did your G have the right units?
you are correct that either equation should work
Fg = Fc ... in orbit ...
recalculate, and watch your units
What I've got so far: so, I think it's possible to use either Fg=GMm/r^2 or Fc=mv^2/r, is that correct? I calculated the force to be 4,795,014,967 N which seems quite big to me and is incorrect. In that calculation, I used 6,949,000 m for r as Sputnik would have been orbiting about 578,000 m above Earth. Obviously I made a mistake somewhere.
Thanks in advance!
you are correct that either equation should work
Fg = Fc ... in orbit ...
recalculate, and watch your units
Thanks.
Fg = (G * (m1 * m2)) / r^2
Where:
- Fg is the gravitational force between two objects
- G is the gravitational constant, which is approximately 6.67430 x 10^-11 m^3/(kg*s^2)
- m1 and m2 are the masses of the two objects (in this case, the mass of Sputnik and the mass of the Earth)
- r is the distance between the centers of the two objects (in this case, the radius of the Earth plus the altitude of Sputnik from the Earth's surface)
So, let's calculate the gravitational force step-by-step:
Step 1: Convert the radius of the Earth from kilometers to meters:
Radius of the Earth (r) = 6371 km
r = 6371 km * 1000 m/km
r = 6,371,000 m
Step 2: Calculate the distance between the center of the Earth and Sputnik:
Distance (r) = Radius of the Earth (r) + altitude of Sputnik
r = 6,371,000 m + 578000 m
r = 6,949,000 m
Step 3: Calculate the gravitational force:
Fg = (G * (m1 * m2)) / r^2
Fg = (6.67430 x 10^-11 m^3/(kg*s^2) * (83.6 kg * (5.972 x 10^24 kg))) / (6,949,000 m)^2
Fg = (6.67430 x 10^-11 * 83.6 * (5.972 x 10^24)) / (6,949,000)^2
Using these calculations, the correct gravitational force that Sputnik applies to the Earth during its orbit is approximately 1.08 x 10^17 N.
Fg = (G * m1 * m2) / r^2
Where:
Fg is the gravitational force between two objects
G is the gravitational constant (6.67430 x 10^-11 m^3 kg^-1 s^-2)
m1 is the mass of the first object (Sputnik)
m2 is the mass of the second object (Earth)
r is the distance between the centers of the two objects (radius of the Earth plus the altitude of Sputnik)
Given:
Mass of Sputnik (m1) = 83.6 kg
Velocity of Sputnik (v) = 7574 m/s
Radius of the Earth (rEarth) = 6371 km = 6,371,000 m
Mass of the Earth (m2) = 5.972 x 10^24 kg
First, convert the units of the radius of the Earth from kilometers to meters:
rEarth = 6,371,000 m
Next, add the altitude of Sputnik to the radius of the Earth to get the distance (r) between Sputnik and the center of the Earth during its orbit:
altitude = 578,000 m
r = rEarth + altitude
Now, you can use the formula for gravitational force to calculate the force exerted by Sputnik on the Earth:
Fg = (G * m1 * m2) / r^2
Substitute the given values into the formula:
Fg = (6.67430 x 10^-11 m^3 kg^-1 s^-2 * 83.6 kg * 5.972 x 10^24 kg) / (r^2)
Calculate the value of r^2:
r^2 = (rEarth + altitude)^2
Plug in the values and calculate the result:
Fg = (6.67430 x 10^-11 m^3 kg^-1 s^-2 * 83.6 kg * 5.972 x 10^24 kg) / ((rEarth + altitude)^2)
The result is the gravitational force exerted by Sputnik on the Earth during its orbit.