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Prove that in a properly elliptic orbit, the angle between r ⃗ and v ⃗ is π/2 only at the apogee and perigee.

Clue: Do so by showing v ⃗⊥r ⃗ if and only if ε≠0, then τ is maximized (apogee) or minimized (perigee)when θ=0 or π
Prove that in a properly elliptic orbit, the angle between r ⃗ and v ⃗ is π/2 only at the apogee and perigee.

Clue: Do so by showing v ⃗⊥r ⃗ if and only if ε≠0, then τ is maximized (apogee) or minimized (perigee)when θ=0 or π
I understand Hubble noticed (or perhaps published) the fact that the universe is expanding in 1929.

I also understand that the brightness of 'standard candles' (such as Cepheid variable stars) can be used to calculate their distance from us.

My questions are - how much further from us are things now than they were when the distance was measured in 1929?

Do calculations using standard candles completely agree with Hubble's findings?

Thanks.
Assuming earth re emits all the radiations it receives from the sun.Calculate the temperature of the earth(given stefan’s constant and E)
in the last five seconds of the championship match between teams A and B, the scores were tied at 75 when a player was fouled and was awarded two free throws. On the first attempt, he released the ball with a velocity of 6.0 m/s at 45 degerees above the horizontal from a height of 2.0 m from the floor.
a.)Is this a miss or a basket?
b.) For the second throw, the player shoots again at 45 degrees from the same point of release. What must the initial speed of the ball be so that it will go through thr basket?
What will be the consequences on earth when gravity becomes zero
If you have infinite energy can you release infinite power forever by just releasing half of the remains energy each second?
Write down Friedman equation and sketch its solutions. Which one of these solutions correspond to the contracting universe ?
What is a quasar ? Sketch the spectrum of a quasar and describe its main characteristics.
Explain Hubble's scheme of galaxy classification. What is the type assigned to the Milky way galaxy ?
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