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properly elliptic orbit, the angle between 7 and v is only at theProve that in a2apogee and perigee.Clue: Do so by showing v ir if and only if a0, then T is maximized (apogee) orminimized (perigee)when 0=0 or TT

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I need help with calculus question that deals with physics and elliptical orbits.

properly elliptic orbit, the angle between 7 and v is only at the
Prove that in a
2
apogee and perigee.
Clue: Do so by showing v ir if and only if a
0, then T is maximized (apogee) or
minimized (perigee)when 0=0 or TT
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properly elliptic orbit, the angle between 7 and v is only at the Prove that in a 2 apogee and perigee. Clue: Do so by showing v ir if and only if a 0, then T is maximized (apogee) or minimized (perigee)when 0=0 or TT

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Step 1

Apogee is the farthest point from Sun and Perigee is the nearest point.

Consider the motion of Earth around Sun in elliptical orbit. The direction of velocity is tangential to the elliptical path. The angular momentum about Sun is conserved.

Write the expression for angular momentum.

r is the distance from Sun to orbit
[v is thevelocity
e is the angle between r and v
mrvsine
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r is the distance from Sun to orbit [v is thevelocity e is the angle between r and v mrvsine

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Step 2

The radial distance and centripetal force are parallel to each other, hence the torque will be zero.

0
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0

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Step 3

Thus angular momentum will be...

[sin 0 should be equal to 1 or -1
L=mrvsine
| hen ce, =90°
= mrv
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[sin 0 should be equal to 1 or -1 L=mrvsine | hen ce, =90° = mrv

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