A satellite moves in a circular orbit around
the Earth at a speed of 6.2 km/s.
Determine the satellite’s altitude above
the surface of the Earth. Assume the
Earth is a homogeneous sphere of radius
6370 km and mass 5.98 × 10
24
kg. The
value of the universal gravitational constant
is 6.67259 × 10
−11
N · m2
/kg
2
Answer in units of km
It would be appreciated if u can show the steps
Thank you in advance :)
the Earth at a speed of 6.2 km/s.
Determine the satellite’s altitude above
the surface of the Earth. Assume the
Earth is a homogeneous sphere of radius
6370 km and mass 5.98 × 10
24
kg. The
value of the universal gravitational constant
is 6.67259 × 10
−11
N · m2
/kg
2
Answer in units of km
It would be appreciated if u can show the steps
Thank you in advance :)
-
Thank you for putting all the constants in. It saves a responder all kinds of time.
mv^2/r = G M*m/r2
M = 5.98 *10^24 kg
G = 6.67 * 10^-11
v = 6.2 km/s =6.2 km/s * [ 1000 m / 1 km]
v = 6.2 * 10^3 m/s
m = ??? the satellite's mass, but it does not matter since m is on both sides of the equation and will cancel out.
mv^2/r = G M*m/r2 Cancel out m on both sides and multiply by r^2. Cancel out one r.
v^2 * r = G M
r = G*M/v^2
r = 6.67 * 10^-11 * 6 * 10^24/[6.2 * 10^3]^2
r = 1.04 * 10^4 km
The earth's radius is 6.370 * 10^3 km
So the satellite is 1.04 * 10^4 - 6.370 * 10^3 = 4041 km above the earth's surface.
Comment
=======
I have rounded your numbers off. As an exercise, you should go back and use your more accurate numbers to see if you get anwhere near the answer I got.
mv^2/r = G M*m/r2
M = 5.98 *10^24 kg
G = 6.67 * 10^-11
v = 6.2 km/s =6.2 km/s * [ 1000 m / 1 km]
v = 6.2 * 10^3 m/s
m = ??? the satellite's mass, but it does not matter since m is on both sides of the equation and will cancel out.
mv^2/r = G M*m/r2 Cancel out m on both sides and multiply by r^2. Cancel out one r.
v^2 * r = G M
r = G*M/v^2
r = 6.67 * 10^-11 * 6 * 10^24/[6.2 * 10^3]^2
r = 1.04 * 10^4 km
The earth's radius is 6.370 * 10^3 km
So the satellite is 1.04 * 10^4 - 6.370 * 10^3 = 4041 km above the earth's surface.
Comment
=======
I have rounded your numbers off. As an exercise, you should go back and use your more accurate numbers to see if you get anwhere near the answer I got.