Mercury orbit has a semi major axis a=5.791 ×1010 m with an eccentricity e= 0.2056. Mercury Sun a MMercury = 3.3011 × 10²3 kg a) What is the velocity of Mercury at the aphelion (point of maximum distance to the Sun)? b) What is the total mechanical energy of Mercury? c) What is the velocity of Mercury at the perihelion (point of minimum distance to the Sun)?

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Mercury orbit has a semi major axis a=5.791 x1010 m with an eccentricity e=
0.2056.
Mercury
Sun
a
MMercury = 3.3011 × 1023 kg
a) What is the velocity of Mercury at the aphelion (point of maximum distance
to the Sun)?
b) What is the total mechanical energy of Mercury?
c) What is the velocity of Mercury at the perihelion (point of minimum distance
to the Sun)?
d) What is the velocity of Mercury when its distance from the Sun is 0.371 AU?
(1 AU = 1.496 x 1011 m)
e) What is the orbital period of Mercury? (Only for this question you can the
assume that the orbit is circular, with a radius equal to the semi major axis)
f) If the period observed for Mercury is 87.969 earth days, compare (calculate
percent difference) with the period you calculated in question e). Consider
the value given in f) as the actual (i.e. experimental) one. Is the value obtained
theoretically in question e) accurate?
Transcribed Image Text:Mercury orbit has a semi major axis a=5.791 x1010 m with an eccentricity e= 0.2056. Mercury Sun a MMercury = 3.3011 × 1023 kg a) What is the velocity of Mercury at the aphelion (point of maximum distance to the Sun)? b) What is the total mechanical energy of Mercury? c) What is the velocity of Mercury at the perihelion (point of minimum distance to the Sun)? d) What is the velocity of Mercury when its distance from the Sun is 0.371 AU? (1 AU = 1.496 x 1011 m) e) What is the orbital period of Mercury? (Only for this question you can the assume that the orbit is circular, with a radius equal to the semi major axis) f) If the period observed for Mercury is 87.969 earth days, compare (calculate percent difference) with the period you calculated in question e). Consider the value given in f) as the actual (i.e. experimental) one. Is the value obtained theoretically in question e) accurate?
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