the space shuttle. Assume that the mass of the Earth is 5.98x1024 kg and the radius of the Earth is 6370 km

Compare (as %) the acceleration due to gravity at the altitude of the space shuttle to the local acceleration due to gravity at the surface of the Earth, 9.80 m/s2

the F of gravity is equal to (G*m1*m2)/(d^2) where g is the gravitational constant (6.673e-11 N*m^2/kg^2, notice the units are m not km), m1 is the mass of one object, m2 is the mass of the other object, and d= the distance between the centers of each object.

in this situation,
m1= 1.0 kg
m2 = 5.98e24 kg (i assume you meant 5.98x10^24)
d= 335 km + 6370 km. or 335000 m + 6370000 m

since it would look strange if i showed you how to put it into a calculator, i'll assume you can figure that out.

your answer is 8.87615 N, as the m^2 and 1/kg^2 in G cancel out all other units save N.

since F=mass*acceleration, and the Fgav for the object is 8.87615 and the mass is 1.0 kg, then the acceleration is equal to F/m = 8.87615/1 = 8.87615.

to get the percent, 8.87615/9.8 = x/100

the % is about 90.573%, and you would know better than I what decimal place you are expected to round it to.

also, if u need further help i recommend:physicsclassroom,com/Class/circles/u6l3c

To calculate the gravitational force on the 1.0 kg sphere inside the space shuttle, we can use the formula for gravitational force:

F = (G * m1 * m2) / r^2

Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 x 10^-11 N(m/kg)^2),
m1 is the mass of one object (in this case, the mass of the Earth),
m2 is the mass of the other object (in this case, the mass of the 1.0 kg sphere),
and r is the distance between the centers of both objects.

First, we need to convert the orbital altitude of the space shuttle from km to meters:
Altitude = 335 km = 335,000 meters

Next, we need to calculate the distance from the center of the Earth to the space shuttle:
Distance = radius of the Earth + altitude
Distance = 6,370 km + 335 km = 6,705 km = 6,705,000 meters

Now we can calculate the gravitational force:
F = (6.67430 x 10^-11 N(m/kg)^2 * 5.98 x 10^24 kg * 1.0 kg) / (6,705,000 meters)^2

Calculating this equation, we get:
F ≈ 8.68 x 10^2 N (Newtons)

To compare the acceleration due to gravity at the altitude of the space shuttle to the local acceleration due to gravity at the surface of the Earth, we need to calculate both accelerations.

Acceleration due to gravity at the altitude of the space shuttle:
g1 = G * (m1 / r1^2)
where G is the gravitational constant, m1 is the mass of the Earth, and r1 is the distance from the center of the Earth to the space shuttle.

Acceleration due to gravity at the surface of the Earth:
g2 = 9.80 m/s^2 (given)

Now we can calculate the percentage difference between the two accelerations:
Percentage difference = ((g1 - g2) / ((g1 + g2) / 2)) * 100

Substituting the values, we get:
Percentage difference = ((g1 - 9.80) / ((g1 + 9.80) / 2)) * 100

To calculate g1, we use the same equation as before:
g1 = G * (m1 / r1^2)

Calculating g1 using the known values, we get:
g1 ≈ 8.68 m/s^2

Finally, we can calculate the percentage difference:
Percentage difference = ((8.68 - 9.80) / ((8.68 + 9.80) / 2)) * 100

Calculating this equation, we get:
Percentage difference ≈ -11.4%

Therefore, the acceleration due to gravity at the altitude of the space shuttle is approximately 11.4% lower than the local acceleration due to gravity at the surface of the Earth.

To calculate the gravitational force on a 1.0 kg sphere inside the space shuttle, we can use Newton's law of universal gravitation.

First, let's find the gravitational force at the surface of the Earth using the formula:

F = (G * m1 * m2) / r^2

where F is the gravitational force, G is the gravitational constant (approximately 6.67430 x 10^-11 Nm^2/kg^2), m1 is the mass of the Earth, m2 is the mass of the object, and r is the radius of the Earth.

Plugging in the values:

F = [(6.67430 x 10^-11 Nm^2/kg^2) * (5.98 x 10^24 kg) * (1.0 kg)] / (6370000 m)^2

Calculating this equation gives us the gravitational force at the surface of the Earth.

Next, let's find the gravitational force at an altitude of 335 km above the surface of the Earth.

The distance from the center of the Earth at this altitude will be the sum of the radius of the Earth and the altitude above the surface:

Distance = 6370000 m + 335000 m

Now, we can calculate the gravitational force at this altitude using the same formula as before. Substitute the new distance into the equation and calculate. This will give us the gravitational force at the altitude of the space shuttle.

Now, to find the percentage difference in acceleration due to gravity between these two locations, we need to compare the two forces.

Divide the difference between the two gravitational forces by the gravitational force at the surface of the Earth and multiply by 100 to get the percentage:

Percentage difference = [(Force at altitude - Force at surface) / Force at surface] * 100

This will give us the percentage difference in the acceleration due to gravity between the space shuttle's altitude and the surface of the Earth.