What is the formula to get the speed of satellite in Circular Motion?

What is the formula to get the speed of satellite in Circular Motion?



My given information is:

Speed of the Satellite orbiting at a height = 700km above the Earth's surface.

Mass of Earth = 5.98 x 10^24kg

Radius of Earth = 6.38 x 10^6mWhat is the formula to get the speed of satellite in Circular Motion?The force on the satellite due to the Earth is given by



F = G(me * ms)/r^2



me = 5.98 x10^24 kg

ms = mass of satellite

G = Gravitational Constant = 6.67 x 10^-11 N(m/kg)^2

r = 6.38 x10^6 + 700 kg



We also know that an object moving in a circular motion will have force given by



F = (ms * v^2)/r



If we equate the above equations we get



G(me*ms)/r^2 = (ms * v^2)/r



which simplifies to



v = sqrt(G*me / r )



Last step is to plug in the values to find vWhat is the formula to get the speed of satellite in Circular Motion?Acceleration in polar coordinates.

a = (r.. - rtheta.^2)e_r + (rtheta..+2r.theta.)e_theta

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Since the satellite is orbiting the Earth, r. and r.. are zero. Therefore, the equation becomes

a = (-rtheta.^2)e_r + (rtheta..)e_theta

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Sum the forces in the e_r and e_theta.

e_r : -GMm/r^2 = -m*rtheta.^2

e_theta: 0 = m(rtheta..)

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Use the e_r component to solve for theta.

theta. = sqrt(GM/r^3)

where,

G = 6.673*10^-11 m^3/kgs^2

M = 5.98*10^24 kg

r = Re + 700,000 = 7,080,000 m

Therefore,

theta. = 0.001 rad/s

theta. = V/r

V = 7,507.5 m/sWhat is the formula to get the speed of satellite in Circular Motion?mv2/r=ma

m=mass

v=velocity(speed at any given point)

r=distance from the centre of the Earth= (700 + 6.38*10^6)m

a=accelaration



As satellite is only 700km fromsurface of the Earth where accel. is 9.8m/s2 we will use that accel. in this problem

mv2/r=ma

v2/r=a

v2=ar

v=ar(square rooted)

v=7987.93m/s