#
A satellite of mass m moves along an elliptical path around the earth. The areal velocity of the satellite is proportional to,

a) m

b) m^-1

c) m^°

d) m^1/2

1
by basuRana

Log in to add a comment

a) m

b) m^-1

c) m^°

d) m^1/2

by basuRana

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

B) m^-1

The way a planet revolves around a Sun, the satellite moves around the Earth.* * We apply the laws of Kepler.

ris the position vector of the satellite with Earth at the origin*. v*(t) is the linear velocity. L is the angular momentum. p is the linear momentum along the elliptical path. ΔA is the area covered by the radial vector in time duration t to t+Δt.

Aerial velocity = ΔA/Δt = dA/dt

*r*(t), ** r'**(t),** r'**(t+Δt),** v**(t), *p*, *L* are all vector quantities.

ΔA = 1/2**r**(t) X r(t+Δt) = 1/2 r(t) X [r(t) + r '(t) Δt] = 1/2 r(t) X r '(t) Δt

ΔA / Δt = 1/2 r(t) X r '(t) = 1/2 r (t) X v(t) =*r*(t) X **p**(t) / (2m) = L /2 m

we know that the angular momentum L for a satellite is constant. Reason is that dL/dt = torque = r(t) X dp(t)/dt = r(t) X F(t)

Here in case of gravitation, the force is central force ie., along the radius r.

Hence , torque is zero. hence L is a constant.

d*A*/dt = *L*/(2m)

Hence aerial velocity is inversely proportional to the mass of the satellite.

The way a planet revolves around a Sun, the satellite moves around the Earth.

r

Aerial velocity = ΔA/Δt = dA/dt

ΔA = 1/2

ΔA / Δt = 1/2 r(t) X r '(t) = 1/2 r (t) X v(t) =

we know that the angular momentum L for a satellite is constant. Reason is that dL/dt = torque = r(t) X dp(t)/dt = r(t) X F(t)

Here in case of gravitation, the force is central force ie., along the radius r.

Hence , torque is zero. hence L is a constant.

d

Hence aerial velocity is inversely proportional to the mass of the satellite.