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A satellite is in a 89.5 min period circular orbit 400km above Earth's surface. What is its speed?
Wiki User
∙ 13y ago
Re = Radius of earth (6.38EE6)
H = Height of satellite (780km => 780,000m)
Me = Mass of earth (5.98EE24)
Ms = Mass of satellite
G = Universal Gravity (6.67EE-11)
V = Orbital Speed
Fg= Force of gravity
Fc= Centripetal force
Use the formula Fg=Fc
(((G)(Me)(Ms))/ (Re+H)^2)= (Ms)(V^2)/(Re+H)
Ms cancel out
((G*Me)/ ((Re+H)^2)) = (V^2)/(Re+H)
Solve for V
V = sqrt( ((G*Me)/((Re+H)^2)) * (Re+H) )
= sqrt( ((6.73EE-11*5.98EE24)/((6.38EE6+780,000)^2)) * (6.38EE6+780,000) )
= 7465.426831 m/s
Wiki User
∙ 12y ago
Wiki User
∙ 14y ago26,836 Km/h
Solution:To calculate speed, we need to divide the distance travelled by the time. We are given the time of one orbit, so we now must calculate the distance the satellite travels in one orbit. To do that, we need one more piece of information: the Earth's radius, which is 6,378 Km.
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The satellite scribes a circle around the earth as it orbits, and the circumference of that circle is the distance the satellite travels in one orbit. We know that the circumference of a circle is obtained from the following equation:
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C = 2 * PI * r
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where 'r' is the radius of the circle. In the case of the satellite's orbit, the radius is 755 + 6378 Km in our problem, yielding a circumference of 44,817 Km.
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Let's assume we are calculating the speed in Km/h, not m/s. 99.7 minutes is 1.67 hours, so the speed of our satellite is:
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S = D / t
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where D is distance (44,817 Km)
t is time (1.67 h)
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So Speed (S) is calculated at 26, 836 Km/h.
Wiki User
∙ 13y agoYou can use the the formula Fgravity=ma to derive v2=(GM/R) where G is Newton's universal gravity constant, M is the mass of the Earth and R is measured from the center of the earth.
Using this formula you obtain:
v=sqrt(GM/R)
=sqrt((6.67E-11m3/(kg*s2))(5.98E24kg)/(631*1000m+6.37E6m)
remember to convert to meters and add the radius of the earth
=7.548*103m/s
Wiki User
∙ 13y agoformula:
s=d/t
solution:
s=400km/89.5mins
answer:
s=4.47km/mins
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